On the solvability of dynamic elastic‐visco‐plastic contact problems

Source abstract

Abstract We consider two dynamic contact problems between an elastic‐visco‐plastic body and an obstacle, the so‐called foundation. The contact is frictionless and it is modelled with normal compliance of such a type that the penetration is not restricted in the first problem, but is restricted with unilateral constraint, in the second one. We derive a variational formulation of the first problem and then prove its unique weak solvability, by using arguments on nonlinear evolution equations with monotone operators and fixed point. Then, we derive a variational formulation of the second problem and prove its weak solvability. To this end we consider a sequence of regularized problems which have a unique solution, derive a priori estimates and use compactness properties to obtain a solution to the original model, by passing to the limit as the regularization parameter converges to zero.