The Finite Element Method for the Analysis of Non-Linear and ...

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Hypoelastic Material In this case, stress increments are calculated from strain increments dσ ij = C ijrs dɛ rs The material moduli C ijrs are defined as functions of stress strain fracture criteria loading and unloading parameters maximum strains reached and so on Example Concrete models (*Hypoelasticity is not an elastic type of behavior in the sense that it does not exhibit path independence) Institute of Structural Engineering Method of Finite Elements II 20
Inelasticity Elastoplasticity, Creep and Viscoplasticity are types of Inelastic behavior Elastic behavior ⇒ stresses can be directly calculated from the strain Inelastic behavior ⇒ the stress at time t depends on the stress strain history In the incremental analysis of inelastic response we had three main scenarios Small displacements-rotations / small strains ⇒ use linear elastic solution, engineering stress and strain measures Large displacements-rotations / small strains ⇒ use TL formulation by substituting the appropriate stress - strain measures (PK2, Green-Lagrange) in the place of the engineering stress and strain measures Large displacements-rotations / large strains ⇒ use either TL or UL formulation, more complex constitutive laws Institute of Structural Engineering Method of Finite Elements II 21
Page 1 and 2: The Finite Element Method for the A
Page 3 and 4: Constitutive Relations It is necess
Page 5 and 6: Solution Flowchart General Solution
Page 7 and 8: Elastic Material For an elastic mat
Page 9 and 10: Elastic Material Important Note “
Page 11 and 12: Example Consider the four node elem
Page 13 and 14: Example Therefore, we ultimately ha
Page 15 and 16: Example Then, the Cauchy stress at
Page 17 and 18: Example The Jaumann stress is conne
Page 19: Hyperelastic Material Hyperelastic
Page 23 and 24: Elastoplasticity The strain and str
Page 25 and 26: Elastoplasticity Isotropic & Kinema
Page 27 and 28: Thermoelastoplasticity and Creep Th
Page 29 and 30: Relaxation A relaxation test is def
Page 31 and 32: Viscoplasticity The elastic respons
Page 33 and 34: NL FE Special Considerations - The
Page 35 and 36: Contact Conditions Usual term Cont
Page 37 and 38: Definitions used in Contact Analysi
Page 39 and 40: Contact Analysis-Interface Conditio
Page 41 and 42: Contact Analysis Complexities In th

The Finite Element Method for the Analysis of Non-Linear and ...

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