A dynamic viscoelastic problem with friction and rate-depending contact interactions

International audience ; The aim of this work is to study a dynamic problem that constitutes a unified approach to describe some rate-depending interactions between the boundaries of two viscoelastic bodies, including relaxed unilateral contact, pointwise friction or adhesion conditions. The classical formulation of the problem is presented and two variational formulations are given as three and four-field evolution implicit equations. Based on some approximation results and an equivalent fixed point problem for a multivalued function, we prove the existence of solutions to these variational evolution problems.