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Simulation of Several Glass Types Loadedby Air Blast WavesMartin LarcherPUBSY JRC48240

Distribution ListLechner S.Anthoine A.Casadei F.Dyngeland T.Géradin M.Giannopoulos G.Gutierrez E.Larcher M. (5 copies)Paffumi E. (JRC Petten)Pegon P.Solomos G.DG TRENExternal:Bung H. (CEA)Faucher V. (CEA)Galon P. (CEA)Kill N. (Samtech)Potapov S. (EDF)S. Lechner

CONTENTS1 Introduction ...................................................................................................................................52 Developments of the Shell Elements in EUROPLEXUS..............................................................62.1 Integrations Points................................................................................................................62.2 M_ELEM_CHARS..............................................................................................................62.3 Dimensioning .......................................................................................................................72.4 New Input Syntax for the Integration...................................................................................72.5 Output in the Postscript and avi Files ..................................................................................82.6 CEA Shell Elements for JRC Material with Sandwich........................................................93 Glass ............................................................................................................................................103.1 Behaviour of Glass.............................................................................................................103.2 Several Glass Types ...........................................................................................................113.2.1 Annealed Glass (Float Glass).........................................................................................123.2.2 Tempered (Toughened) Glass........................................................................................123.2.3 Laminated Glass.............................................................................................................123.2.4 Wired Glass....................................................................................................................133.2.5 Insulating Glass..............................................................................................................133.3 Material Parameters of Glass and PVB..............................................................................134 Simulation of Annealed Glass.....................................................................................................164.1 Material Law for Annealed Glass ......................................................................................164.2 Implementation of a Failure Model for Material VM23....................................................174.3 Model for the Strain Rate Effect of Glass..........................................................................204.4 Verification ........................................................................................................................215 Laminated Glass ..........................................................................................................................275.1 Material Law for Laminated Glass ....................................................................................285.1.1 Layered Elements...........................................................................................................295.1.2 Two Coincident Shells ...................................................................................................295.1.3 Smeared Model ..............................................................................................................295.1.4 Models with Three or More Elements Through Thickness ...........................................315.2 Verification with Static Experiments.................................................................................315.3 Verification with a Dynamic Experiment ..........................................................................355.4 Implementation of a Layered Model in EUROPLEXUS...................................................425.4.1 Calculations of the Experiments of Kranzer ..................................................................425.4.2 Cracks in Two Directions ..............................................................................................515.4.3 Comparison between Element Types.............................................................................525.4.4 Number of Integration Points.........................................................................................565.4.5 Higher Loading of the Window .....................................................................................575.5 Experiments with a Failure of the Interlayer (Hooper)......................................................605.5.1 Experiment .....................................................................................................................605.5.2 Calculations....................................................................................................................625.5.3 Variation of the Hardening of PVB ...............................................................................675.5.4 Influence of the Mesh Size.............................................................................................705.5.5 Influence of the Element Type.......................................................................................715.5.6 Crack in Two Directions, Reduction Factor ..................................................................746 Conclusion...................................................................................................................................757 References ...................................................................................................................................778 Apendix .......................................................................................................................................808.1 EUROPLEXUS Code ........................................................................................................808.2 Sample Input Files .............................................................................................................884

1 IntroductionThis work is being conducted in the framework of the project RAILPROTECT, which deals withthe security and safety of rail transport against terrorist attacks. The bombing threat is onlyconsidered, and focus is placed on predicting the effects of explosions in railway and metro stationsand rolling stock and on assessing the vulnerability of such structures.The project is based on numerical simulations, which are carried out with the explicit FiniteElement Code EUROPLEXUS that is written for the calculation of fast dynamic fluid-structureinteractions. This program has been developed in a collaboration of the French Commissariat àl'Energie Atomique (CEA Saclay) and the Joint Research Centre of the European Commission (JRCIspra).The aim of this project is to calculate the behaviour of structures loaded by air blast waves. Thefaçades of railway stations as well as large parts of the lightweight structures of trains are often builtfrom glass. In comparison to the mechanical structure of a station or of a train, the glass is muchmore fragile and fails much earlier since the thickness of the glass is mostly very small. The failedparts of a façade or of a train results in release areas for the air blast pressure. The behaviour of theglass should therefore be taken into account for the simulations. This technical note presents severalapproaches about different glass types loaded by air blast waves.5

2 Developments of the Shell Elements in EUROPLEXUS2.1 Integrations PointsEUROPLEXUS provides several shell elements for the calculation with different materials. Shellelements are developed by CEA (e.g. DKT3, Q4GS) and by the JRC (e.g. CQD4).Some of these shell elements are usable with different numbers if integration points through thethickness. In addition, the degenerated shell elements CQDx can be used with a reduced and a fullintegration in the lamina. Other possibilities are given with laminated shell elements which allowdifferent materials over the thickness.The input syntax of the integration points through the thickness is not consistent – the CEAelements use other syntax as the JRC elements. The storage of the information about the integrationof shell elements is also done in different ways. An effective output (neither in the postscript filesnor in the avi files) of the results of integration points in a certain laminar was not yet possible. Theobjective of this development was, to allow the output of a lamina (or layer) in shell elements.2.2 Module M_ELEM_CHARSSome materials store some parameters, which are connected to element properties. Theseparameters should be stored in the new module M_ELEM_CHARS that these parameters can beused from each element. The following variables are defined in the new module:• ELEM_NGPZ = number of Gauss points through thickness for plate/shell/beam• ELEM_INTE = type of lamina integration for some shell elements (selective, reduced, full)• ELEM_ALPHA = participation to bending, used only by shell elements that adopt a globalmodel (i.e. which are not integrated through the thickness). The default value is 2/3.• ELEM_BETA = participation to membrane, used only by shell elements that adopt a globalmodel (i.e. which are not integrated through the thickness). The default value is 1.• ELEM_SK = shear correction factor. The default value is 5/6.• ELEM_NGPTRUE = true number of Gauss points of the element. The maximum number ofGauss points is defined in inico1.ff (ncel(2,ityp)); this number is used as a default value.The variable ELEM_NGPTRUE is defined for all elements; all the other variables are only definedin a case of the existence of one shell element.6

2.6 CEA Shell Elements for JRC Material with Sandwich StructureSince the number of accurate shell element types, which can be used with JRC elements and withthe sandwich structure (multi layer formulation) is small, several CEA elements are extended.This is done for the triangle shell elements T3GS, DKT3 and for the quadrilateral shell elementsQ4GS, Q4GR, QPPS. These elements can now be used with the materials VM23, DONE, GLAS,LSGL, LEMA, VMJC, VMZA, VMLP, VMLU, VMSF, and DPSF also in a sandwich structure.9

3 GlassGlass is a brittle material. The stiffness of the glass is well known and constant. In contrast, thestrength of glass varies over a wide range due to the fact that the microstructure of the glass resultsin cracks. Several procedures allow the increasing in the strength or the minimisation of the rangeof the strength, for example tempering, laminating.The value of the strength depends on the purpose of the investigation. While in a calculation wherethe glass should resist to external forces the strength has to be chosen as a small fractile value, thestrength should be the average in calculations where the failure of the glass is helpful to reduce, forexample, the internal pressure inside a structure.The behaviour of the microstructure could also be calculated but it doesn’t make a sense if thefailure of glass sheets loaded by air blast waves should be calculated. Due to the fact that the failurestarts at a certain point and growth through the glass, the element sizes for a calculation should beas small as possible, especially in the case of laminated glass. In contrast to this need the elementsshould be as large as possible to allow a calculation of large structures.Brendler [5] shows, for example, that the element size for a glass sheet loaded by a pendulum (1m/s velocity) should have a value smaller than 20 cm (for annealed glass).3.1 Behaviour of GlassIn the micro and the macro level glass is an amorphous material. That means that in the material nostructure can be observed. This is not right at the nano level. The chemical construction of glass isbuilt with rings (see Figure 3). In the case of a quartz crystal the atomic structure is well definedand regular. This is not the case in quartz glass. Some rings are broken and the size of the ringsdiffers. These parts are start points for the fracture at the nano level and the reason for the missingof the plasticity of glass. Therefore, the material can only deform elastically with a brittle failure.The nano behaviour is also the reason for the wide range of the strength of glass.The strength of the macro level is affected by several reasons:• Specimen size• Aspect ratio of the glass sheet• Load durationThese influences are defined, for example, in the European standards for glass prEN 13474-1 [33]and prEN and 13474-2 [34]. The aspect ratio and the specimen size impacts the strength of the sheet10

y the probability of failures in the nano level in the highest loaded part of the glass. The loadduration affects the starting of the cracking. Therefore, annealed glass has a strain rate effect whichshould be considered by calculations of annealed glass.Figure 3: Chemical construction of glass: SiO z as a crystal – SiO z as quartz glass (From Wikipedia)3.2 Several Glass TypesSeveral glass types are shown in Figure 4.Figure 4: Glass types11

3.2.1 Annealed Glass (Float Glass)The cooling of this glass is done slowly in a controlled way to relieve internal stresses in the glass.The strength of this relatively inexpensive glass is small. The variation of strength is large. It iswidely used for windows in cases where security against impact and blast is not important andwhere the failure of the splinters does not affect human bodies.3.2.2 Tempered (Toughened) GlassTempered glass is two or more times stronger than annealed glass. The production is done in such away that residual stresses are remaining in the glass which increases the bending strength. Thisouter part of the glass is under compression, the inner part is under tension. Therefore, the residualcompression stresses overpressures the tensile stresses resulting from the load.Due to the fact that residual stresses increase the inner energy of the glass, this glass shatters intomany small fragments which prevent major injuries. Tempered glass is widely used in cases wherea higher strength is of interest: glass façades, sliding doors, building entrances, and bath and showerenclosures. This glass should not be used in cases where flying splinters can occur. In these casesthe splinters can be the reason of injuries. However, these splinters are mostly much edgeless thanthe splinter from annealed glass.The production can be done on two ways. A special heat treating can impose the residual stresses,which results in higher strength. This procedure is widely used for architectural glass. The otherpossibility is to use chemical strengthening, which produces a higher mechanical resistance. Theseglasses are more used in industry for thin, strong glasses.3.2.3 Laminated GlassGlass sheets loaded by air blast results in the case of the failure of the glass in flying splinters. Toprevent this, two glass types of safety glass can be used: laminated and wired glass.Laminated glass is a combination of two or more glass sheets with one or more interlayers of plastic(Polyvinylbutyral, PVB). In case of breakage, the interlayer holds the fragments together andprevents that the splinters are flying into the structure which should be saved. This glass is thereforewidely used in cases where the resistance of the sheet after the failure is important (e.g. shop-fronts,balconies, stair-railings, roof glazing). The production is done by bonding two or more glass sheets(this could be annealed or tempered glass) with the PVB interlayer under heat and pressure.12

3.2.4 Wired GlassWired glass is replaced more and more with laminated glass. Wired glass includes a steel meshwhich prevents in a case of breakage that pieces of the glass are flying away. Historically, this glassis used for accessible glass roofs. The steel mesh is insert when the glass is produced.3.2.5 Insulating GlassThis glass is built from a combination of two or more glass sheets with an interface filled withdehydrated air or gas. The glass reduces the thermal losses. In the case of loading this glass by airblast waves, both glasses and the behaviour of the gas between the glasses have to be considered.Firstly, this gas results in a damping of the structural behaviour, secondly, at a certain time oneglass sheet can contact the other one and results in a contact loading.3.3 Material Parameters of Glass and PVBSeveral material parameters of glass are shown in Table 1. The value of the strength is discussedlater (see Table 2).Value for EUROPLEXUS[m, s, kg]Density 2.2 – 2.5 (2.5) g/cm³ 2500Tensile strength 30 – 100 (50) N/mm 2 30 – 100 (50)E-Modulus 70000 N/mm 2 7E10Poisson's ratio 0.22 0.22Table 1: Material parameters for glass; the values in parentheses are the values mostly usedPolyvinylbutyral (PVB) shows a significant influence of the loading time. PVB is creeping underlong-time loading. The influence of the temperature has also to be considered.The bulk modulus seems to be relatively constant and can be chosen as K=2.0 GPa (see Van Duser[10], Flocker [14]). Wei [39] uses a value of 20 GPa for the bulk modulus.The influence of the temperature on the shear modulus is presented by D’Haene [8] (shown byTimmel [38]) and Krüger [26]. While the shear modulus reaches values of 120 MPa with a13

temperature less than 0 degrees Celsius, the shear modulus decreases up to 1 MPa with atemperature of more than 30 degrees Celsius.The short-time shear modulus of PVB reaches values of G 0 ≈ 500 MPa (more or less a glassymodulus); while the long-time shear modulus has only a value of G ∞ ≈ 0.1 MPa (rubbery modulus).The relation between the shear modulus and the load duration (or strain rate) is shown inexperiments of Van Duser [10] and D’Haene [9] (see also Figure 5). These values are determinedby using several dynamic tests with different frequencies at different temperatures. The values ofdifferent temperatures can be shifted to values for different relaxation times by using the Williams-Landell-Ferry equation (see Van Duser). Due to the fact that the influence of the relaxation time issmall (in the range of milliseconds), Wei [39] uses a fixed value for G by setting G = G 0 = 330MPa. This value of the shear modulus under high strain rates is only investigated using lowertemperatures. It seems to be dangerous to use these values instead of a material parameter from highstrain rate experiments.1E+91E+8D'HaeneVan DuserG(t) [Pa]1E+71E+61E+51E+41E-12 1E-9 1E-6 1E-3 1E+0 1E+3 1E+6 1E+9Relaxation time [sec]Figure 5: Relation between shear modulus and relaxation time for PVBThe relaxation time in a calculation can be taken into account using a generalized Maxwell Seriesof the experimental values (see Van Duser) or by using an exponential equation shown by Wei [39].14

The Young’s modulus and the Poisson’s ratio for short-time loading can be calculated using thefollowing continuum mechanics equation:E9 KG 3 2,K −= υ =G0 00 03K + G0 6K + 2G0(1)This leads to the values for the Young’s modulus E 0 = 938 MPa and for the Poisson’s ratioν 0 = 0.42.The long-time behaviour of the PVB is viscoelastic. The long-time behaviour can be described witha linear viscoelastic material proposed by Ferry [11] (see Van Duser). This material law splits thedeviatoric and the hydrostatic pressures and uses then time dependent shear and bulk modulus.Alternative, a hyperelastic material law can be used (e.g. Blatz-Ko or Mooney-Rivlin, see Timmel[38]).Wei [39] proposes that these more complex material laws are not necessary due to the fact that thebehaviour of the interlayer in the range of milliseconds is brittle. The tensile failure strain of PVB isdefined by Nguyen [31] as 300 %. This corresponds to the value, which is given from Morison [28].The material behaviour of PVB under high strain rates is investigated by Bennison [4], Iwasaki [18][19], and Morison [28]. The investigations show that the behaviour of PVB under high strain ratesis much more elastoplastic. An elastoplastic material law is recommended.353025Stress [MPa]20151050Bennison 89 1/sBennison 8 1/sBennison 0.7 1/sBennison 0.07 1/sIwasaki 0.033 1/sIwasaki 118 1/sMorison 74 1/s0 50 100 150 200 250 300 350Strain [%]Figure 6: Strain rate behaviour of PVB15

4 Simulation of Annealed Glass4.1 Material Law for Annealed GlassThe failure of glass is brittle. Therefore, a plastic equivalent strain corresponds not to the physicalbehaviour of glass. An elastic behaviour up to a brittle failure describes the material behaviourmuch better.This raises the question, which value should be used for the failure of the glass. Due to the fact thatan elastic-brittle material law is used, strain and stress based criteria produces the same results.The theoretical strength of glass reaches values of 21,000 MPa (see Overend [32]). On freshlydrawn glass fibres the tensile stresses of 5,000 MPa can be measured (also [32]) while the usablestrength is approximately 1,200 MPa. Architectural glasses fail with strength between 8 and 45MPa, whereas the environmental and loading conditions have a significant influence. The failure ofglass depends on the surface of the glass panels. Glass has a lot of flaws (Griffith-flax). Griffith [15]postulated that fracture starts at these flaws.These flaws are distributed statistical over the surface. Therefore, the failure of a glass panel can berepresented by a one or two parameter Weibull distribution, for example, shown from Beason [2]and Overend [32]. Then, the strength can be calculated depending on the risk of failure. Therefore,not only the experimental values vary, also the values used for numerical calculations differ due tothe fact that the risk of failure depends on the purpose of the investigation.Overend [32] gives an overview over several failure stresses used by different failure models orcodes. The failure stresses for a probability of failure of 8e-3 vary from 10.19 to 26.24 MPa; thefailure stresses for a probability of failure of 1e-3 vary from 7.20 to 20.89 MPa. Stewart [36] uses amean value of 84.8 MPa (COV 0.28) for annealed glass and a value of 159.6 MPa (COV 0.10) forfully tempered glass.Timmel [38] and Kolling [23] use a strain limit of 0.13 % (double-layer safety glass) up to 0.30 %(single-layer safety glass) for their calculations of laminated safety glass. This corresponds to astrength of 91 up to 210 MPa. They use a smaller strain limit for the double-layer safety glass dueto the fact that the bonding behaviour is reduced because of the interlayer.The development of fracture in glass depends also on the loading time (=strain rate effect), the sizeof the glass panel (i.e. negligible) and the size of the affected part of the panel (tension).16

