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Adaptive numerical analysis in primal elastoplasticity with hardening. (English) Zbl 0956.74049

Summary: The quasi-static viscoplastic respectively elastoplastic evolution problem with isotropic or kinematic hardening is considered with emphasis on optimal convergence and adapted mesh-refining in the spatial discretization. Within one time-step of an implicit time-discretization, the finite element method leads to a minimisation problem for non-smooth convex functions on discrete subspaces. For piecewise constant respectively affine ansatz functions, the stress respectively displacement approximations are experimentally and theoretically shown to converge linearly. An a posteriori error estimate then justifies an automatic adaptive mesh-refining algorithm. Numerical examples support the superiority of the adapted mesh.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
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