Well-Posedness of an Elastic-Viscoplastic Contact Problem
DOI:
https://doi.org/10.65135/atsf.2025.2Keywords:
Elastic-viscoplastic material; frictionless contact; normal compliance; unilateral constraint; variational inequality; fixed point; convergence criterion; well-posedness conceptsAbstract
We consider a mathematical model which describes the contact of an elastic-viscoplastic body with a foundation. The contact is frictionless and is modeled with normal compliance and unilateral condition. The weak formulation of the model is in a form of a system which couples a variational inequality for the displacement field with an implicit nonlinear equation for the stress field. We prove the unique solvability of the problem by using a fixed point argument for history-dependent operators. Next, we provide necessary and sufficient conditions which guarantee the convergence to the solution of this elastic-viscoplastic contact model. We use these results in order to obtain a continuous dependence result and to introduce two well-posedness concepts for the problem. Finally, we consider a one-dimensional example which allows us to compare the two well-posedness concepts employed.
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