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Analysis of a dynamic elasto-viscoplastic frictionless antiplan contact problem with normal compliance. (English) Zbl 1463.74095

Summary: We consider a mathematical model which describes the dynamic evolution of a thermo elasto viscoplastic contact problem between a body and a rigid foundation. The mechanical and thermal properties of the obstacle coating material near its surface. A variational formulation of this dynamic contact phenomenon is derived in the context of general models of thermo elasto viscoplastic materials. The displacements and temperatures of the bodies in contact are governed by the coupled system consisting of a variational inequality and a parabolic differential equation. The proof is based on a classical existence and uniqueness result on parabolic inequalities, differential equations and fixed point arguments.

MSC:

74M15 Contact in solid mechanics
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
49J40 Variational inequalities
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
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