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Adaptive finite element methods for a class of evolution problems in viscoplasticity. (English) Zbl 0612.73072

Adaptive finite element procedures are presented for the analysis of broad class of two-dimensional problems in viscoplasticity which involve internal state variables. Several a posteriori error estimates are developed and used as a basis for refinements of meshes of triangular and quadrilateral elements. Algorithms are presented which reduce the computational complexity of the adaptive process and provide for the use of arbitrary local estimates of the approximation error. The results of numerical experiments are given which illustrate the effectiveness of the adaptive algorithms and various error indicators.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
74H99 Dynamical problems in solid mechanics
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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