The strain rate effect is founded on the fact that the flaw needs time to grow. The influence for blastanalysis is quit big – the strength is increased up to 3 times. This behaviour should be thereforeregarded.There are several laws to consider this behaviour. Brown [6] (see Beason [2]) proposes a model thatbases on the assumption that the resistance to failure K f can be expressed with:ft f0[ σ ()]nK = ∫ t dt(2)With the nominal tensile stresses at the flaw σ(t) and the duration of the loading t f . The failureoccurs if the value of K f reaches a critical value depending on the flaw. This equation allows theconversion of a given load duration to a load duration, at which the strength is well known i.e. thefailure stresses are often defined in terms of 60-sec duration. The following equation can be used totranslate a given (principal) stress-time history to an equivalent, constant stress σt d:σtd1td⎡ ⎤ nn⎢∫σ1()t dt⎥0= ⎢ ⎥⎢ td⎥⎢⎢⎣⎥⎥⎦(3)The 3D-behaviour of glass (e.g. impact) can be modelled with the Johnson-Holmquist brittledamage model [20] that provides an improved model for the failure surface.4.2 Implementation of a Failure Model for Material VM23Glass reacts very brittle. Therefore, a failure model with element erosion can be used to considerthe behaviour of glass. Such is model is implemented for the Lemaitre material model (LEM1) sofar. This material describes a combination of a plastic material with damage. The failure isintroduced by using the damage parameter.Using damage models with glass doesn’t make a sense due to the fact that the behaviour of glassunder compression and under tension is elastic and the failure occurs without damage or plasticity.In addition to a criterion based on damage, there are different possibilities to identify a failure. LS-DYNA for instance uses the following limits: maximum pressure, minimum principal strain,minimum pressure, principal stress, equivalent stress, maximum principal strain, shear strain,threshold stress, Tuler-Butcher criterion (fracture intensity) and a failure time. All these criteria canalso be combined.17

To calculate the behaviour of glass a special failure criterion for glass should be implemented inEUROPLEXUS. Therefore, the following failure criteria are implemented in the material VM23:• VMIS – Von Mises stress. An integration point fails if the von Mises stress reaches thedefined limit• PEPS – Principal strain. An integration point fails if the maximum principal strain(tension) is beyond the limit.• PRES – Pressure. An integration point fails if the hydrostatic stress is higher than thegiven limit (or the pressure is smaller than the limit).• PEPR – Principle strain combined with pressure. An integration point fails if themaximum principle strain is beyond the limit and the pressure is in tension.If an integration point is failed the variable ECRO(12) is set to 1.0 to identify later the failedintegration points. All other element variables are set to 0.0 (except for sound speed and currentyield stress).The material VM23 is an elastic-plastic material. The failure can be used also in the elastic partby setting the plastic limit to a high value.The option OPTI FAIL specifies element erosion. The parameter can set in a range between 0.0and 1.0 while 0.0 means that an element is eroded if one integration point of the element isfailed. 1.0 means that an element is eroded if all integration points of the element are failed.A benchmark is also insert that uses a cantilever built from shell elements. The cantilever isfixed on the left and is loaded by nodal forces on the right. Calculations with the principal straincriterion show that the elements fail also in regions with compression (see Figure 7). The reasonis the transversal contraction.18

Figure 7: Failure of a cantilever beam, criteria principal strain (pressures)The failure criterion PEPR (principal strain in combination with the hydrostatic stress) can avoid afailure in a case of compression. Therefore, the benchmark shows a more realistic behaviour of thebrittle failure (see Figure 8).Figure 8: Failure of a cantilever beam, criteria principal strain in combination with hydrostaticpressure (pressures)This failure model should be used to calculate the different models with glass to consider only atensile failure.With one of these failure models a common glass sheet can be calculated. The glass sheet has a sizeof 1.0 m x 1.4 m with a relative thin thickness of 0.1 mm and is supported at the borders. Thematerial parameters are chosen as:19

MATE VM23 RO 2500 YOUN 7E10 NU 0.23 ELAS 1.756E10FAIL PEPR LIMI 0.1TRAC 2 1.756E10 0.15 1.8E10 1.15The loading of the glass sheet is performed with the AIRB command (see Larcher [27]). Theexplosion is located at a distance of 3.5 m.Figure 9: Failure of a glass sheet (displacements orthogonal to the sheet)4.3 Model for the Strain Rate Effect of GlassThe failure of glass depends also on the duration of the load – or in other words on the strain rate(see section 4.1). This effect is implemented in the new material GLAS. This material uses an20

elastic behaviour in combination with a failure criterion depending on the equivalent constant stressσt d(see also section 4.1).The material model uses two internal variables (ECRO(3) and ECRO (10)) to calculate formula (3).ECR(10) stores the current equivalent constant stress σ , ECR(3) stores the area below the σ1 ()n t -time curve, the principal stress σ () t is dived by 1 106 to avoid too high numbers (ECR variables areREAL(4)).• The routine D3DIAG is used to calculate the principal stresses. The highest principal stress(SIGMAX) will be used (tension).The formulas presented result in too high values (with standard units). The stresses are dividedtherefore by a factor (10 6 ). The resulting equivalent, constant stress will be multiplied by this factor.• If the equivalent, constant stress is larger than 0 (tension), the variable PSAR is set toPSAR = ECR(3) + DT1 * (SIGMAX/FACT) ** CORRECR(3) is the old value of this variable. DT1 is the current time step size, CORR is thestress corrosion constant, which has to be defined in the input and is recommended to 16.• PSAR is stored in ECR(3)• The equivalent, constant stress is calculated bySIGTD = ((PSAR/(60.D0))**(1.D0/CORR))*FACT• The internal variable ECR(10) is overwritten with the value of SIGTD.The procedure leads to the calculation of the area below the principal-stress-time curve. If theequivalent constant stress SIGTD reaches a defined value, the integration point fails.4.4 VerificationThe calculation of blast loaded float glass can be verified with the numerical results byKrauthammer [25]. Krauthammer uses a linear approximation of the pressure history. Thedeflections of the glass sheet and the stresses inside the glass loaded by this pressure history arecalculated with an analytical classical plate theory (Timoshenko). He uses the procedure of Beason[2] to calculate the equivalent constant strain and with them the probability of failure.Krauthammer calculates two different sizes of glass sheets and compares the results with twocomputational tools for glass. The approach divides the effects of the positive and the negativet d21

phase. This results in the conclusion, that for glass sheets loaded by air blast waves with largescaled distances the influence of the negative phase is predominant.Only the results of the probability of failure are shown in this paper. The equivalent constantstresses can be calculated using the probability of failure-scaled distance curve. This curve is shownin Figure 10 (with SI units for the scaled distance).The probability of failure can be calculated with the following formula:Pfm−kAσs= 1− e(4)The values of the surface strength parameters are taken from Beason [2] and are given to:m k m Pa−45 −2 −6= 6; = 7.19⋅ 10(5)Then, the constant equivalent stress can be calculated by converting equation (4) to:ln(1 − Pf)σ ms= − (6)kA10.8negativ phasepositive phaseProbability of failure0.60.40.200 20 40 60 80 100Scaled distance [m/kg 1/3 ]Figure 10: Probability of failure, glass sheet 1.4 m x 1.4 m, thickness 9.63 mm, 10 kg TNT,Krauthammer [25]22

6E+7IP1equivalent constant stress σ5E+74E+73E+72E+7Krauthammerfailure probobility 0.1 %IP2Krauthammer, positive phaseKrauthammer, negative phase1E+70E+00 10 20 30 40Z [m/kg 1/3 ]Figure 11: Failure of a glass sheet, Krauthammer [25] (10 kg TNT)Figure 11 shows the equivalent constant stresses for a charge of 10 kg TNT resulting fromconverting the failure probability curve. The equivalent constant stresses are smaller for the positivephase. The conclusion of Krauthammer is that for large distances the negative phase has moreinfluence than the positive phase.Figure 12 and Figure 13 show the development of the failure of a glass sheet. This sheet has thedimensions of 1.4 m x 1.4 m and a thickness of 9.63 mm. The Young’s Modulus is set to 70 10 9N/m 2 . The Stress corrosion fraction is chosen as 16. The equivalent constant stress is used as 84.8MPa (see Stewart [36], annealed glass, mean value). The structure is loaded by the AIRB command(see Larcher [27]). All models use a load of 10 kg TNT with different distances from the object.The first loading of the sheet with a scaled distance of 7 m/kg 1/3 results in shearing of the glass. Theloading is too fast that the glass has the time to bend. At the time 6.8 ms the glass sheet is bended.The glass begins to vibrate in the first natural mode. At the time 17.6 ms, the glass is bended in theopposite direction. Then, the equivalent constant stress is relatively constant over the sheet (seeFigure 13).At the time 22.4 ms, the glass starts to fail at the edges. The crack growth to the centre and finallythe splinter becomes flying debris.23

Figure 12: Failure of a glass sheet (displacements), Z = 7 m/kg 1/324

Figure 13: Failure of a glass sheet (equivalent constant stresses), Z = 7 m/kg 1/3Figure 11 shows the equivalent constant strains calculated with the material model presented. Theequivalent constant stresses are printed for the inner and the outer integration point. The stresses area little bit higher than the results by Krauthammer. The reason could be that the failure in thenumerical results starts at the edges, whereas Krauthammer defines the failure with a maximumdeflection of the sheet in the centre. Nevertheless, the results are in the same order.Another possibility to compare the results is the diagrams of Fletcher [13].The main aspects ofFletcher’s report are the velocity and the size of the fragments of a broken glass sheet. The reportprovides also a diagram which can be used to determine the size of a glass sheet that fails with aprobability of 50% by a given peak overpressure. This diagram gives a peak overpressure of 8000Pa for a sheet of 1.96 m 2 and a thickness of 0.946 cm. This peak pressure corresponds to a scaleddistance of 22.7 m/kg 1/3 , which is similar to the results of Krauthammer (6100 Pa, 27.7 m/kg 1/3 ).Fletcher’s is produced with much bigger charges (greater than 1000 kg TNT).These results raise the question, which value for the equivalent constant stress should be used forthe calculation. There is not only one answer. The mean value should be used if the calculation25

should show a realistic behaviour of the glass structure, but this value must not be used forcalculation about the safety of a structure. For this kind of calculations a fractile should be used(0.8% up to 0.1 % fractile).As a conclusion, Table 2 shows the suggested values for the different approaches (in addition toTable 1). The coefficient of variation for the tempered glass is much smaller. This indicates thattempered glass is more robust than annealed glass.FailureStandardCoefficientFailureFailureprobability ofdeviationof variationprobability ofprobability of50%0.8%0.1%Annealed glass 84.8 23.74 0.28 27.59 11.43Toughened glass(fully tempered)159.6 15.96 0.10 121.1 110.3Table 2: Strength of glass [MPa] (see Stewart [36])26

5 Laminated GlassLaminated glass is built from two or more glass sheets (plies) which are combined with one or morePVB interlayers. The glass sheets could be annealed or tempered. The thickness of the interlayer isin a range of 1 mm, the thickness of the glass sheets varies between 1 mm and 1 cm.The behaviour of static loaded laminated glass is described, for example, by Behr 0. Several tests oflaminated glass leads to the summation that laminated glass behaves similar to monolithic glass ofthe same nominal thickness under short-term lateral pressures. Short term means in his case thatcreeping is negligible.The objective of this composite material is to prevent the development of splinters which could beinjured people. After the failure of the glass, the interlayer glues the splinters together. The failureof a laminated glass sheet can be distinguish in five phases:1 Elastic behaviour of both glass plies.2 The first glass ply is broken, the other glass ply is still intact, interlayer is not damaged.3 The second glass ply fails. The interlayer reacts elastic.4 The interlayer reacts plastic.5 The interlayer fails. The failure can occur due to reaching the failure limit or when the glasssplinters cuts the interlayer.Figure 14: Phases of the failure of laminated glass27

Laminated glass is widely used in all cases where a glass sheet should resist forces after the failureof the glass. Windshields of cars, for example, are typically built with two glass layers with athickness of 2x2.1 mm and a PVB interlayer with a thickness of 0.76 mm. Nowadays also thewindows of trains are built with laminated glass to prevent the development of splinters in the caseof an impact. Other applications for laminated glass are accessible glass roofs and the glazing ofsecurity sensitive buildings.5.1 Simulation Models for Laminated GlassThere are several models in the literature to simulate laminated glass. An overview over thesemodels is shown in Figure 15 and is presented below.Figure 15: Finite Element Models for laminated glass28

5.1.1 Layered ElementsLayered elements can represent the material behaviour of the layers by using different materiallaws. These elements are use mainly to calculate the orthotropic behaviour of laminated fibrematerials but are also applicable for LSG.Müller [29] uses a layered shell element (LS-DYNA) and a user defined material model for theglass. This material model allows a failure of the glass. After the failure of the glass, the stresses ina fixed direction are set to 0 if the strains into this direction are higher than 0 (tension). The materialcan react to the stress in this direction, if the strains are smaller than 0 (compression). If the stressesin the direction normal to the direction of the fixed crack reach also the failure limit, onlycompression stresses can be transmitted. If the interlayer reaches the strength of PVB, the elementis deleted. The contribution of the glass splinters to the interlayer is considers by multiplying theYoung’s modulus by a composite factor. Müller uses his model to calculate air blast wave loadedwindows and gets a good correlation to experiments.5.1.2 Two Coincident ShellsThis model uses two coincident shells with the material laws for glass and the interlayer. One shellrepresents the glass; the other shell represents the interlayer. This model is used, for example, byNguyen [31]. The model can represent the behaviour of laminated glass under tension failure andthe behaviour of laminated glass under bending up to the failure of the glass.The behaviour of the model after failure is too soft in a case of a bending loading due to the fact thatthe failed glass (tension) cannot represent the compression resistance of the other shape.5.1.3 Smeared ModelThe post failure under bending loading can be simulated with the model with layered shell elementsas well as with a smeared model (see Timmel [38], Kolling [23]). Two coincident shells are usedwith two different material laws. Thickness, density and Young’s modulus of these two shellelements are calculated in a way that both shell elements represents the behaviour of the sheetbefore the failure and that the behaviour of the sheet after the failure of one of the glass layers isrepresented by one of the shell elements. Therefore, the stiffness of the shell element, which failsafter the breakage of one of the glass layers, is much smaller than the stiffness of the other shellelement.29

The thickness of both shell elements t E is calculated by the assumption of the same stiffness of theplate before the failure. Therefore, the effect of the interlayer and the area moment of inertia of theglasses (Steiner’s theorem) by moving the axis to the centre of the sheet have to be considered.The thickness of each of these shell elements can be calculated with this formula of Timmel:Et = 3 t + 3 t ( t + t ) + t(7)3 2 PVB 3E G G G PVB PVB2EGwith the thickness of the glass t G , the thickness of the interlayer t PVB , the Young’s modulus of glassE G and of the interlayer E PVB .In the most cases the influence of the stiffness of the interlayer can be disregarded. Therefore, theequation can be reduced to:3t = t + 3 t ( t + t )(8)3 2E G G G PVBThe density has to be readjusted to maintain the same dynamic behaviour of the plate, for examplewith this equation by Timmel:⎛ 1 ⎞ρ = ⎜ρ t + ρ t ⎟ t⎝ 2 ⎠E G G PVB PVB E(9)After the failure, only one of the glass plies carries the load, while the other ply fails by tension.Therefore, the Young’s modulus of the glass layer, which remains, has to be reduced. This can bedone by calculating the stiffness of the remaining glass sheet and the PVB interlayer relating to thenew centre of gravity. With the thickness of the second shell element t E , the stiffness of the secondshell element can be calculated with this formula:II 1E = ⎡E t + t t + E t + t tt ⎣3E( 3 3 2 ) ( 3 32)G E G PVB PVB PVB PVB G⎤⎦(10)Then, the Young’s modulus of the first shell element is modified withIIIE = 2E − E(11)These formulas assume that the bonding between the interlayer and the glass sheets is full. Thismay be the case in short time loadings of laminated glass. However, due to the creep behaviour ofthe interlayer the bonding shows a significant influence of the loading time (see Figure 16). Apossibility is to use an additional factor α in the parallel axis theorem according toG∑ iαsi i(12)I = I + ⋅z ⋅A30

