History-dependent contact models for viscoplastic materials

International audienceWe consider two mathematical models which describe the frictionless process of contact between a ratetypeviscoplastic body and a foundation. The contact is modelled with normal compliance and memoryterm such that penetration is not restricted in the first problem, but is restricted with unilateral constraintin the second one. For each problem, we derive a variational formulation in terms of displacements, whichis in a form of a history-dependent variational equation and a history-dependent variational inequality.Then we prove the unique weak solvability of each model. Next, we prove the convergence of the weaksolution of the first problem and the weak solution of the second problem, as the stiffness coefficientof the foundation converges to infinity. Finally, we provide numerical simulations which illustrate thisconvergence result