Inexact Newton solvers in plasticity: theory and experiments

Abstract

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An Adaptive Least‐Squares Mixed Finite Element Method for Elasto‐Plasticity

“…where homogeneous boundary conditions are imposed. The solution of (2.8) for σ : Ω → IR 3×3 are then sought in σ N + H Γ N (div, Ω) 3 , where σ N ∈ H(div, Ω) 3 satisfies the boundary conditions σ N • n = g on Γ N . In connection with the incremental formulation (2.8), g stands for the increment of the boundary traction.…”

“…In connection with the incremental formulation (2.8), g stands for the increment of the boundary traction. The solution space for u : 3 . For the case of von Mises plasticity with isotropic hardening, the stress response is given by…”

“…The corresponding least-squares formulation consists in minimizing (2.14) among all suitable (σ, u) ∈ H(div, Ω) 3 × H 1 (Ω) 3 . More precisely, our aim is to find 3 . For hardening laws which satisfy (2.12), the well-posedness of the system (2.8) is studied in [15,Section 8].…”

“…Even earlier, several error indicators were investigated about their suitability for problems of elastoplasticity from an engineering point of view in [4]. The solution of the nonlinear algebraic systems associated with finite element discretizations of elasto-plastic models was the subject of [3], [6] and [24]. As in [24], multigrid methods were applied in [16] to the solution of elasto-plastic deformation models discretized by finite elements.…”

Multigrid methods for Prandtl-Reuss plasticity

“…The non-linear solution process is defined by elastoplastic moduli C(ε( u), σ, q). In general, there are many possibilities for defining suitable tangent operators for obtaining a conver-gent non-linear process (see [4] for a comparison of different non-linear approaches). Since the underlying problem is convex, in general global convergence can be obtained by appropriate damping (this is proved for the consistent elastoplastic moduli in [2]).…”