Timmel shows that this factor α could be chosen as 0.55 in static tests and uses this procedure withwindshield glasses and pendulum impact tests.Figure 16: Influence of the creeping of the interlayerMore information about the creeping of the interlayer is shown in section 3.3.5.1.4 Models with Three or More Elements Through ThicknessSeveral possibilities are given by using three or more element through the thickness. Sun 0 uses amodel with 3 elements through the thickness. The PVB interlayer is built with a solid element and ahyperelastic material law, the glass layers are built with shell elements, which node offset is definedin a way that the nodes of the interlayer can be used for the simulation. The model is used tocalculate impacted windshields.Wei [39] uses solid elements for the glass as well as for the interlayer: four elements through thethickness for each glass layer and two elements through the thickness for the interlayer. The meshin the sheet is built with 60 x 60 elements. He simulates with this model laminated glass sheetsloaded by air blast waves and compares the solutions with analytical solutions by using platetheory. The failure of the glass is not taken into account.5.2 Verification with Static ExperimentsThe numerical results can be verified with a static four-point bending test from Sobek [35],presented by Timmel [38] and Haufe [16]. A laminated glass plate with a length of 1.1 m, a widthof 0.36 m and a total thickness of 12.72 mm (PVB interlayer 0.72 mm) is supported by twocylinders of a diameter 0.05 m and distance of 1 m. The load is applied quasi static (load velocity0.4 mm/sec) with two cylinders with a diameter of 0.05 m and a distance of 0.2 m.Figure 17: Experiments with laminated safety glass31

Timmel [38] uses the smeared model to calculate the load displacement curve of this plate. Hechanges the bonding parameter between the two glass plates from full bonding to no bonding (α=1 /α =0). The numerical results of Timmel and the experimental results are shown in Figure 18.Force [N]35003000250020001500Experimentalpha=1alpha=0.6alpha=0.55alpha=0.4alpha=0100050000 5 10 15 20 25 30Displacement [mm]Figure 18: Experiments with laminated safety glassThe calculations show that the bonding between the glass and the interlayer is represented in thebest way by choosing the bonding factor as α=0.55. Then, the stiffness of the glass panel is thesame as in the experiments. The numerical force-displacement curve represents the experimentalvalues up to the first crack. After the first failure, the force decreases up to 0. The behaviour afterthe failure should be much stiffer. The reason for the numerical behaviour is the contact algorithmwhich is used for the boundaries.The reason for this bonding factor is the creep behaviour of the interlayer. For a dynamiccalculation, the bonding factor should be chosen as α=1.0.The experiments can be compared with a quasi static calculation. Quasi static means that theexplicit time integration is used with damping of the first system mode. A dynamic calculationwithout damping is performed to get the frequency of the first system mode. In the proposed modelthe first system mode has a size of 19277 Hz. This value is used for the "QUASI STATIQUE"option fsys. The damping factor is set to 0.1.32

5.3 Verification with Dynamic ExperimentKranzer [24] presents experiments of a 7.5 mm thick laminated glass sheet loaded by several blastloads. The experiment with the shock tube should not be considered here. The experiments withexplosives are performed with the Seismoplast PETN, which explosive energy is 1.4 times higherthan TNT. Three different sizes of the explosive with different distances from the glass sheet areused (see also Figure 21):• 0.125 kg, distance 2.0 m (depending 0.175 kg TNT, Z = 3.58 m/kg 1/3 )• 0.25 kg, distance 3.7 m (depending 0.35 kg TNT, Z = 5.25 m/kg 1/3 )• 0.5 kg, distance 5.75 m (depending 0.7 kg TNT, Z = 6.48 m/kg 1/3 )Figure 21: Experiments with laminated safety glass (Kranzer [24])The glass sheets have a dimension of 1.1 m x 0.9 m and are built with three layers: 3 mm floatglass, 1.52 mm PVB, 3 mm float glass. The sheets are clamped to the rigid frame all around by 50mm restrain. Therefore, the loaded area of the sheet was 1.0 m x 0.8 m.The clamp is built according to EN 13541 with 50 mm width strips of rubber with a thickness of 4mm. The hardness of the rubber is according to ISO 48 50 IHRD. As shown in [30] and [11], theYoung’s Modulus of such a rubber has a value of approximately 3.5 MPa. The prestress of therubber stripes should be 14 N/cm 2 .Three different numerical models are investigated:• Fixed boundary. All boundary conditions (displacements) are fixed at the border of therubber strips. The size of the glass sheet is used as 1.0 x 0.8 m.• Sliding boundary. Only the displacement in the direction of the air blast wave is fixed at theborder of the rubber strips. The displacement in the other directions is fixed at two points.The size of the glass sheet is used as 1.0 x 0.8 m.35

• Elastic boundary. The support is built as in the experiments in an elastic way (see Figure22). The size of the glass sheet is used as 1.1 x 0.9 m. The fixing is built up with solidelements, which use the same nodes as the shell elements (see Figure 22). The nodes on thetop and on the bottom side are fixed. An elastic material is used to describe the behaviour ofthe sealant between the glass and the frame. The calculation fails often at the support sincethe displacements in the sealant are too large. A better description of the rubber like materialof the sealant should be a hyperelastic material. EUROPLEXUS provides still threehyperelastic materials (material HYPE): Mooney Rivlin, Hart Smith and Ogden. Theimplementation is available only for shell elements. The material does not provide thepossibility to use it with layered elements. The implementation of a better material law forthe sealant, which can also be used for the interlayer, will be done later.Figure 22: Model of the elastic supportThe pressure of the experiment is recorded at two places (position 2 and 3, Figure 21). Therefore,the distance from the explosive is not 2 m (in the case of the first experiment). The distance fromthe pressure transducer is 2.24 m. The recorded pressure is compared with the pressure-timefunction used by AIRB (Kingery [21]) in Figure 23. For the calculation of AIRB, the charge is setto 0.175 kg TNT (spherical conditions, reflection). The peak pressure and the time of duration ofthe positive phase are shorter in the experimental approach.The experimental curve can be fit in a good best way by using a charge of 0.09 kg TNT at adistance of 1.8 m (spherical conditions). The difference between the fitted pressure curve and thepressure-time curve of on element midway of the plate results from the displacement of the plate. Adisplacement of the plate results in a longer time of duration.36

160000Kingery (d=2.24 m, Q=0.175 kg)120000KranzerElement at the centre (d=1.8 m, Q = 0.09 kg)Prassure [Pa]800004000000 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004-40000Time [s]Figure 23: Comparison of the pressures of Kranzer [24] with the values by Kingery [21]The first calculations of this problem are performed with the smeared model (see section 5.1.3). Forboth shells an elastic material is used (VM23 with a large elastic limit). The bonding factor is set toα=1.0 due to the fact that the creeping of the interlayer has not to be considered in a fast dynamiccalculation. The parameters of the two shells are shown in Table 3.shell1shell2thickness t E 5.94 mm 5.94 mmdensity ρ Ε 1260 kg/m 3 1260 kg/m 3Poisson ratio ν 0.23 0.23Young’s modulus E 12.4 10 10 N/m 2 1.58 10 10 N/m 2failure limit PEPR with strain limit of 0.12% no failureTable 3: Material parameters for the smeared modelThe numerical models used are shown in Table 4.37

TNT [kg] Distance [m] Boundary ComputationtimeCommentsemi_sm1 0.175 2.0 sliding 750emi_sm2 0.09 1.8 sliding 2577emi_sm3 0.09 1.8 fixed 3088emi_sm4 0.09 1.8 elastic 2207emi_sm5 0.09 1.8 elastic 2082 no failureTable 4: Loading, boundaries for the smeared modelsThe calculations are performed with two different charges. The first one is done with a charge of0.175 kg TNT (spherical conditions, reflection) and a distance of 2.0 m. The pressure history ishigher.Since the air blast load is too large for model emi_sm1 also the displacements are too large (seeFigure 24). The calculation with a charge of 0.09 kg TNT at a distance of 1.8 m gets good results.0.030.025numerical result, d=2 m, Q=1.75 kgDisplacements [m]0.020.0150.01numerical result, d=1.8 m, Q=0.09 kgKranzer0.00500 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009Time [sec]Figure 24: Comparison of experimental displacements (Kranzer [24]) with numerical results –different loadings38

The boundary condition of the frame has also a significant influence on the behaviour of thesimulations. In comparison to the sliding conditions, calculations are also performed with fixedboundary. Then, the principle strains are much higher (see Figure 25).Figure 25: Difference by using fixed boundary (left) or sliding boundary (right)The different boundary conditions result in different displacement histories (Figure 26). After thepeak the influence of the failure of the glass has to be considered. The displacements of the slidingboundaries show the largest displacement. The failure states (Figure 27) show that large parts of thesheet are failed. The rebound appears slower than with the other models.0.020.0150.01Displacements [m]0.0050-0.005-0.01-0.0150 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01Experimental value (Kranzer)smeared model, fixed boundarysmeared model, sliding boundarysmeared model, elastic boundarysmeared model, elastic boundary, fine meshTime [s]Figure 26: Comparison of experimental displacements (Kranzer [24]) with numerical results –different boundary conditions, mesh size39

(sliding)(fixed)(elastic)Figure 27: Failure state of the glass (sliding, fixed, elastic boundary)A calculation with a finer mesh (element size of 1.25 cm instead of 2.5 cm) results in smallerdisplacements. The failure state is similar to the failure state resulting from a coarser mesh and isshown in Figure 28. The comparison with the experimental crack pattern shows a good accordance.40

Figure 28: Failure of the glass; elastic boundary with a fine mesh, experimental result Kranzer [24]Figure 29 presents the reaction forces normal to the plane of the sheet which are calculated bysummarizing the reaction forces of all nodes with boundary conditions. It can be observed that theelastic boundary condition gets more smoothed reaction forces due to the damping of the highfrequencies. The difference between all boundary conditions is small.3000020000fixedslidingelastic10000Forces [N]0-100000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01-20000-30000Time [s]Figure 29: Reaction forces normal to the plane (smeared model)41

The presented results show that the smeared model is an easy and effective way to simulate thebehaviour of laminated glass. The displacements and the failure state are similar to experimentalresults. Nevertheless, this model cannot represent a full membrane reaction of the foil. This modelcan also not be used to simulate the failure of the interlayer.5.4 Implementation of a Layered Simulation Model in EUROPLEXUSThe smeared model can describe the behaviour of the laminated glass of phase 1 and phase 2 (seeFigure 14). The behaviour of the laminated glass after the failure of the second ply cannot bedescribed very well with the smeared model.A model, which uses different material laws for the layers in one shell element, could describe thebehaviour much better (see Figure 30). The PVB interlayer is built up for the first step with elasticmaterial. A new material is developed for the glass (material LSGL). This material reacts elastic upto the failure. After the failure the material can resist compression but cannot resist tension. This isrealised by setting all internal forces of the element to 0 in the case of tension strain. The inputroutine is shown in the Appendix.Figure 30: Layered element5.4.1 Calculations of the Experiments of KranzerThe layered model is verified with the experiments of Kranzer [24] (see section 5.3). The modelsused are shown in Table 5 and Table 6.42

Element Material Boundaryemi_ls3 T3MC LSGL failure slidingemi_ls6 T3MC LSGL without failure fixedemi_ls7 CQD3 LSGL without failure fixedemi_ls8 CQD4 LSGL without failure slidingemi_ls9 CQD4 LSGL failure elasticemi_ls10 T3MC LSGL without failure slidingemi_ls11 T3MC VM23 without failure slidingemi_ls12 CQD4 LSGL without failure slidingemi_ls13 CQD4 LSGL failure slidingemi_ls15 CQD4 LSGL failure elasticTable 5: Parameters for the LSGL modelsliding elastic fixedLSGL, CQD3 13 15 16VM23, CQD3, no failure 8 17 7LSGL, COQI 18 19 20LSGL, COQI, OPOS 21 22 23LSGL, COQI, fine mesh 24 25 26Table 6: Numbers of the modelsAll models use a triangle mesh with an element size of 2.5 cm. The finer meshes use an elementsize of 1.25 cm (emi_ls24, emi_ls25, emi_ls26) and 1.0 cm (emi_ls27).Several elements are tested, which allow defining layers with different properties. Element T3MCresults in very large displacements. It seems that this element considers the membrane forces butnot the bending forces in a right way. The element is therefore not used here. The element CQD3 isa degenerated solid element (Hughes-Liu). The result from this element seems not very precisely.43

0.0250.020.015Displacements [m]0.010.0050-0.005-0.01-0.0150 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01Experimental value (Kranzer)elastic boundary, COQI, LSGL, OPOSelastic boundary, COQI, LSGLTime [s]Figure 32: Influence of the form of the air blast wave – AIRB with and without negative part (OPOS)The failure modes of the different support conditions are be shown in Figure 33.45

Figure 33: Failure state with coarse meshes: sliding (emi_ls18), elastic (emi_ls19), and fixed(emi_ls20); coarse meshCalculations with different element sizes show that the peak displacement depends not much on theelement size (see Figure 34). The rebound effect is smaller for smaller elements. This correspondsto the state of the failure, which is shown in Figure 35 and Figure 36. The smaller the elements are,the bigger is the failure. A bigger failure results in a smaller stiffness for the spring back of thesheet.46

The thickness of the sheet is 0.75 cm. Therefore, much smaller elements than used are notrecommended since the element length should be twice the thickness. Small elements arerecommended for calculations which result in a membrane state. Since the behaviour of the sheetcan also be represented with a very coarse mesh, the layered model can also be used to determinethe displacements of large air blast loaded structures.The comparison between the failure patterns of the different meshes shows that a finer mesh canbuild up the cracks better. The number of these cracks is still small in comparison to the number ofcracks and splinters in the experiments. A reason could be the fact that the Gauss points are set to afailed status for all directions (see Cracks in Two Directions; section 5.4.2).0.020.0150.01Displacements [m]0.0050-0.005-0.010 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01Experimental value (Kranzer)element size 1.0 cmelement size 1.25 cmelement size 2.5 cmelement size 5.0 cm-0.015Time [s]Figure 34: Displacements of several meshes (elastic boundary, COQI)47

Figure 35: Failure state with fine mesh (1.25cm), elastic (emi_ls25)The comparison between the numerical and the experimental crack pattern (see Figure 36) show agood accordance for the principle form of the cracks.Figure 36: Failure state with fine mesh (1cm), elastic (emi_ls27), comparison with experimental crackpatternMüller proposes [29] a reduction factor to smooth the decreasing of the stresses after the failure.This smoothing is performed here in such a way that the tension stresses are multiplied by thisfactor (the value chosen is 0.7) in each step after the failure when the strains are in tension. Thematerial of the laminated glass is extended by the command REDU to allow changes of this factor.The smoothing leads to a higher stiffness since less glass is failed. The rebound effect after the peakis bigger (Figure 37).48

0.020.0150.01Displacements [m]0.0050-0.005-0.01-0.0150 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01Experimental value (Kranzer)REDU 0.7REDU 0.0Time [s]Figure 37: Influence of the reduce factor of the tension stresses (emi_ls25, emi_ls31)Figure 38: Influence of the reduce factor of the tension stresses: REDU 0.0 (emi_ls25) – REDU 0.7(emi_ls31)The computation times are compared in Table 7. It can be shown that the computation times for thesame mesh are similar by using different elements and materials.49

