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Variational analysis of quasistatic viscoplastic contact problems with friction. (English) Zbl 1084.74541
Summary: We consider a nonstandard mathematical problem which describes the frictional contact between an elastic-viscoplastic body and a rigid obstacle. The frictional contact is modeled by a general velocity dependent dissipation functional. We obtain a weak formulation for the model and prove an existence and uniqueness result. The proof is based on the theory of evolution variational inequalities and the Banach fixed point theorem. We describe a number of concrete friction conditions which may be set in this form. We also obtain an existence and uniqueness result for a model of an elastic-viscoplastic material with internal state variables, which in particular, may describe the evolution of the system’s damage.

74M15 Contact in solid mechanics
74M10 Friction 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