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A frictionless contact problem for elastic-viscoplastic materials with normal compliance and damage. (English) Zbl 1042.74039
Summary: We study a quasistatic frictionless contact problem with normal compliance and damage for elastic-viscoplastic bodies. The mechanical damage of the material, caused by excessive stress or strain, is described by a damage function whose evolution is modelled by an inclusion of parabolic type. We provide a variational formulation for the mechanical problem and sketch a proof of the existence of a unique weak solution to the model. We then introduce and study a fully discrete scheme for the numerical solutions of the problem. An optimal order error estimate is derived for the approximate solutions under suitable solution regularity. Numerical examples are presented to show the performance of the method.

MSC:
74M15 Contact in solid mechanics
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
74G25 Global existence of solutions for equilibrium problems in solid mechanics (MSC2010)
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
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