Model Description Number ofshell elementsComputation time[s]emi_ls15 LSGL, CQD3 3594 466emi_ls17 VM23, CQD3 3594 594emi_ls19 LSGL, COQI 3594 494emi_ls25 LSGL, COQI, 1.25 cm mesh 14808 9891emi_ls27 LSGL, COQI, 1.0 cm mesh 23236 18681emi_ls28 LSGL, CQD4, 1.25 cm mesh 6336 1368Table 7: Computation time of some models (elastic boundary conditions)To determine the influence of the material parameters of the interlayer made of PVB calculationswith changed parameters are performed. The influence of Young’s modulus and Poisson ratio issmall (see Figure 39). The influence increases if the sheet is longer loaded by membrane stresses,when the influence of the interlayer is much more important.0.020.0150.01Displacements [m]0.0050-0.005-0.010 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01Experimental value (Kranzer)E=3e6, nu=0.46E=3e6, nu=0.495E=1e9, nu=0.46E=1e9, nu=0.495-0.015Time [s]Figure 39: Influence of material parameters of PVB (emi_ls25)50

All calculations presented are performed without the definition of the failure of the interlayer. Acalculation with a failure strain of 300% of the interlayer shows that the LSG doesn’t fail under theload used.5.4.2 Cracks in Two DirectionsThe method for the failure of the glass material LSGL is extended to a 2D model for the cracks. Theangle of the principle stress (principle strain resp.) is determined in the case of a failure. Theinternal forces orthogonal to this direction are set to 0 in the case of tension strain.The following procedure is used after the first failure:1. Calculation of the stresses with the incremental strains2. Turing of the stresses and the total strains in the coordinate system of the crack3. Checking the stress component tangential to the crack. Reaching the failure limit results in asecond crack orthogonal to the first one. The material is marked as failed in all directions.The element can still react to compression.4. If the total strain normal to the crack is tension (positive) the stress component normal to thecrack is set to 0. Then, the stresses are re-turned to local coordinate system.This method is used with the model emi_ls25. The displacement history is shown in Figure 40. 2Dcracks result in a stiffer behaviour of the sheet after the first failure. This can be observed in thedisplacement history by the faster rebound of the structure. The crack patterns also don’t divergemuch. Therefore, this method is not longer considered.51

0.02Experiment0.0151D cracks2D cracks0.01Displacements [m]0.0050-0.0050 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01-0.01-0.015Time [s]Figure 40: Cracks in two directions (model emi_ls25)cracks in one directioncracks in two directionFigure 41: influence of the cracks in two directions (model emi_ls25)5.4.3 Comparison between Element TypesSeveral elements are extended to allow the calculation of sandwich structures. Model emi_ls25 isused to compare the results, with the element types described in Table 8. The mesh for the52

quadrilateral elements uses the same element length. The number of elements is much smaller(16320 elements instead of 32470 elements).The differences between the computation times can be observed. While all quadrilateral elementsuses similar computation times (also the reduced element), the triangle element DKT3 is the fastestone. The degenerated plate element COQI uses much more time for the calculation.The displacement history shows (Figure 42) that the degenerated shell elements CQD3 and CQD4result in a much faster rebound and should not be used. The COQI element results in a slowerrebound. Except the element CQD3, all triangle elements result in similar crack pattern (see Figure43). Since the computation times for the elements DKT3 and T3GS are much smaller, these triangleelements are recommended.The displacement histories for all quadrilateral elements are similar (except for the degeneratedshell element CQD4). The element types Q4GS and QPPS result in similar crack pattern. Thereduced element Q4GR result in a crack pattern with almost only cracks with 45 degree. Therefore,this element is not recommended.ElementNumberof nodesComputation time[s]CQD3 3 13859COQI 3 15301DKT3 3 6380T3GS 3 9154Q4GS 4 1527Q4GR 4 1615QPPS 4 1636CQD4 4 2106Table 8: Comparison between several element types53

0.020.01Displacement [m]0-0.01-0.020Experiment0.002CQD30.004 0.006 0.008 0.01COQIDKT3DKT3 = T3GST3GSQ4GSQ4GRQPPSCQD4Time [s]Figure 42: Several element types with model emi_ls2554

Figure 43: Crack pattern with several element types (model emi_ls25)55

5.4.4 Number of Integration PointsThe number of integration points through the thickness has also an influence on the numericalresult. Since all models described before use 5 integration points through the thickness (2 for thefirst glass ply, 1 for the interlayer and 2 for the second glass ply), a new calculation is carried outwith 9 integration points. Each material is described with 3 integration points.The calculation shows more cracks at the border of the glass sheet. Therefore, the displacementhistory shows a smaller rebound effect. The integration point in the glass are located closer to thebottom side (or upper side) of the glass. The stresses which are developed by bending of the glassare larger in the integration points closer to the sides. The failure arrives earlier.5 integration points through the thickness 9 integration points through the thicknessFigure 44: Influence of the number of integration points through the thickness (model emi_ls25)56

0.020.015Experiment5 ip9 ip0.01Displacements [m]0.0050-0.0050 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01-0.01-0.015Time [s]Figure 45: Influence of the number of integration points through the thickness (model emi_ls25)5.4.5 Higher Loading of the WindowThe mesh of experiment emi_ls26 (fixed support) is used to make also calculations with biggersizes of explosive to see the failure behaviour of the interlayer. The models used are shown in Table9. All models use a distance of 1.8 m from the charge and a fixed boundary.Modelemi_ls26emi_ls32emi_ls33emi_ls43Charge0.09 kg TNT1 kg TNT5 kg TNT0.3 kg TNTTable 9: Models with different chargesThe results are shown in Figure 47. While the model emi_ls25 with a small charge shows diagonalas well as shear cracks, the influence of the shearing increases with the size of the charge. A charge57

of 0.3 kg TNT results in cracks near the support. The interlayer is not failed. If he charge is chosenas 1 kg TNT, the interlayer fails near the support. There are also some cracks inside the sheet. If thecharge is very large (5 kg TNT), the glass and the interlayer fails immediately after the air blastwave reaches the glass. The failure occurs at the support. The glass plies are also broken inside.The calculation of the glass sheet loaded by the very large amount of TNT is more delicate.Therefore, a new failure criterion is introduced in EUROPLEXUS, which avoids too small timesteps. This can occur due to the fact that an element becomes very small because of largedisplacements immediately before the failure. Such elements can now be erased automatically. Inaddition, the calculation stops often due to an element distortion of an element of the support. Thiscan be reduced by using more elements in the support (see Figure 46).Figure 46: Finer mesh for the support58

emi_ls33 (5.0 kg, t=1e-3) emi_ls32 (1.0 kg, t=5.45e-3 s)emi_ls43 (0.3 kg, t=7.95e-e) emi_ls26 (0.09 kg, t=1e-2 s)Figure 47: Influence of the size of the charge (fixed boundary)59

5.5 Experiments with a Failure of the Interlayer (Hooper)5.5.1 ExperimentThe experiments of Kranzer [24] don’t result in a failure of the interlayer since the tensile strain inthe interlayer is relative small. Two experiments with a larger air blast load are made by Hooper[17]. The amount of C-4 was 15 kg with two different distances of 10 m and 13 m. Each windowhad a size of 1.5 m x 1.2 m with a thickness of 7.5 mm. The LSG was built from two glass plieseach with a thickness of 3 mm. The PVB interlayer had a thickness of 1.52 mm. The window wasbonded with silicone to a steel frame. The silicone had a thickness of 6 mm and a width of 20 mm.The pressures of the air blast wave were measured as incident pressures and not the reflected one.The displacements of the windows were recorded with a high speed camera in such a way that thedeformation of the whole sheet can be determined later using a 3D digital image correlation. Thisallows the determination of the angle between the glass and the frame. In addition, the boundaryforces were measured for both experiments. The angle and the forces should be used to performsmall pull out tests in the laboratory to see the behaviour of the support conditions of the glass planeunder these conditions.The response of the laminated glass sheets depends on the distance from the charge. The laminatedglass with a 10 m stand off distance failed before the rebound has started.Several values of the TNT equivalent are documented in the literature for C-4. A value of 1.2 isused here to determine the pressure-time function using AIRB. The pressure-time function of theexperiment as well as of the approximation of Kingery [21] with 18 kg TNT is presented in Figure48. The displacement histories are presented in Figure 49.60

Overpressure [Pa]10000080000600004000020000Experiment 10 m stand off distance(incident)Kingery incident, hemispherical; 18kgTNT, 10 m distanceExperiment 13 m stand off distance(incident)Kingery incident, hemispherical; 18kgTNT, 13 m distance0-200000 10 20 30 40 50 60Time [ms]Figure 48: Incident pressure histories of the experiments of Hooper [17] in comparison with Kingery(18 kg TNT)0.4Experiment 13 m stand off distanceExperiment 10 m stand off distance0.3Displacement [m]0.2Failure of the interlayer0.100 0.005 0.01 0.015 0.02Time [s]Figure 49: Displacement histories of the experiments of Hooper [17]61

5.5.2 CalculationsSeveral calculations are performed to show the behaviour of the implemented material law also forconditions, when the interlayer fails. All calculations are shown in Table 10. If it is not remarkedthere, all models use triangular elements with a size of 2 cm.NameStand offElementMaterialMaterial for PVBCommentsdistance [m]for glasshooper1 13 COQI LSGL E PVB =1e10 N/m 2hooper2 13 COQI LSGL E PVB =1e9 N/m 2hooper3 10 COQI LSGL E PVB =1e10 N/m 2hooper4 13 COQI smearedhooper5 10 COQI smearedhooper6 13 COQI LSGL plastic materialhooper7 13 COQI LSGL E PVB =1e10 N/m 2 fine mesh for thesupporthooper8 13 DKT3 LSGL plastic material finer mesh (1.25 cm)hooper9 10 COQI LSGL plastic materialhooper10 10 DKT3 LSGL plastic material also elements COQI,CQD3, T3GShooper11 13 DKT3 LSGL plastic materialhooper12 10 DKT3 LSGL plastic material coarser mesh (5 cm)hooper13 13 DKT3 LSGL plastic material coarser mesh (5 cm)hooper14 10 Q4GS LSGL plastic material also elements Q4GR,QPPS, CQD4Table 10: Comparison between several elementsHooper1, hooper2, hooper3These calculations are performed with the degenerated plate element COQI. This element failsvery often since there are some problems with the determination of the normal vectors of the62

element. The failure is therefore not representative. Figure 50 and Figure 51 show thedisplacement history. The initial stiffness of the glass sheet is represented by this element.0.4ExperimentDisplacement [m]0.30.20.10hooper2 (E_PVB=1e9 N/m2)hooper1 (E_PVB=1e10 N/m2)Smeared model0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04-0.1-0.2Time [s]Figure 50: Hooper experiment (13 m stand off distance)0.4Displacement [m]0.30.2ExperimentExperiment after crackhooper3hooper5 (sm)0.100 0.005 0.01 0.015 0.02Time [s]Figure 51: Hooper experiment (10 m stand off distance)63

Hooper4, hooper5These calculations use the smeared model. The rebound effect is too big since the failure isrepresent in a wrong way. Only one of the glass plies can fail. After the failure of both glass plies,the glass sheet is under high tension strain. Then, the smeared model should not be used.Models with plastic material lawThe assumption of a Young’s modulus of 1e10 N/m 2 and a failure strain of 300 % is found in theliterature. The value for the Young’s modulus is calculated from the shear modulus. Severalexperiments are performed in the last years to obtain the behaviour of PVB also under high strainrates (Bennison [4], Iwasaki [18], [19] and Morison [28]). The behaviour of PVB under high strainrates becomes more elastoplastic and is not viscoelastic (see Figure 6). The strain rates of thenumerical calculations are high (up to 200 1/s). Therefore, an elastoplastic material is used for mostcalculations. The material is defined in EUROPLEXUS with the following command:VM23 RO 1100. YOUNG 2.2e8 NU 0.495 ELAS 11E6FAIL VMIS LIMI 2.8e7TRAC 3 11e6 0.05 30e6 2.25 40e6 3.5Most calculations with the elastoplastic material use the more robust element DKT3. The elementcan sustain larger displacements without a failure of the calculation. The results are shown in Figure52 and Figure 53. The calculation of the laminated glass with a stand off distance of 10 shows agood correlation with the experiment. The beginning of the failure of the interlayer is represented.The calculation of the experiment with a stand off distance of 13 m shows a failure of the interlayerbefore reaching the maximum displacements. The experimental displacements are smaller. A reasoncould be that the stiffness of the remaining structure after the failure of both glass plies undermembrane strain is much stiffer than represented since the splinters of the glass are glued onto theinterlayer and can also sustain a part of the tension.64

0.5Failure of the interlayer0.4ExperimentExperiment after crackhooper10 (DKT3)Displacement [m]0.30.20.100 0.005 0.01 0.015 0.02Time [s]Figure 52: Calculations of the experiment of Hooper with a stand off distance of 10 m, elasto-plasticmaterial, element DKT30.4Failure of the interlayer0.3Experimenthooper10Displacement [m]0.20.100 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04-0.1-0.2Time [s]Figure 53: Calculations of the experiment of Hooper with a stand off distance of 13 m, elastoplasticmaterial, element DKT365

The strain rates, which are presented in the calculation hooper10, are shown in Figure 54; thecorresponding failure ratio is presented in Figure 55. It can be observed that the strain rate increaseswhen both glass plies are failed. The range of the strain rates is between 50 and 200. There are onlyexperimental data available up to a strain rate of 118. Therefore, the behaviour of PVB in withstrain rates above this point is hypothetical.200150100Element 10329Element 1656Element 6126Element 9371Strain rate [1/s]500-500 0.005 0.01 0.015 0.02-100-150-200Time [s]Figure 54: Strain rates for calculation hooper10 of several elements66

1.2Failure ratio of the whole element10.80.60.40.2Element 10329Element 1656Element 6126Element 937100 0.005 0.01 0.015 0.02Time [s]Figure 55: Failure ratio for calculation hooper10 of several elements5.5.3 Variation of the Hardening of PVBIf both glass plies failed and the laminated glass is under membrane loading, the material law usedconsiders only the behaviour of the PVB. This seems to be wrong in the way that not only theinterlayer reacts but also the splinters, which are glued onto the interlayer (see Figure 56). Thesesplinters take part on the strain stress relation of the structure. The behaviour is very complex andcan not be taken into account with a layered element in a proper way.Figure 56: Splinters glued onto the interlayerAn idea to implement this behaviour in a very simple way is to use a higher hardening as it isobserved in the experimental data of PVB. This is done here with different α-values, which indicate67

the ratio of the initial Young’s modulus (see Figure 57). The stiffness of the hardening E hard iscalculated as:Ehard= α ⋅ E(13)0120Stress [MPa]1008060approaches for thecombination ofinterlayer and splintersα=0.2α=0.1Bennison 89 1/sBennison 8 1/sBennison 0.7 1/sBennison 0.07 1/sIwasaki 0.033 1/sIwasaki 118 1/sMorison 74 1/s40α=0.042000 50 100 150 200 250 300 350Strain [%]Figure 57: Changed hardening parameter to simulate the splinters on the interlayerThe influence of the parameter α for the stand off distance of 10 m is presented in Figure 58. Thecalculation is performed with the model hooper10 with the element DST3. Only the calculationusing α=0.04 results in a failure of the interlayer. All other calculation doesn’t show a failure. Acalculation without any failure results in a stiffer remaining structure with a bigger rebound effect,which is visible in the numerical results.The influence of α on the calculations with a stand off distance of 13 m is much smaller (see Figure59). Only the calculation with α=0.04 results in a failure of the interlayer. The increased hardeningdoesn’t result in a better description of the experiment. The behaviour of the splinters glued onto theinterlayer has to be taken into account in a more proper way. This could be possible, for example,using 3D solid elements.68

Displacement [m]0.50.40.30.2ExperimentExperiment after crackalpha=0.04alpha=0.1alpha=0.2Failure of the interlayer (α = 0.04)0.100 0.005 0.01 0.015 0.02Time [s]Figure 58: Influence of the changed hardening parameter (10 m stand off distance)0.4Failure of the interlayer (α = 0.04)Displacement [m]0.30.20.10Experimentalpha=0.04alpha=0.1alpha=0.20 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04-0.1-0.2Time [s]Figure 59: Influence of the changed hardening parameter (13 m stand off distance)69

