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

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Overview of Material Descriptions We can discriminate amongst the following major classes of material behavior Elastic, linear or nonlinear Hyperelastic Hypoelastic Elastoplastic Creep Viscoplastic Institute of Structural Engineering Method of Finite Elements II 4
Solution Flowchart General Solution process in incremental nonlinear FE Known Solution at t: Stresses t σ, strains t ε, Internal material parameters t κ Known Quantities at iterations i- 1 : Nodal Displacements at first Iteration: and hence Element strains t+Δt ε i−1 t+Δt U i−1 Calculate at t+ Δt: t+Δt Stresses σ i−1 Repat till Convergence Tangent stress strain matrix C i−1 Internal material parameters t+Δt κ i−1 • Elastic Analysis: directly obtain t+Δt t+Δt σ i−1 , C i−1 from ε i−1 • Inelastic Analysis: Integrate to get t+Δt σ i−1 t t+Δti−1 = σ + ∫ dσ t Calculate: Incremental Displacement Vector ΔU i: t+Δt K i−1 ΔU i = Then, t+Δt R − t+Δt F i−1 t+Δt t+Δt U i = U i−1 + ΔU i Institute of Structural Engineering Method of Finite Elements II 5
Page 1 and 2: The Finite Element Method for the A
Page 3: Constitutive Relations It is necess
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 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

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