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

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Elastoplasticity Response for cyclic loading Isotropic hardening: the yield stress is higher as the cyclic loading progresses Kinematic hardening: the difference between unloading stress and new yield stress in the opposite direction of loading is constant and equal to 2σ y. Figure: isotropic hardening in tension Figure: kinematic hardening Institute of Structural Engineering Method of Finite Elements II 26
Thermoelastoplasticity and Creep This behavior exhibits the time effect of increasing strains under constant loads or decreasing stress under constant deformations (relaxation) Typical examples of such behavior are metals at high temperatures The thermal strain(ɛ = α∆T ) and the creep strain now enter the formulation of the stress strain relationships. Creep Creep is the tendency of a solid material to slowly move or deform permanently under constant stresses. Creep tests measure the strain response due to a constant stress. The classical creep curve represents the evolution of strain as a function of time in a material subjected to uniaxial stress at a constant temperature. The creep test, for instance, is performed by applying a constant force/stress and analyzing the strain response of the system. In general, this curve usually shows three phases or periods of behavior. Institute of Structural Engineering Method of Finite Elements II 27
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: Elastoplasticity Isotropic & Kinema
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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