5.5.4 Influence of the Mesh SizeThe influence of the mesh size is small with respect to the displacement behaviour (see Figure 60and Figure 61). The failure of the interlayer can only be represented, if the elements are smallenough.Several authors use a maximum displacement criterion to define the failure of the interlayer.Morison [28], for example, determines a failure if the displacements reaches approximately 30 % ofthe span of a glass sheet. This value depends also on the temperature of the glass.Since the displacement is represented quite well also with relative coarse meshes, a maximumdisplacement criterion can be used in much larger calculations, when a finer mesh is not possible.0.5Failure of the interlayer(element size 2cm)0.4Displacement [m]0.30.20.10ExperimentExperiment after crackelement size 2 cm (hooper10)element size 5 cm (hooper12)0 0.005 0.01 0.015 0.02Time [s]Figure 60: Influence of the element size (10 m stand off distance), α=0.04, DKT370

Displacement [m]0.40.30.20.10Failure of the interlayer(element size 2 cm)Experimentelement size 1.25 cm (hopper8)element size 2.0 cm (hooper6)element size 5.0 cm (hooper13)0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04-0.1-0.2Failure of the interlayer(element size 1.25 cm)Time [s]Figure 61: Influence of the element size (13 m stand off distance), α=0.04, DKT35.5.5 Influence of the Element TypeThe influence of the different element types is also investigated with the experiment of Hooper.The computation time of the elements investigated is shown in Table 11. The computation time forthe element COQI is much longer than for all other elements due to much smaller time steps. Thetime steps are much smaller due to stability problems of only some elements. The computation timeof the element Q4GR (reduced integration) is longer than the computation time of the elementQ4GS (full integration). Except the results for the element CQD4, the displacement history of allcalculations is similar (see Figure 62). The failure behaviour of the interlayer diverges depending onthe element type (see Table 11). The failure of the first elements occurs too late for the elementtypes CQD3 and QPPS. Figure 63 shows the failure of the glass sheet at t=2e-2 s. Since the locationof the failure in the experiment was not investigated, a numerical crack cannot be validated usingexperimental results.In summary, the element types CQD3, COQI, Q4GR, QPPS and CQD4 are not recommended forsuch investigations. Good results are given using the element types DKT3, T3GS, and Q4GS.71

ElementNumberComputation timeFailure of theof nodes[s]first element [s]CQD3 3 3341 1.75E-02COQI 3 17275 *) 6.11E-03DKT3 3 6306 8.52E-03T3GS 3 3478 8.74E-03Q4GS 4 2190 7.19E-03Q4GR 4 3247 9.25E-03QPPS 4 1343 1.77E-02CQD4 4 8505 *) 6.23E-03Table 11: Comparison between several element types*) failure of the calculation before the end of the calculationDisplacement [m]0.50.40.30.2ExperimentExperiment (crack)CQD3COQIDKT3T3GSQ4GSQ4GRQPPSCQD40.100 0.005 0.01 0.015 0.02Time [s]Figure 62: Influence of the element type (hooper10), displacement history72

Figure 63: Influence of the element type (hooper10), crack pattern5.5.6 Crack in Two Directions, Reduction FactorThe model hooper10 is also calculated with the reduction factor and the procedure which producescracks depending on the direction of the principle strain/principle stress.The influence is shown in Figure 64. Both methods shows a rebound effect, which does notcorrespond with the experimental data. It is therefore not recommended to use neither the reductionfactor nor the cracks in two directions.Displacement [m]0.50.40.30.2ExperimentExperiment after crackalpha=0.04redu=0.7crack 2 directionsFailure of the interlayer (crack 2d)Failure of the interlayer (crack 1d)0.100 0.005 0.01 0.015 0.02Time [s]Figure 64: Influence of the reduction factor and the cracks in two directions (hooper10)74

6 ConclusionThis Technical Note presents several simulation methods for different types of glass loaded by airblast. The objective of this Technical Note is to develop a simulation model for the glass used intrains and stations.A new material model is introduced in EUROPLEXUS for the calculation of annealed glass. Theinfluence of the loading time (strain rate) is taken into account in this model. The model showsgood correlation with analytical results.The behaviour of laminated glass is more complex. The idea of laminated glass is to avoid flyingsplinters using a plastic interlayer (mostly PVB) between two or more glass plies. The behaviour ofthis interlayer is viscoelastic for small strain rates and becomes more and more elasto-plastic forhigher strain rates. The interlayer fails with a strain of approx. 300 %. Another failure modus is thatthe splinters cut the interlayer.Two simulation methods for laminated glass are presented. The smeared model uses twocoincident shell elements. The stiffness of both shell elements is the same as of the unbrokenlaminated glass. One of these shell elements can fail. The stiffness of the remaining shell element iscalculated in such a way that it represents the stiffness of one glass ply together with the interlayer.The calculations show that the behaviour of laminated glass can be represented using the smearedmodel if the membrane strains in the glass are not too large.A simulation with layered shell elements requires a special material model for the glass. Theimplemented material for the glass plies allows a failure of the glass. The stresses of a failedintegration point are set to 0 if the strain is positive (tension). In the case of negative strain(compression) the material is still active with the initial stiffness. The calculations have shown thatthis model can also represent experiments with a large membrane strain. The tearing of theinterlayer can be built up using a strain limit of 300 %.Two experiments with air blast loaded windows are used to verify the models. The first experimentdoesn’t show a failure of the interlayer; the tension strain in the laminated glass is small. Bothsimulation models show a good correlation with the results of the experiment.The behaviour of the failure of the interlayer is shown in another experiment. The tensile strains ofsuch an experiment are much larger. Therefore, the smeared model can not represent the behaviourof the interlayer. The calculations with the layered model show a good representation of theexperiments for the displacement history as well as for the time of the failure.75

Several parameters influence the results of the calculations like the element type, the number ofintegration points over the thickness, the reduction factor to smooth the decreasing of the stressesafter a failure, and the procedure with cracks in two directions. Since the influence of all parameterstogether is not small the choice of these parameters should be done carefully.In addition, several investigations should be done to clarify effects, which are not yet described withthe presented model:• The strain of the interlayer is very large. A hyperelastic material should therefore be usedinstead of an elasto-plastic one.• Experiments of PVB loaded by high strain rates are only performed up to 120 1/s. The strainrate observed in the calculations reaches values of about 200 1/s and more. Experimentswith higher strain rates should close this gap.• After the failure of both glass plies, the simulation with layered shell elements uses only theinterlayer in the case of positive membrane strain. In reality, several splinters are glued ontothe interlayer and should also be considered.• The failure of the interlayer is defined with a strain limit. The interlayer could also fail if itis cut by splinters. This should be verified.The mesh size has a small influence on the displacement behaviour. The failure behaviour of thelaminated safety glass can only be represented with fine meshes. A coarse mesh doesn’t show afailure.The meshes, which should used to simulate the trains and the stations for the RAIPROTECT projectare very large. The design of air blast loaded windows is mostly done with single degree of freedommethods with a displacement criterion of approx. 30% of the span of the window. A coarse meshusing layered shell elements in combination with such a displacement criterion is recommended forthe calculation of the laminated safety glass windows in the train and in the station.76

7 References[1] Baker, W.E.; Cox, P.A.; Westine, P.S.; Kulesz, J.J. and Strehlow, R.A.: Explosion Hazardsand Evaluation, Elsevier, Amsterdam, 1983.[2] Beason, W.Lynn, Morgan, James R.: Glass failure prediction model. Journal of StructuralEngineering, 110 (2), pp. 197-212, 1984.[3] Behr, R.A. and Minor, J.E. and Norville, H.S.: Structural behaviour of architectural laminatedglass. Journal of Structural Engineering, 119, p 202-222, 1993.[4] Bennison, Stephen; Sloan, J.G.; Kistunas, D.F.; Buehler, P.J.; Amos, T. and Smith, C.A.:Laminated glass for blast mitigation: Role of interayer properties. In Glass Processing Days,2005.[5] Brendler, S.: Rechnerisches Bemessungskonzept für absturzsichernde Glastafeln.Dissertation, Technischen Universität Braunschweig, 2007.[6] Brown, W.G.: A Practicable Formulation for the Strength of Glass and Its Special Applicationto Large Plates. Publication No. NRC 14372, National Research Council of Canada, Ottawa,1974.[7] Dharani, L.R.; Wei, J.; Ji, F.S.: Failure analysis of laminated architectural glass panelssubjected to blast loading, Structures Under Shock an Impact VII, 2003. 7th Int. Conf. onStructures under Shock and Impact, Montreal, Canada, pp. 37-46, 2002.[8] D’Haene, P.: Experimental data of PVB. Belgium: Solutia Europe SA/NV; 2002.[9] D’Haene, P. and Savineau, G.: Mechanical properties of laminated safety glass – FEM study.Glass Performance Days 2007, http://www.gpd.fi; 2007.[10] Van Duser, A.; Jagota, A. and Bennison, S.J.: Analysis of glass/polyvinyl butyral laminatessubjected to uniform pressure. Journal of Engineering Mechanics, 125 (4) p. 435-442, 1999.[11] ERIKS group: Technical Handbook, http://o-ring.info/, 2008.[12] Ferry, J.D.: Viscoelastic properties of polymers, 3 rd Ed., Wiley, New York, 1980.[13] Fletcher, E.R.; Richmond, D.R.; Yelverton, J.T.: Glass Fragment Hazard from WindowsBroken by Airblast. Topical Report No. A428501, Lovelace Biomedical and EnvironmentalResearch Institute, New Mexico, 1980.[14] Flocker, F. W. and Dharani L. R.: Stresses in laminated glass subject to low velocity impact,Engineering Structures 19 (10), pp.851 – 856, 1997.[15] Griffith, A.A.: The phenomena of rupture and flow of solids. Theoretical Transactions of theRoyal Society of London, 221, pp. 163-179, 1920.[16] Haufe, André; Nguyen, Ngoc Bao; Sonntag, Bärbel; Kolling, Stefan: Zur Simulation vonSicherheitsglas unter stoßartiger Belastung, Teil II: Validierung eines FE-Modells fürVerbundsicherheitsglas, 3. LS-DYNA Anwenderforum, Bamberg 2004.[17] Hooper, P.; Dear, J.; Blackman, B.; Smith, D.; Hadden, D. and Sukhram R.: Strength ofstructural silicone glazing joints under blast loading. In Department of Defense ExplosivesSafety Board Seminar, 12-14 august, Palm Springs, CA, USA, 2008.[18] Iwasaki, R. and Sato C.: The influence of strain rate on the interfacial fracture toughnessbetween PVB and laminated glass. Journal de Physique IV (Proceedings), 134:1153–1158,2006.[19] Iwasaki, R.; Sato, C; Latailladeand, J. L. and Viot P.: Experimental study on the interface77

fracture toughness of PVB (polyvinyl butyral)/glass at high strain rates. International Journalof Crashworthiness, 12(3):293–298, 2007.[20] Johnson, G.R., Holmquist, T.J.: An improved computational constitutive model for brittlematerials, Joint AIRA/APS Conference, Colorado Springs, Colorado, June 1993.[21] Kingery, Charles N., Bulmash, Gerald: Airblast Parameters from TNT Spherical Air Burstand Hemispherical Surface Burst; Defence Technical Information Center, Ballistic ResearchLaboratory, Aberdeen Proving Ground, Maryland; 1984.[22] Kinney, Gilbert F.; Graham, Kenneth J.: Explosive Shocks in Air, Springer, Berlin, 1985.[23] Kolling, S., Haufe, A., Du Bois, P. A.: On the numerical Simulation of single-layer andlaminated Safety Glass under Impact Loading, In: Proceedings of EURODYN 2005,September, 4th-7th, Paris, France, 2005.[24] Kranzer, C.; Gürke, G.; Mayrhofer, C.: Testing of bomb resistant glazing systems.Experimental investigation of the time dependent deflection of blast loaded 7.5 mm laminatedglass. Glass Processing Days 2005, http://www.gpd.fi, 2005.[25] Krauthammer, T.; Altenberg, A.: Negative phase blast effects on glass panels, InternationalJournal of Impact Engineering, 24 (1), pp. 1-18; 2000.[26] Krüger, G.: Temperature effects on the structural behaviour of laminated safety glass. Otto-Graf-Journal Vol. 9, Otto-Graf-Institut (FMPA), Universität Stuttgart, 1998.[27] Larcher, Martin: Pressure-Time Functions for the Description of Air Blast Waves. JRCTechnical Note, JRC46829, Ispra 2008.[28] Morison, Colin; Zobec, Marc and Frenceschet, Alberto: The measurement of PVB propertiesat high strain rates, and their application in the design of laminated glass under bomb blast,ISIEMS 2007, International Symposium on Interaction of the Effects of Munitions withStructures, 17.-21.09., Orlando, US, 2007.[29] Müller, R. and Wagner, M.: Berechnung explosionshemmender Fenster- undFassadenkonstruktionen. Webpage http://www.ibdrm.de[30] Müller, Heinz Konrad and Nau, Bernard S.: www.fachwissen-dichtungstechnik.de, 2008.[31] Nguyen, Ngoc Bao; Haufe, André; Sonntag, Bärbel; Kolling, Stefan: Zur Simulation vonSicherheitsglas unter stoßartiger Belastung, Teil I: FE-Modelle für Einscheiben- undVerbundsicherheitsglas, 3. LS-DYNA Anwenderforum, Bamberg 2004.[32] Overend, M.; Parke, G.A.R.; Buhagiar, D.: Predicting failure in glass – A general crackgrowth model. Journal of Structural Engineering, 133(8), pp. 1146-1155, 2007.[33] prEN 13474-1. (1999). Glass in building – Design of glass panes – Part 1: General basis ofdesign. Draft, January 1999.[34] prEN 13474-2. (2000). Glass in building – Design of glass panes – Part 2: Design foruniformly distributed loads. Draft, February 2000.[35] Sobek, W.; Maier, F.; Kutterer, M.: Versuche an Verbundsicherheitsgläsern zur Beurteilungder Resttragfähigkeit und des Verbundverhaltens, Universität Stuttgart, Institut für leichteFlächentragwerke, Forschungsbericht 1/98.[36] Stewart, M.G., Netherton, M.D.: Security risks and probabilistic risk assessment of glazingsubject to explosive blast loading. Reliability Engineering and System Safety 93 (4), pp. 627-638, 2008.[37] Sun, D.Z.; Andrieux, F.; Ockewitz, A.; Klamser, H. and Hogenmüller, J.: Modelling of thefailure behaviour of windscreens and component tests. 5 th European LS-DYNA Users78

Conference, 25. - 26. Mai 2005, Birmingham, UK.[38] Timmel, M.; Kolling, S.; Osterrieder, P.; Du Bois, P.A.: A finite element model for impactsimulation with laminated glass, International Journal of Impact Engineering, 34, p. 1465-1478, 2007.[39] Wei, J. and Dharani, L.R.: Response of laminated architectural glazing subjected to blastloading. International Journal of Impact Engineering, 32, p 2032-2047. 2006.79

