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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.

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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