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

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Notation Main Stress - Strain pairs: Material Nonlinearity (small deformations) Engineering Stress σ Engineering Strain ε TL formulation (large deformations) 2nd Piola-Kirchhoff Stress S Green-Lagrange Strain ɛ UL formulation (large deformations) Cauchy Stress τ Almansi Strain ɛ A Institute of Structural Engineering Method of Finite Elements II 6
Elastic Material For an elastic material the stress is a function of strain only The stress path is the same both in loading and unloading Linear Elastic The elasticity (constitutive) tensor components, C ijrs are constant Nonlinear Elastic The elasticity (constitutive) tensor components, C ijrs are a function of strain Example: Almost all materials under small stress σ ε Institute of Structural Engineering Method of Finite Elements II 7
Page 1 and 2: The Finite Element Method for the A
Page 3 and 4: Constitutive Relations It is necess
Page 5: Solution Flowchart General Solution
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 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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