8 Apendix8.1 EUROPLEXUS CodeThe following EUROPLEXUS files are affectedfrom the development of this Technical Noteand are not presented here:• m_elem_chars• m_material_vm23m_material_glas.ffMODULE M_MATERIAL_GLAS** material of type glas*USE M_MATERIALS_ARRAY*IMPLICIT NONESAVE*PRIVATEPUBLIC MAT_GLAS, GLAS*CONTAINS*=======================================SUBROUTINE MAT_GLAS(INUMLDC)** ------------------------------------------------------------------* larcher 02-08* glass material* ------------------------------------------------------------------** inumldc : numero (de la loi) associe explicitement* (mot-cle "loi") ou implicitement (=rang)* au materiau courant** organisation of newmat%matval:* matval(1) : masse volumique initiale* matval(2) : young's modulus* matval(3) : poisson's ratio* matval(4) : stress corrosion constant* matval(5) : chosen failure criterion* (0=none,1=vmis,2=peps,3=pres,4=pepr,5=psar)* matval(6) : chosen failure limit value*INCLUDE 'NONE.INC'*INCLUDE 'CARMA.INC'INCLUDE 'REDCOM.INC'INCLUDE 'POUBTX.INC'*INTEGER, INTENT(IN) :: INUMLDC** local variables*INTEGER, PARAMETER :: IFIX = 6INTEGER :: LENX***INTEGER, PARAMETER :: NMOT=IFIX, NMOTFA=5CHARACTER*4 MOT(NMOT),MOTFAI(NMOTFA)CHARACTER*32 BLAFAIINTEGER KOPT(NMOT), I, IOP, IF1, IOP1REAL*8 YOUNG, EPS1, EPS, EPS2, EIM1, SIM1LOGICAL :: IMPRIMDATA MOT/'RO ','YOUN','NU ','CORR','FAIL','LIMI'/DATA MOTFAI/'VMIS','PEPS','PRES','PEPR','PSAR'/*CHARACTER(32), PARAMETER :: NOM='GLAS :GLASS WITH STRAIN RATE'INTEGER, PARAMETER :: N_MSG = IFIX , LG_FMT =44CHARACTER(LG_FMT) :: GET_FMT(N_MSG)DATA GET_FMT(:) /1'DENSITY',2'YOUNG''S MODULUS',3'POISSON''S RATIO',4'STRESS CORROSION',5'FAILURE CRITERION',6'FAILURE LIMIT'/*BLAFAI='NOT DEFINED'*CALL CREATE_MATERIAL (IFIX, 0, 0)NEWMAT%NAME = NOMNEWMAT%TYPE = LG_FMTNEWMAT%NUMLDC = INUMLDCNEWMAT%LGECR = LGECR(NEWMAT%TYPE)KOPT(:) = 0 ! INITIALIZE WHOLE ARRAY*11 CALL LIRMOT(MOT,NMOT,IOP)IF(IOP > 0) THENSELECT CASE (IOP)CASE (5) ! FAIL** "fail", read sub-keyword*CALL LIRMOT(MOTFAI,NMOTFA,IOP1)SELECT CASE (IOP1)CASE (1)** "vmis"*NEWMAT%MATVAL(5)=1.D0KOPT(5)=1BLAFAI='VON MISES'CASE (2)** "peps"*NEWMAT%MATVAL(5)=2.D0KOPT(5)=2BLAFAI='PRINCIPAL STRAIN'CASE (3)** "pres"*NEWMAT%MATVAL(5)=3.D0KOPT(5)=3BLAFAI='MINIMUM PRESSURE'CASE (4)80

** "pepr"*NEWMAT%MATVAL(5)=4.D0KOPT(5)=4BLAFAI='PRINCIPAL STRAIN + TENSION PRESS'CASE (5)** "psar"*NEWMAT%MATVAL(5)=5.D0KOPT(5)=5BLAFAI='INTEGRAL OF THE PRINCIPAL STRESS'CASE DEFAULTGO TO 9END SELECTCASE DEFAULT** "ro" or "youn" or ... (but not "inte" nor "fail") : read value*CALL LIRE(3)NEWMAT%MATVAL(IOP)=DPRECKOPT(IOP)=1END SELECT*GO TO 11*ENDIF**----- donnees completes ? (1 a 6 indispensables)DO I=1,6IF(KOPT(I) == 0) GOTO 9END DO**----- impressions ( debut )WRITE(BLABLA,1001)NEWMAT%NUMLDC,NEWMAT%NAMECALL MECTSG(BLABLA)IF(IMPRIM(8)) THENCALL MECVAL(GET_FMT(1),NEWMAT%MATVAL(1))CALL MECVAL(GET_FMT(2),NEWMAT%MATVAL(2))CALL MECVAL(GET_FMT(3),NEWMAT%MATVAL(3))CALL MECVAL(GET_FMT(4),NEWMAT%MATVAL(4))CALL MECTEX(GET_FMT(5) ,BLAFAI)CALLMECVAL(GET_FMT(6),NEWMAT%MATVAL(6))ENDIFRETURN9 CONTINUE**--- the errorsWRITE(BLABLA,2001)CALL ERRMSS('MAT_GLAS',BLABLA)STOP ' MAT_GLAS'**IF FRANCAIS1001 FORMAT('LOI NUMERO',I5,' : ',A)2001 FORMAT('LA DIRECTIVE "GLAS" ESTINCOMPLETE')CELSE1001 FORMAT('LAW NUMBER',I5,' : ',A)2001 FORMAT('THE DIRECTIVE "GLAS" ISINCOMPLETE')CENDIF*END SUBROUTINE MAT_GLAS*==========================================SUBROUTINE GLAS(ITAU,IPLANC,XMAT,DEPS,SIG,ECR, PI,CSON,IG,IGMAX)**-----------------------------------------------------------------------* larcher 02-08* 2d or 3d (also with zero normal stress) stress-strain law forelastic* materials (incremental form)* several failure criteria specially with strain rate dependencyfor glass*-----------------------------------------------------------------------** itau : number of shear stress components (sig(3),sig(5),sig(6))* iplanc : 0 = no plane stress condition* 1 = plane stress condition (sig(4)=0)* 2 = uniaxial stress condition (sig(2)=sig(4)=0)* xmat() : vector of material properties for this material (seemaglas)* xmat(1) : masse volumique initiale* xmat(2) : young's modulus* xmat(3) : poisson's ratio* xmat(4) : stress corrosion constant* xmat(5) : chosen failure criterion* (0=none,1=vmis,2=peps,3=pres,4=pepr,5=psar)* xmat(6) : chosen failure limit value* deps(1) --> deps1 : x-strain increment* deps(2) --> deps2 : y-strain increment* deps(3) --> dgam12 : xy-strain increment* deps(4) --> deps3 : z-strain increment* deps(5) --> dgam23 : yz-strain increment (only 3-d)* deps(6) --> dgam13 : xz-strain increment (only 3-d)* sig(1) --> sig1 : x-stress* sig(2) --> sig2 : y-stress* sig(3) --> tau12 : xy-stress* sig(4) --> sig3 : z-stress* sig(5) --> tau23 : yz-stress (only 3-d)* sig(6) --> tau13 : xz-stress (only 3-d)* ecr(1) --> ecr1 : current hydrostatic pressure (1/3(sx+sy+st))* ecr(2) --> ecr2 : current equivalent stress (von mises)* ecr(3) --> psar : area under the principal stress-time curve* between the current time and the last change ofsign of PRSIG* ecr(4) --> eps1 : cumulated x-strain* ecr(5) --> eps2 : cumulated y-strain* ecr(6) --> gam12 : cumulated xy-strain* ecr(7) --> eps3 : cumulated z-strain* ecr(8) --> gam23 : cumulated yz-strain (only 3-d)* ecr(9) --> gam13 : cumulated xz-strain (only 3-d)* ecr(10) --> lcos : last change of sign of princ stress (seeecr(3))* ecr(11) --> cson : sound speed (added 26.2.92)* ecr(12) --> fail : failure flag (0=virgin gp, 1 = failed gp)* pi() : vector of new stress components (same organization assig)* cson : sound speed* ig : current gauss point index for this element* igmax : total n. of gauss points for this element*USE M_FAILED_ELEMENTS ! FOR THE EROSION*IMPLICIT NONE*INCLUDE 'CONTRB.INC'INCLUDE 'COPT.INC'81

INCLUDE 'PILOT.INC'INCLUDE 'TEMPS.INC' ! DT1 : CURRENT TIME STEPSIZEINCLUDE 'TEMPX.INC' ! T = CURRENT TIME!!---- Variables Globales!REAL(8), INTENT(IN) :: XMAT(*), SIG(*)REAL(8), INTENT(OUT) :: PI(*), CSONREAL(8), INTENT(INOUT) :: DEPS(*), ECR(*)INTEGER, INTENT(IN) :: ITAU, IPLANC, IG, IGMAX!!---- Variables locales!INTEGER :: FAIL_CRITREAL(8) :: G2,D,CS,AM,XNU,YMX,T1,T2,T3,PRESS,CORR,PSAR,SIGTD,& A01,A02,A03,SEQ,V,FAIL_LIMIT,FAIL_LIMIT_ELEM,& DIAG(3),TENS(3,3),PEPSMAX,SIGMAX,FACT** material properties*YMX=XMAT(2)XNU=XMAT(3)CORR=XMAT(4)FAIL_CRIT = XMAT(5)FAIL_LIMIT = XMAT(6)T1=1.D0+XNUT2=1.D0-2.D0*XNUT3=1.D0-XNUCS=YMX/XMAT(1)D=XNU*YMX/(T1*T2)G2=YMX/T1*FAIL_LIMIT_ELEM = FAIL_LIMIT*IF (FAIL_CRIT /= 0) THENPEPSMAX = -HUGE(PEPSMAX)** check previous failure*IF (ECR(12) /= 0.D0) THEN* current gauss point was previously failed, so let's just skip it ...SEQ = 0.D0PRESS = 0.D0FAIL_LIMIT_ELEM = 0.D0PEPSMAX = HUGE(PEPSMAX)GO TO 990ENDIFENDIF*GOTO(100,101,102),IPLANC+1102 DEPS(2)=-(SIG(4)+D*DEPS(1))/(G2+2.D0*D)101 DEPS(4)=-(SIG(4)+D*(DEPS(1)+DEPS(2)))/(G2+D)100 CONTINUE*4 V=D*(DEPS(1)+DEPS(2)+DEPS(4))PI(1)=SIG(1)+G2*DEPS(1)+VPI(2)=SIG(2)+G2*DEPS(2)+VPI(4)=SIG(4)+G2*DEPS(4)+VA01=PI(1)-PI(2)A02=PI(2)-PI(4)A03=PI(4)-PI(1)SEQ=(A01*A01+A02*A02+A03*A03)*.5D0GOTO(200,201,202,203),ITAU+1203 PI(6)=SIG(6)+G2*DEPS(6)*.5D0SEQ=SEQ+3.D0*PI(6)*PI(6)202 PI(5)=SIG(5)+G2*DEPS(5)*.5D0SEQ=SEQ+3.D0*PI(5)*PI(5)201 PI(3)=SIG(3)+G2*DEPS(3)*.5D0SEQ=SEQ+3.D0*PI(3)*PI(3)200 SEQ=DSQRT(SEQ)PRESS=(PI(1)+PI(2)+PI(4))/3.D0*ECR(1)=PRESSECR(2)=SEQ** cumulated strain*ECR(4)=ECR(4)+DEPS(1)ECR(5)=ECR(5)+DEPS(2)ECR(7)=ECR(7)+DEPS(4)GOTO(400,401,402,403),ITAU+1403 ECR(9)=ECR(9)+DEPS(6)402 ECR(8)=ECR(8)+DEPS(5)401 ECR(6)=ECR(6)+DEPS(3)400 CONTINUE**----- sound speed*CSON=CSGOTO(500,501,502),IPLANC+1500 CSON=CSON*T3*T3/T2501 CSON=CSON/(T1*T3)502 CSON=DSQRT(CSON)ECR(11)=CSON** principal stress*TENS(1,1)=PI(1)TENS(2,2)=PI(2)TENS(3,3)=PI(4)TENS(1,2)=PI(3)TENS(2,1)=PI(3)TENS(1,3)=PI(6)TENS(3,1)=PI(6)TENS(2,3)=PI(5)TENS(3,2)=PI(5)!--- call d3diag est remplace par eigen3CALL EIGEN3VALUE(TENS,DIAG)!! SIGMAX=MAX(DIAG(1),DIAG(2),DIAG(3)) inutile carD1>D2>D3SIGMAX=DIAG(1)* the value of psar is sometimes bigger than 1e38.* therefore, the value is used in an other unit by dividing withfact* only tension is consideredFACT = 1.D6SIGTD = 0.D0IF (SIGMAX > 0.D0) THENPSAR = ECR(3) + DT1 * (SIGMAX/FACT) ** CORRECR(3) = PSAR!fc following test is just to avoid too big numbers for curveplotting!fc IF (PSAR > 1.D38) THEN!fc CALL ERRMSS('GLAS','Value of ECR(3) too big')!fc!fcSTOP ' GLAS'ENDIFSIGTD = ((PSAR/(60.D0))**(1.D0/CORR))*FACTENDIFECR(10) = SIGTD** check for failure if needed*SELECT CASE (FAIL_CRIT)82

CASE (0) ! NO FAILURE CRITERIONCASE (1) ! VMISIF (SEQ >= FAIL_LIMIT_ELEM) THENECR(12) = 1.D0 ! FLAG THIS G.P. AS FAILEDENDIFCASE (2) ! PEPSTENS(1,1)=ECR(4)TENS(2,2)=ECR(5)TENS(3,3)=ECR(7)TENS(1,2)=ECR(6)TENS(2,1)=ECR(6)TENS(1,3)=ECR(9)TENS(3,1)=ECR(9)TENS(2,3)=ECR(8)TENS(3,2)=ECR(8)!--- call d3diag est remplace par eigen3CALL EIGEN3VALUE(TENS,DIAG)*--- pepsmax=max(diag(1),diag(2),diag(3)) inutile card1>d2>d3PEPSMAX=DIAG(1)IF (PEPSMAX >= FAIL_LIMIT_ELEM) THENECR(12) = 1.D0 ! FLAG THIS G.P. AS FAILEDENDIFCASE (3) ! PRESIF (PRESS>= FAIL_LIMIT_ELEM) THEN*pressure is defined as negativ for tensionECR(12) = 1.D0 ! FLAG THIS G.P. AS FAILEDENDIFCASE (4) ! PEPRTENS(1,1)=ECR(4)TENS(2,2)=ECR(5)TENS(3,3)=ECR(7)TENS(1,2)=ECR(6)TENS(2,1)=ECR(6)TENS(1,3)=ECR(9)TENS(3,1)=ECR(9)TENS(2,3)=ECR(8)TENS(3,2)=ECR(8)!--- call d3diag est remplace par eigen3CALL EIGEN3VALUE(TENS,DIAG)*--- pepsmax=max(diag(1),diag(2),diag(3))) inutile card1>d2>d3PEPSMAX=DIAG(1)IF (PEPSMAX >= FAIL_LIMIT_ELEM .AND. PRESS >=0.D0) THENECR(12) = 1.D0 ! FLAG THIS G.P. AS FAILEDELSEPEPSMAX = -HUGE(PEPSMAX)ENDIFCASE (5) ! PSAR INTERGAL OF THE PRINCIPALSTRESSIF (SIGTD >= FAIL_LIMIT_ELEM) THENECR(12) = 1.D0 ! FLAG THIS G.P. AS FAILEDENDIFCASE DEFAULTCALL ERRMSS ('SGDI', 'WRONG FAILURECRITERION!')STOP 'SGDI : WRONG FAILURE CRITERION'END SELECT990 IF ((FAIL_CRIT /= 0) .AND. (ECR(12) /= 0.D0)) THEN* failure. so, pi and ecr are set to 0SELECT CASE (ITAU)CASE (0)PI(1:4) = 0.D0CASE (1)PI(1:4) = 0.D0CASE (2)PI(1:5) = 0.D0CASE (3)PI(1:6) = 0.D0END SELECTECR(1:9) = 0.D0ENDIF** erosion (optional)*IF (DAMAGE_ELEM_GHOST) THENSELECT CASE (FAIL_CRIT)CASE (0) ! NO FAILURE CRITERIONCASE (1) ! VMISCALL TEST_FAILED_ELEM (IG, IGMAX, SEQ,FAIL_LIMIT_ELEM)CASE (2) ! PEPSCALL TEST_FAILED_ELEM (IG, IGMAX, PEPSMAX,FAIL_LIMIT_ELEM)CASE (3) ! PRESCALL TEST_FAILED_ELEM (IG, IGMAX, -PRESS,FAIL_LIMIT_ELEM)CASE (4) ! PEPRCALL TEST_FAILED_ELEM (IG, IGMAX, PEPSMAX,FAIL_LIMIT_ELEM)CASE (5) ! PSARCALL TEST_FAILED_ELEM (IG, IGMAX, SIGTD,FAIL_LIMIT_ELEM)END SELECTENDIF*RETURNEND SUBROUTINE GLAS*============================================END MODULE M_MATERIAL_GLASm_material_lsglMODULE M_MATERIAL_LSGL** material of type lsgl*USE M_MATERIALS_ARRAY*IMPLICIT NONESAVE*PRIVATEPUBLIC MAT_LSGL, LSGL*CONTAINS*===========================================SUBROUTINE MAT_LSGL(INUMLDC)** ------------------------------------------------------------------* larcher 03-08* material for laminated safety glass* ------------------------------------------------------------------** inumldc : numero (de la loi) associe explicitement* (mot-cle "loi") ou implicitement (=rang)* au materiau courant** organisation of newmat%matval:* matval(1) : masse volumique initiale* matval(2) : young's modulus* matval(3) : poisson's ratio* matval(4) : stress corrosion constant* matval(5) : chosen failure criterion83

