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5.1.2. Aluminum Foam Modeling Figure 5. 2. Effective plastic stress-stain curve. Several foam models are available in LS-DYNA explicit finite element simulation program for Al closed cell foams. These models are Mat-26 Honeycomb model (Hanssen, et al. 2002, Meguid, et al. 2004b, Reyes, et al. 2004, Santosa and Wierzbicki 1998a), Mat-63 Crushable foam model (Mamalis, et al. 2008, Wang, et al. 2005), Mat-126 Modified Honeycomb model,(Altenhof, et al. 2002, Hanssen, et al. 2000c) Mat-154 Desphande and Fleck foam model(Hanssen, et al. 2006, Zhang and Cheng 2007), Among the models listed above, the most widely used foam model namely Deshpande and Fleck foam model was used to simulate the foam filler deformation behavior in the present study. The schematic of honeycomb material geometrical model is shown in Figure 5.3. Honeycomb material model is essentially anisotropic when 84
considered in axial and transverse directions; therefore, material parameters are required to be determined separately for each direction. Figure 5. 3. Schematic of the honeycomb structure and tension, compression and shear behavior. . The material parameters of the honeycomb model are listed below (Hallquist 2006), E, Young modulus for the fully compacted material, , Poisson’s ratio for the compacted material, LCA, load curve for aa vs. volumetric strain, LCB, load curve for bb vs. volumetric strain; LCC, load curve for cc vs. volumetric strain, LCS, load curve for shear stress vs. volumetric strain, , relative volume at which honeycomb is fully compacted, , elastic modulus in uncompressed condition, , elastic modulus in uncompressed condition, , elastic modulus in uncompressed condition, , elastic shear modulus in uncompressed condition, , elastic shear modulus in uncompressed condition, , elastic shear modulus in uncompressed condition, 85
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OPTIMIZATION OF THE AXIAL CRUSHING
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ACKNOWLEDGEMENTS My PhD quest has b
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ÖZET KAPALI HÜCRELİ ALUMİNYUM K
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CHAPTER 4 EXPERIMENTAL DETAILS ....
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CHAPTER 8 ALUMINUM CRASH BOX OPTIMI
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Figure 3.7. Simulations of the defo
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Figure 4.9. Dimensions of tensile t
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Figure 6.21. Sequential deformation
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Figure 7.20. Sequential deformation
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LIST OF TABLES Table Page Table 4.1
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Figure 1. 1. The body in white stru
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Figure 1. 4. Commercial crash boxes
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CHAPTER 2 AL CLOSED CELL FOAMS: PRO
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The processing methods and mechanic
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Figure 2. 5 The preferred particle
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Figure 2. 8. Typical cellular struc
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Figure 2. 10. Manufacturing cost of
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Figure 2. 12. Laser assisted foamed
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Figure 2.16. Shear strength, normal
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Figure 2. 19. Yield strength vs. re
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Figure 2. 21. Unit cell geometry an
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Figure 2. 24. Load-displacement cur
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Figure 2. 26. The photographs of a
Page 51 and 52: CHAPTER 3 CRUSHING BEHAVIOR OF TUBU
Page 53 and 54: Figure 3.2. Diamond deformation mod
Page 57 and 58: deformation mode transition from ax
Page 59 and 60: Figure 3.8. Energy absorption of qu
Page 61: (a) (c) Figure 3.10. Deformation mo
Page 65 and 66: (a) (b) Figure 3.13. a) Schematic o
Page 67 and 68: (a) (b) (c) Figure 3.15. a) Load-di
Page 72 and 73: Figure 3.18. The crush terminology.
Page 75 and 76: The quasi-static compression behavi
Page 77 and 78: Figure 3.22. The variation of speci
Page 79 and 80: Figure 3.24. Deformation modes of e
Page 81 and 82: Figure 3.27. SEA values of empty an
Page 83 and 84: Figure 3.29. (cont.) 3.5. Motivatio
Page 85 and 86: CHAPTER 4 EXPERIMENTAL DETAILS 4.1.
Page 87 and 88: (a) (b) Figure 4.3.Pictures of a) f
Page 89 and 90: oxes are shown in Figure 4.6. The l
Page 91 and 92: Figure 4.7. The method of trigger m
Page 93 and 94: 4.4. Compression Tests of Crash Box
Page 95 and 96: 4.5.2. Uniaxial Compression Testing
Page 97 and 98: Table 4.1 (Cont.) G1 T3 F2 G1T3F2 3
Page 99 and 100: Table 4.2 (Cont.) G1 T2.5 WP F2 G1T
Page 101: CHAPTER 5 SIMULATION AND OPTIMIZATI
Page 109 and 110: were constrained. Since the width o
Page 116 and 117: 5.4. The Crashworthiness Optimizati
Page 118 and 119: great effect on the crushing behavi
Page 120: CHAPTER 6 EXPERIMENTAL RESULTS 6.1.
Page 124 and 125: Figure 6.3.Tensile stress-strain cu
Page 126 and 127: (a) (b) Figure 6.5. Sequential defo
Page 128 and 129: plate (Figure 6(b)). The trigger is
Page 130 and 131: (a) (b) Figure 6.9. Deformation seq
Page 132 and 133: Figure 6.12. Sequential deformation
Page 138 and 139: Figure 6.18. (cont.) (c) (a) (b) Fi
Page 140 and 141: Figure 6.20.(cont.). (b) (c) 6.5.4.
Page 142 and 143: Figure 6.21.(cont.) (b) (c) 122
Page 144 and 145: Figure 6.22.(cont.) (c) Figure 6.23
Page 146 and 147: Figure 6.24.(Cont.) (b) (c) (a) Fig
Page 148 and 149: Figure 6.26.(cont.) (b) (c) 6.6. Dy
Page 150 and 151: Figure 6.27. (cont.) (b) (c) 130
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CHAPTER 7 MODELING RESULTS OF FOAM,
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experimental tensile stress-strain
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significant effect of weld seem ope
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Figure 7.7. Deformation photo of fi
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Figure 7.11. Deformation photos of
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(a) (b) (c) Figure 7.14. Load-displ
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7.4. Simulation of Empty and Partia
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Figure 7.16. (cont.) (c) (a) Figure
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(a) (b) Figure 7.18. Sequential def
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Figure 7.19. (cont.) (b) (c) 150
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Figure 7.20. (cont.) (c) (a) Figure
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(a) (b) Figure 7.26. Experimental a
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The constructed response surface of
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Table 8.1. R 2 , Radj 2 and RMSE va
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(a) (b) Figure 8.7. Response surfac
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an empty tube wall thickness higher
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where, K is a dimensionless constan
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The dynamic simulation and analytic
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Figure 9.4. (cont.) (c) (d) Figure
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Figure 9.6. (cont.) (c) (d) (a) Fig
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Equation 9.7 can also be rewritten
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(a) (b) Figure 9.10. Energy-absorbi
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Figure 9.11. (cont.) (d) The variat
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foam filling were evaluated. The re
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13. The interaction between foam fi
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Arora, J. S.,2004,Introduction to O
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Dannemann, K. A. and Lankford, J.,
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Hall, I. W., Guden, M. and Yu, C. J
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Kim, D-K. and Lee, S., 1999, Impact
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Mamalis, A. G., Manolakos, D. E., I
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Pugsley, A. G. and Macaulay, M., 19
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T. Miyoshi, M. Itoh S. Akiyama A. K
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Zhao, H., Elnasri, I. and Girard, Y
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