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

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Viscoplasticity Viscoplasticity describes the rate-dependent inelastic behavior of solids. Rate-dependence in this context means that the deformation of the material depends on the rate at which loads are applied[1]. The inelastic behavior that is the subject of viscoplasticity is plastic deformation which means that the material undergoes unrecoverable deformations when a load level is reached. Rate-dependent plasticity is important for transient plasticity calculations. The main difference between rate-independent plastic and viscoplastic material models is that the latter exhibit not only permanent deformations after the application of loads but continue to undergo a creep flow as a function of time under the influence of the applied load. Typical examples of such behavior are Polymers and Metals Institute of Structural Engineering Method of Finite Elements II 30
Viscoplasticity The elastic response of viscoplastic materials can be represented in one-dimension by Hookean spring elements. Rate-dependence can be represented by nonlinear dashpot elements. Plasticity can be accounted for by adding sliding frictional elements. In the figure E is the modulus of elasticity, λ is the viscosity parameter and N is a power-law type parameter that represents non-linear dashpot σ = λ dɛ 1/N . The sliding element can dt have a yield stress (σy) that is strain rate dependent, or even constant, as shown in Figure (c). Institute of Structural Engineering Method of Finite Elements II 31
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 and 20: Hyperelastic Material Hyperelastic
Page 21 and 22: Inelasticity Elastoplasticity, Cree
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: Relaxation A relaxation test is def
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

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