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

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Elastoplasticity In this formulation we encounter a linearly elastic behavior until yield and usually a gardening post yield behavior Examples Metals, soild and Rocks when subjected to high stresses Institute of Structural Engineering Method of Finite Elements II 22
Elastoplasticity The strain and stress increments are given by: dɛ rs = dɛ E rs + dɛ P rs dσ ij = C E ijrs (dɛ rs − dɛ P rs) where C E ijrs are the components of the elastic constitutive tensor and dɛ rs, dɛ E rs, dɛ P rs are the components of the total strain increment. To calculate the plastic strains we use the following three properties: Yield Function f y(σ, ɛ P ) f y < 0 ⇒ Elastic behavior f y = 0 ⇒ Plastic behavior f y > 0 ⇒ Inadmissible Flow rule The yield function is used in the flow rule in order to obtain the plastic strain increments λ is a scalar to be determined dɛ P ij = λ ∂fy ∂σ ij Hardening rule This specifies how the yield function is modified during plastic flow Institute of Structural Engineering Method of Finite Elements II 23
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: Inelasticity Elastoplasticity, Cree
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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