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A frictionless contact problem for elastic-viscoplastic materials with internal state variable. (English) Zbl 1271.74362
Summary: We study a mathematical model for frictionless contact between an elastic-viscoplastic body and a foundation. We model the material with a general elastic-viscoplastic constitutive law with internal state variable and the contact with a normal compliance condition. We derive a variational formulation of the model. We establish existence and uniqueness of a weak solution, using general results on first order nonlinear evolution equations with monotone operators and fixed point arguments. Finally, we study the dependence of the solution on perturbations of contact conditions and prove a convergence result.
74M15 Contact in solid mechanics
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
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