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Variational and numerical analysis of the Signorini’s contact problem in viscoplasticity with damage. (English) Zbl 1064.74134
Summary: We consider the quasistatic Signorini’s contact problem with 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 modeled 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. We then introduce and study a fully discrete scheme for numerical solutions of the problem. An optimal-order error estimate is derived for approximate solutions under suitable solution regularity. Numerical examples are presented to show the performance of the method.

MSC:
74M15 Contact in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
74R20 Anelastic fracture and damage
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