* (0=none,1=vmis,2=peps,3=pres,4=pepr,5=psar)* matval(6) : chosen failure limit value* matval(7) : factor for the reduction of the tensilestresses* matval(8) : flag for 2d cracks*INCLUDE 'NONE.INC'*INCLUDE 'CARMA.INC'INCLUDE 'REDCOM.INC'INCLUDE 'POUBTX.INC'*INTEGER, INTENT(IN) :: INUMLDC** local variables*INTEGER, PARAMETER :: IFIX = 8INTEGER :: LENX*INTEGER, PARAMETER :: NMOT=IFIX, NMOTFA=5*CHARACTER*4 MOT(NMOT),MOTFAI(NMOTFA)CHARACTER*32 BLAFAIINTEGER KOPT(NMOT), I, IOP, IF1, IOP1REAL*8 YOUNG, EPS1, EPS, EPS2, EIM1, SIM1LOGICAL :: IMPRIM*DATA MOT/'RO ','YOUN','NU','CORR','FAIL','LIMI','REDU','CR2D'/DATA MOTFAI/'VMIS','PEPS','PRES','PEPR','PSAR'/*CHARACTER(32), PARAMETER :: NOM='LSGL :LAMINATED SAFETY GLASS'INTEGER, PARAMETER :: N_MSG = IFIX , LG_FMT =63CHARACTER(LG_FMT) :: GET_FMT(N_MSG)DATA GET_FMT(:) /1'DENSITY',2'YOUNG''S MODULUS',3'POISSON''S RATIO',4'STRESS CORROSION',5'FAILURE CRITERION',6'FAILURE LIMIT',7'FACTOR FOR TENSILE REDUCTION',8'FLAG FOR 2D CRACKS'/*BLAFAI='NOT DEFINED'*CALL CREATE_MATERIAL (IFIX, 0, 0)NEWMAT%NAME = NOMNEWMAT%TYPE = LG_FMTNEWMAT%NUMLDC = INUMLDCNEWMAT%LGECR = LGECR(NEWMAT%TYPE)NEWMAT%MATVAL(7)=0.0 ! DEFAULT VALUENEWMAT%MATVAL(8)=0.0 ! DEFAULT VALUEKOPT(:) = 0 ! INITIALIZE WHOLE ARRAY*11 CALL LIRMOT(MOT,NMOT,IOP)IF(IOP > 0) THENSELECT CASE (IOP)CASE (5) ! FAIL** "fail", read sub-keyword*CALL LIRMOT(MOTFAI,NMOTFA,IOP1)SELECT CASE (IOP1)CASE (1)** "vmis"*NEWMAT%MATVAL(5)=1.D0KOPT(5)=1BLAFAI='VON MISES'CASE (2)** "peps"*NEWMAT%MATVAL(5)=2.D0KOPT(5)=2BLAFAI='PRINCIPAL STRAIN'CASE (3)** "pres"*NEWMAT%MATVAL(5)=3.D0KOPT(5)=3BLAFAI='MINIMUM PRESSURE'CASE (4)** "pepr"*NEWMAT%MATVAL(5)=4.D0KOPT(5)=4BLAFAI='PRINCIPAL STRAIN + TENSION PRESS'CASE (5)** "psar"*NEWMAT%MATVAL(5)=5.D0KOPT(5)=5BLAFAI='INTEGRAL OF THE PRINCIPAL STRESS'CASE DEFAULTGO TO 9END SELECTCASE (8) !CR2DNEWMAT%MATVAL(8)=1.D0CASE DEFAULT** "ro" or "youn" or ... (but not "inte" nor "fail") : read value*CALL LIRE(3)NEWMAT%MATVAL(IOP)=DPRECKOPT(IOP)=1END SELECT*GO TO 11*ENDIF**----- donnees completes ? (1 a 6 indispensables)DO I=1,6IF(I==4) CYCLEIF(KOPT(I) == 0) GOTO 9END DOIF(NEWMAT%MATVAL(5)==5.D0.AND.KOPT(4)==0)GOTO 9**----- impressions ( debut )WRITE(BLABLA,1001)NEWMAT%NUMLDC,NEWMAT%NAMECALL MECTSG(BLABLA)IF(IMPRIM(8)) THENCALL MECVAL(GET_FMT(1),NEWMAT%MATVAL(1))84

CALL MECVAL(GET_FMT(2),NEWMAT%MATVAL(2))CALL MECVAL(GET_FMT(3),NEWMAT%MATVAL(3))CALL MECVAL(GET_FMT(4),NEWMAT%MATVAL(4))CALL MECTEX(GET_FMT(5) ,BLAFAI)CALLMECVAL(GET_FMT(6),NEWMAT%MATVAL(6))CALLMECVAL(GET_FMT(7),NEWMAT%MATVAL(7))IF(NINT(NEWMAT%MATVAL(8))==1) THENCALLMECVAL(GET_FMT(8),NEWMAT%MATVAL(8))ENDIFENDIFRETURN9 CONTINUE**--- the errorsWRITE(BLABLA,2001)CALL ERRMSS('MAT_LSGL',BLABLA)STOP ' MAT_GLAS'**IF FRANCAIS1001 FORMAT('LOI NUMERO',I5,' : ',A)2001 FORMAT('LA DIRECTIVE "LSGL" ESTINCOMPLETE')CELSE1001 FORMAT('LAW NUMBER',I5,' : ',A)2001 FORMAT('THE DIRECTIVE "LSGL" ISINCOMPLETE')CENDIF*END SUBROUTINE MAT_LSGL*=========================================SUBROUTINE LSGL(XMAT,DEPS,SIG,ECR,PI,CSON,IG,IGMAX)**-----------------------------------------------------------------------* larcher 04-08* 2d or 3d (also with zero normal stress) stress-strain law forelastic* materials (incremental form)* only for shell elements (sig_z=0)* several failure criteria specially with strain rate dependencyfor glass*-----------------------------------------------------------------------** xmat() : vector of material properties for this material (seemalsgl)* xmat(1) : masse volumique initiale* xmat(2) : young's modulus* xmat(3) : poisson's ratio* xmat(4) : stress corrosion constant* xmat(5) : chosen failure criterion* (0=none,1=vmis,2=peps,3=pres,4=pepr,5=psar)* xmat(6) : chosen failure limit value* xmat(7) : factor for the reduction of the tensile stresses* deps(1) --> deps1 : x-strain increment* deps(2) --> deps2 : y-strain increment* deps(3) --> dgam12 : xy-strain increment* deps(4) --> deps3 : z-strain increment* deps(5) --> dgam23 : yz-strain increment* deps(6) --> dgam13 : xz-strain increment* sig(1) --> sig1 : x-stress* sig(2) --> sig2 : y-stress* sig(3) --> tau12 : xy-stress* sig(4) --> sig3 : z-stress (=0)* sig(5) --> tau23 : yz-stress* sig(6) --> tau13 : xz-stress* ecr(1) --> ecr1 : current hydrostatic pressure (1/3(sx+sy+st))* ecr(2) --> ecr2 : current equivalent stress (von mises)* ecr(3) --> psar : area under the principal stress-time curve* between the current time and the last change ofsign of PRSIG* ecr(4) --> eps1 : cumulated x-strain* ecr(5) --> eps2 : cumulated y-strain* ecr(6) --> gam12 : cumulated xy-strain* ecr(7) --> eps3 : cumulated z-strain* ecr(8) --> gam23 : cumulated yz-strain* ecr(9) --> gam13 : cumulated xz-strain* ecr(10) --> lcos : last change of sign of princ stress (seeecr(3))* ecr(11) --> cson : sound speed* ecr(12) --> fail : failure flag (0=virgin gp, 1 = failed gp)* ecr(13) --> phi_cr : angle of the crack (>pi if two cracks)* pi() : vector of new stress components (same organization assig)* cson : sound speed* ig : current gauss point index for this element* igmax : total n. of gauss points for this element*USE M_FAILED_ELEMENTS ! FOR THE EROSION*IMPLICIT NONE*INCLUDE 'CONTRB.INC'INCLUDE 'COPT.INC'INCLUDE 'PILOT.INC'INCLUDE 'TEMPS.INC' ! DT1 : CURRENT TIME STEPSIZEINCLUDE 'TEMPX.INC' ! T = CURRENT TIME!!---- Variables Globales!REAL(8), INTENT(IN) :: XMAT(*), SIG(*)REAL(8), INTENT(OUT) :: PI(*), CSONREAL(8), INTENT(INOUT) :: DEPS(*), ECR(*)INTEGER, INTENT(IN) :: IG, IGMAX!!---- Variables locales!INTEGER :: FAIL_CRIT, I, FAIL_STATE, CALCREAL(8) :: G2,D,CS,AM,XNU,YMX,T1,T2,T3,PRESS,CORR,PSAR,SIGTD,& A01,A02,A03,SEQ,V,FAIL_LIMIT,PEPSMAX,SIGMAX,FACT,& PHI,PAR1,SIG1,SIG2,PARA_PI,STRAIN_HYD,EPS1,EPS2,& FAIL_VALUE, PI_T(3), STR(3), STR_T(3)LOGICAL :: CR2D*PARA_PI = 2.D0*ACOS(0.D0)IF(NINT(XMAT(8))==1) THENCR2D = .TRUE.ELSECR2D = .FALSE.ENDIFFAIL_STATE = NINT(ECR(12))** material properties*YMX=XMAT(2)XNU=XMAT(3)85

***CORR=XMAT(4)FAIL_CRIT = XMAT(5)FAIL_LIMIT = XMAT(6)T1=1.D0+XNUT2=1.D0-2.D0*XNUT3=1.D0-XNUCS=YMX/XMAT(1)D=XNU*YMX/(T1*T2)G2=YMX/T1DEPS(4)=-(SIG(4)+D*(DEPS(1)+DEPS(2)))/(G2+D)V=D*(DEPS(1)+DEPS(2)+DEPS(4))PI(1)=SIG(1)+G2*DEPS(1)+VPI(2)=SIG(2)+G2*DEPS(2)+VPI(4)=SIG(4)+G2*DEPS(4)+VA01=PI(1)-PI(2)A02=PI(2)-PI(4)A03=PI(4)-PI(1)SEQ=(A01*A01+A02*A02+A03*A03)*.5D0PI(6)=SIG(6)+G2*DEPS(6)*.5D0SEQ=SEQ+3.D0*PI(6)*PI(6)PI(5)=SIG(5)+G2*DEPS(5)*.5D0SEQ=SEQ+3.D0*PI(5)*PI(5)PI(3)=SIG(3)+G2*DEPS(3)*.5D0SEQ=SEQ+3.D0*PI(3)*PI(3)SEQ=DSQRT(SEQ)PRESS=(PI(1)+PI(2)+PI(4))/3.D0ECR(1)=PRESSECR(2)=SEQ**----- cumulated strain*ECR(4)=ECR(4)+DEPS(1)ECR(5)=ECR(5)+DEPS(2)ECR(7)=ECR(7)+DEPS(4)ECR(9)=ECR(9)+DEPS(6)ECR(8)=ECR(8)+DEPS(5)ECR(6)=ECR(6)+DEPS(3)STRAIN_HYD=(ECR(4)+ECR(5))/2.D0**----- sound speed*CSON=DSQRT(CS/(T1*T3))ECR(11)=CSON*SELECT CASE (FAIL_CRIT)CASE (0) ! NO FAILURE CRITERIONCALC = 0 !NO CALCULATION OF PRINCIPALSTRESSES / STRAINSCASE (1) ! VMISCALC = 0 !NO CALCULATION OF PRINCIPALSTRESSES / STRAINSCASE (2) ! PEPSCALC = 2 !PRINCIPAL STRAINCASE (3) ! PRESCALC = 0 !NO CALCULATION OF PRINCIPALSTRESSES / STRAINSCASE (4) ! PEPRCALC = 2 !PRINCIPAL STRAINCASE (5) ! PSAR INTERGAL OF THE PRINCIPALSTRESSCALC = 1 !NO CALCULATION OF PRINCIPALSTRESSES / STRAINSEND SELECT*PHI = 0.D0SIGMAX = 0.D0SELECT CASE (CALC)CASE(1) ! PRINCIPAL STRESSIF(CR2D) THENIF(FAIL_STATE/=0) THEN !ALREADY FAILEDCALL TURN_VALUE(PI,PI_T,ECR(13))SIGMAX = PI_T(1)ELSEIF((PI(1)-PI(2))/=0.D0)THENPHI = 0.5D0 * ATAN(2.D0 * PI(3)/(PI(1)-PI(2)))ENDIFIF(PHI= FAIL_LIMIT) THEN86

SELECT CASE (FAIL_STATE)CASE (0)FAIL_STATE = 1 ! FLAG THIS G.P. AS FAILED INONE DIRECTIONECR(13) = PHICALL TURN_VALUE(PI,PI_T,ECR(13))CASE (1)IF(CR2D) FAIL_STATE = 2 ! FLAG THIS G.P. ASFAILED IN BOTH DIRECTIONSEND SELECTENDIFCASE (2) ! PEPSIF (PEPSMAX >= FAIL_LIMIT) THENSELECT CASE (FAIL_STATE)CASE (0)FAIL_STATE = 1 ! FLAG THIS G.P. AS FAILED INONE DIRECTIONECR(13) = PHICALL TURN_VALUE(PI,PI_T,ECR(13))CASE (1)IF(CR2D) FAIL_STATE = 2 ! FLAG THIS G.P. ASFAILED IN BOTH DIRECTIONSEND SELECTENDIFCASE (3) ! PRESIF (PRESS>= FAIL_LIMIT) THEN*pressure is defined as negativ for tensionSELECT CASE (FAIL_STATE)CASE (0)FAIL_STATE = 1 ! FLAG THIS G.P. AS FAILED INONE DIRECTIONECR(13) = PHICALL TURN_VALUE(PI,PI_T,ECR(13))CASE (1)IF(CR2D) FAIL_STATE = 2 ! FLAG THIS G.P. ASFAILED IN BOTH DIRECTIONSEND SELECTENDIFCASE (4) ! PEPRIF (PEPSMAX >= FAIL_LIMIT .AND. PRESS >= 0.D0)THENSELECT CASE (FAIL_STATE)CASE (0)FAIL_STATE = 1 ! FLAG THIS G.P. AS FAILED INONE DIRECTIONECR(13) = PHICALL TURN_VALUE(PI,PI_T,ECR(13))CASE (1)IF(CR2D) FAIL_STATE = 2 ! FLAG THIS G.P. ASFAILED IN BOTH DIRECTIONSEND SELECTELSEPEPSMAX = -HUGE(PEPSMAX)ENDIFCASE (5) ! PSAR INTERGAL OF THE PRINCIPALSTRESSIF (SIGTD >= FAIL_LIMIT) THENSELECT CASE (FAIL_STATE)CASE (0)FAIL_STATE = 1 ! FLAG THIS G.P. AS FAILED INONE DIRECTIONECR(13) = PHICALL TURN_VALUE(PI,PI_T,ECR(13))CASE (1)IF(CR2D) FAIL_STATE = 2 ! FLAG THIS G.P. ASFAILED IN BOTH DIRECTIONSEND SELECTENDIFCASE DEFAULTCALL ERRMSS ('LSGL', 'WRONG FAILURECRITERION!')STOP 'LSGL : WRONG FAILURE CRITERION'END SELECTIF (FAIL_STATE /= 0) THENIF (STRAIN_HYD>=0.D0) THEN*hydrostatic strain is positive (tension) material reacts likerubbleIF(CR2D.AND.FAIL_STATE==1) THENPI_T(2)=0.D0 !PI_T(1) IS COMPRESSION,PI_T(2) TENSIONCALL TURN_VALUE(PI_T,PI,-ECR(13)) !TURNBACKWARDSELSEDO I=1,6PI(I)=PI(I)*XMAT(7)ENDDOENDIFENDIFIF((FAIL_STATE==2).OR.(FAIL_STATE==1.AND..NOT. CR2D))THENIF (DAMAGE_ELEM_GHOST) THENFAIL_LIMIT = 0.0FAIL_VALUE = 1.0IF(FAIL_CRIT>0) THENCALLTEST_FAILED_ELEM(IG,IGMAX,FAIL_VALUE,FAIL_LIMIT)ENDIFIF(IS_FAILED(IEL)) THENDO I=1,6PI(I)=0.D0ENDDOENDIFENDIFENDIFENDIFECR(12) = FAIL_STATE*RETURNEND SUBROUTINE LSGL*=========================================SUBROUTINE TURN_VALUE(TEN_IN,TEN_OUT,PHI)**-----------------------------------------------------------------------* larcher 04-08* turn stresses and strains*-----------------------------------------------------------------------*REAL(8), INTENT(IN) :: TEN_IN(3),PHIREAL(8), INTENT(OUT) :: TEN_OUT(3)TEN_OUT(1) = 0.5D0*(TEN_IN(1)+TEN_IN(2))+> 0.5D0*(TEN_IN(1)-TEN_IN(2))*COS(2.D0*PHI)+> TEN_IN(3)*SIN(2.D0*PHI)TEN_OUT(2) = 0.5D0*(TEN_IN(1)+TEN_IN(2))-> 0.5D0*(TEN_IN(1)-TEN_IN(2))*COS(2.D0*PHI)-> TEN_IN(3)*SIN(2.D0*PHI)TEN_OUT(3) = -0.5D0*(TEN_IN(1)->TEN_IN(2))*SIN(2.D0*PHI)+TEN_IN(3)*COS(2.D0*PHI)END SUBROUTINE TURN_VALUE*=============================================END MODULE M_MATERIAL_LSGL87

8.2 Sample Input Fileskraut2.dgibiOPTI echo 1;OPTI dime 3 elem tri3;den=0.04;DENS den;sizx = 1.40;sizz = 1.40;p0 = 0 0 0;x0 = sizx 0. 0.;x1 = sizx 0 sizz;z0 = 0. 0. sizz;*volume of the airsur = p0 droi x0 tran z0 coul bleu;sur1 = sur coul roug;lbq = p0 d z0 d x1 d x0 d;geom_new = sur et lbq et sur1;elim geom_new;TASS geom_new;OPTI sauv form 'kraut2.msh';sauv form geom_new;*list (nbno geom_new);list (nbel(geom_new));fin;kraut6_50prokraut6 - failure with glas, PSAR, DKT3ECHOCONV winTRID LAGR FAIL 0.0CAST FORM 'kraut2.msh' geon_newDIMEPT6L 30246 DKT3 9800 CL3T 9800 ZONE 3FORC 100TABL 1 3PRES 33 26TERMGEOMDKT3 surCL3T sur1TERMCOMP EPAI 9.63E-3 LECT sur TERMMATE GLAS RO 2500 YOUN 7E10 NU 0.23 CORR 16.0FAIL PSAR LIMI 84.8e6LECT sur TERMIMPE AIRB X 0.7 Y 60 Z 0.7 MASS 10 TINT -159.7e-3LECT sur1 TERM* Z = 40 (40/1)* Z = 32 (15/0.1)* Z = 7 (15/10)LINK COUP FREQ 1BLOQ 2 LECT lbq TERMBLOQ 123 LECT p0 TERMBLOQ 3 LECT x0 TERMECRI FICH ALIC TFREQ 4e-4FICH ALIC TEMP TFREQ 1e-5ELEM LECT 2500 776 TERMPOIN LECT 1264 TERMOPTI NOTEcsta 0.5 log 1CALCUL TINI 0. TEND 64D-3*====================================PLAYCAME 1 EYE 5.00000E-01 -4.30116E+00 7.00000E-01! Q 7.07107E-01 7.07107E-01 0.00000E+000.00000E+00VIEW 0.00000E+00 1.00000E+00 2.05102E-10RIGH 1.00000E+00 0.00000E+00 0.00000E+00UP 0.00000E+00 -2.05102E-10 1.00000E+00FOV 2.48819E+01SCEN GEOM NAVI FREEFACE SBACPOIN SPHPISO FILL FIEL ECRO 10 !DEPL 3!SUPP LECT stru TERMTEXT ISCACOLO PAPELIMA ONsler cam1 1 nfra 1trac offs fich avi nocl nfto 160 fps 5 kfre 10 comp -1obje NFAI lect sur term rend!trac offs fich avi cont noclrendtfreq 4e-4 freq 0gotr loop 158 offs fich avi cont noclobje NFAI lect sur term rendgotrac offs fich avi contobje NFAI lect sur term rendENDPLAY*====================================SUITPost-treatment (time curves from alice temps file)ECHORESU ALIC TEMP GARD PSCRSORT GRAPAXTE 1.0 'Time [s]'*COUR 1 'elem_330' ECRO COMP 1 ELEM LECT 2500 TERMtrac 1 TEXT axes 1.0 'Pressure [Pa]'COUR 2 'elem_330' ECRO COMP 11 ELEM LECT 776 TERMtrac 2 TEXT axes 1.0 'Main strain'COUR 3 'node_2564' DEPL COMP 3 NOEU LECT 1264TERMtrac 3 TEXT axes 1.0 'displacement'COUR 4 'elem_330' ECRO COMP 10 ELEM LECT 776 TERMtrac 4 TEXT axes 1.0 'dam'finemi_ls25.dgibiOPTI echo 1;OPTI dime 3 elem tet4;den=0.0125;DENS den;sizx = 1.1;sizy = 0.9;rand = 0.05;b11 = rand rand 0;b12 = (sizx-rand) rand 0;b13 = (sizx-rand) (sizy-rand) 0;b14 = rand (sizy-rand) 0;li1 = b11 d b12 d b13 d b14 d;a_airb = surf li1 plan;b31 = 0 0 0;b32 = sizx 0 0;li3 = b31 d b32 d b12 d b11 d;a3 = surf li3 plan;88

41 = sizx sizy 0;li4 = b32 d b41 d b13 d b12 d;a4 = surf li4 plan;b51 = 0 sizy 0;li5 = b41 d b51 d b14 d b13 d;a5 = surf li5 plan;li6 = b31 d b11 d b14 d b51 d;a6 = surf li6 plan;a_rand = a3 et a4 et a5 et a6;a_glass1 = a_airb et a_rand;p1 = 0 0 0.004;p2 = 0 0 -0.004;v1 = a_rand volu 'TRAN' p1;v1 = v1 et (a_rand volu 'TRAN' p2);ch1 = ((sizx+rand)/2.) ((sizy+rand)/2.) 1.8;pcent = ((sizx+rand)/2.) ((sizy+rand)/2.) 0;pdis = a_glass1 poin 'PROC' pcent;edis1 = a_glass1 ELEM CONTENANT pdis;a_v1 = v1 enve;kod1 = faux;REPE I0 (NBEL (a_v1 ELEM TRI3));xx yy zz = coor (bary (a_v1 ELEM TRI3 &I0));SI ( zz ega 0.004 0.001);si (kod1);bound=bound et (a_v1 ELEM TRI3 &I0);sinon; bound = a_v1 ELEM TRI3 &I0;kod1 = vrai;fins;FINS;SI ( zz ega -0.004 0.001);si (kod1);bound=bound et (a_v1 ELEM TRI3 &I0);sinon; bound = a_v1 ELEM TRI3 &I0;kod1 = vrai;fins;FINS;FIN I0;modell = v1 et a_glass1 et a_airb et pdis etedis1 et ch1 et bound;elim modell;TASS modell;OPTI sauv form 'emi_ls25.msh';sauv form modell;emi_ls25.epxemi_ls25 with model lsgl$ECHOCAST 'emi_ls25.msh' modellTRID LAGR FAIL 1.0OPTI TOLC 1e-1$DIMEPT6L 12000 ZONE 3PR6 5708 CL3T 14808 COQI 14808ECRO 3373652MNTI 102NGPZ 5TERM$GEOMPR6 v1COQI a_glass1CL3T a_airbTERM$COMPEPAI 0.0075 LECT a_glass1 TERMSAND 3FRAC 0.4 0.2 0.4NGPZ 2 1 2LECT a_glass1 termMATELSGL RO 2500 YOUN 7E10 NU 0.23 CORR 16.0 REDU0.0FAIL PEPR LIMI 0.0012LECT a_glass1 TERMlaye lect 1 3 termVM23 RO 1100. YOUNG 3E6 NU 0.46 ELAS 3.45E9TRAC 1 3.45E9 15LECT a_glass1 TERMlaye lect 2 termVM23 RO 2770. YOUNG 3.5e6 NU 0.42 ELAS 3.45E9TRAC 1 3.45E9 0.15LECT v1 TERMIMPE AIRB NODE LECT ch1 TERM CONF 1 MASS 0.09TAUTLECT a_airb TERMLINK BLOQ 123 boundECRI FICH ALIC tfreq 1e-4FICH ALIC TEMP tfreq 1e-5POIN LECT pdis TERMELEM LECT 4148 1628 1698 edis1 TERM$OPTI NOTE LOG 1$CALC TINI 0 TEND 10e-3*======================================SUITPost-treatment (time curves from alice temps file)ECHORESU ALIC TEMP GARD PSCRSORT GRAPAXTE 1.0 'Time [s]'COUR 99 'dz_pdis' DEPL COMP 3 NOEU LECT pdis TERMtrac 99 text axes 1.0 'DISPL. [M]'*======================================SUITemi12_aviECHOCONV WINRESU ALIC GARD PSCROPTI PRIN*SORT VISU NSTO 1PLAYCAME 1 EYE 5.00000E-01 4.00000E-01 6.42268E+00! Q 1.00000E+00 0.00000E+00 0.00000E+000.00000E+00VIEW 0.00000E+00 0.00000E+00 -1.00000E+00RIGH 1.00000E+00 0.00000E+00 0.00000E+00UP 0.00000E+00 1.00000E+00 0.00000E+00FOV 1.08819E+0189

SCEN GEOM NAVI FREEFACE SBACPOIN SPHPISO FILL FIEL ECRO 12 SCAL A14TEXT ISCACOLO PAPEsler cam1 1 nfra 1freq 100gotrac offs fich bmpobje lect a_glass1 term rendENDPLAYFINhooper1.dgibiOPTI echo 1;OPTI dime 3 elem tet4;den=0.02;DENS den;sizx = 1.5;sizy = 1.2;rand = 0.02;b11 = rand rand 0;b12 = (sizx-rand) rand 0;b13 = (sizx-rand) (sizy-rand) 0;b14 = rand (sizy-rand) 0;li1 = b11 d b12 d b13 d b14 d;a_airb = surf li1 plan;b31 = 0 0 0;b32 = sizx 0 0;li3 = b31 d b32 d b12 d b11 d;a3 = surf li3 plan;b41 = sizx sizy 0;li4 = b32 d b41 d b13 d b12 d;a4 = surf li4 plan;b51 = 0 sizy 0;li5 = b41 d b51 d b14 d b13 d;a5 = surf li5 plan;li6 = b31 d b11 d b14 d b51 d;a6 = surf li6 plan;a_rand = a3 et a4 et a5 et a6;a_glass1 = a_airb et a_rand;a_airb = a_glass1 coul roug;p1 = 0 0 -0.006;v1 = a_rand volu 'TRAN' p1;ch1 = ((sizx+rand)/2.) ((sizy+rand)/2.) 11;pcent = ((sizx+rand)/2.) ((sizy+rand)/2.) 0;pdis = a_glass1 poin 'PROC' pcent;edis1 = a_glass1 ELEM CONTENANT pdis;a_v1 = v1 enve;kod1 = faux;REPE I0 (NBEL (a_v1 ELEM TRI3));xx yy zz = coor (bary (a_v1 ELEM TRI3 &I0));SI ( zz ega -0.006 0.001);si (kod1);bound=bound et (a_v1 ELEM TRI3 &I0);sinon; bound = a_v1 ELEM TRI3 &I0;kod1 = vrai;fins;FINS;FIN I0;modell = v1 et a_glass1 et a_airb et pdis etedis1 et ch1 et bound;elim modell;TASS modell;OPTI sauv form 'hooper1.msh';sauv form modell;hooper10.epxhooper1 with model lsgl$ECHOCAST 'hooper1.msh' modellTRID LAGR FAIL 1.0OPTI TOLC 1e-1$DIMEPT6L 12000 ZONE 3PR6 5708 CL3T 14808 DKT3 14808ECRO 3373652MNTI 102NGPZ 5TERM$GEOMPR6 v1DKT3 a_glass1CL3T a_airbTERM$COMPEPAI 0.0075 LECT a_glass1 TERMSAND 3FRAC 0.4 0.2 0.4NGPZ 2 1 2LECT a_glass1 termMATELSGL RO 2500 YOUN 7E10 NU 0.23 CORR 16.0 REDU 0.0FAIL PEPR LIMI 0.0012LECT a_glass1 TERMlaye lect 1 3 termVM23 RO 1100. YOUNG 2.2e8 NU 0.495 ELAS 11E6FAIL VMIS LIMI 2.8e7TRAC 3 11e6 0.05 30e6 2.25 40e6 3.5LECT a_glass1 TERMlaye lect 2 termVM23 RO 2770. YOUNG 3.5e6 NU 0.495 ELAS 3.45E9TRAC 1 3.45E9 0.15LECT v1 TERMIMPE AIRB X 0.77 Y 0.62 Z 10 CONF 4 MASS 18 TAUTLECT a_airb TERMLINK BLOQ 123 boundECRI FICH ALIC tfreq 2e-4FICH ALIC TEMP tfreq 5e-5POIN LECT pdis TERMELEM LECT edis1 TERM$OPTI NOTE LOG 1$CALC TINI 0 TEND 20e-3*=============================================SUITECHO90

*RESU ALIC TEMP GARD PSCRSORT GRAPAXTE 1.0 'Time [s]'COUR 1 'sig_edis' ECRO COMP 1 ELEM LECT edis1 TERMCOUR 2 'dz_pdis' DEPL COMP 3 NOEU LECT pdis TERMtrac 1 axes 1.0 'SIG'trac 2 text axes 1.0 'DISPL. [M]'*=============================================SUITPost-treatmentECHOCONV WINRESU ALIC GARD PSCROPTI PRIN*SORT VISU NSTO 1PLAYCAME 1 EYE 7.50000E-01 6.00000E-01 4.80234E+00! Q 1.00000E+00 0.00000E+00 0.00000E+000.00000E+00VIEW 0.00000E+00 0.00000E+00 -1.00000E+00RIGH 1.00000E+00 0.00000E+00 0.00000E+00UP 0.00000E+00 1.00000E+00 0.00000E+00FOV 2.08819E+01SCEN GEOM NAVI FREEFACE SBACPOIN SPHPISO FILL FIEL ECRO 2 GAUZ 3 SCAL A14COLO PAPEsler cam1 1 nfra 1trac offs fich bmpobje NFAI lect a_glass1 term rendfreq 1gotr loop 198 offs fich bmpobje NFAI lect a_glass1 term rendgotrac offs fich bmpobje NFAI lect a_glass1 term rendENDPLAYFIN91

European CommissionJoint Research Centre – Institute for the Protection and Security of the CitizenTitle: Simulation of Several Glass Types Loaded by Air Blast WavesAuthor: Martin Larcher2008 – nnnn pp. – 21.0 x 29.7 cmAbstractThis work is being conducted in the framework of the project RAILPROTECT, which deals with the security andsafety of rail transport against terrorist attacks. The bombing threat is only considered, and focus is placed onpredicting the effects of explosions in railway and metro stations and rolling stock and on assessing thevulnerability of such structures.The project is based on numerical simulations, which are carried out with the explicit Finite Element CodeEUROPLEXUS that is written for the calculation of fast dynamic fluid-structure interactions. This program hasbeen developed in a collaboration of the French Commissariat à l'Energie Atomique (CEN Saclay) and the JointResearch Centre of the European Commission (JRC Ispra).The aim of this project is to calculate the behaviour of structures loaded by air blast waves. The façades ofrailway stations as well as large parts of the lightweight structures of trains are often built from glass. Incomparison to the mechanical structure of a station or of a train, the glass is much more fragile and fails muchearlier since the thickness of the glass is mostly very small. The failed parts of a façade or of a train results inrelease areas for the air blast pressure. The behaviour of the glass should therefore be taken into account forthe simulations. This technical note presents several approaches about different glass types loaded by air blastwaves.92

The mission of the JRC is to provide customer-driven scientific and technical supportfor the conception, development, implementation and monitoring of EU policies. As aservice of the European Commission, the JRC functions as a reference centre ofscience and technology for the Union. Close to the policy-making process, it servesthe common interest of the Member States, while being independent of specialinterests, whether private or national.93