Analysis of a class of dynamic unilateral contact problems with friction for viscoelastic bodies

摘要

In this paper, we extend the existence results obtained in [1], for adynamic unilateral contact problem with nonlocal friction between a Kelvin-Voigt viscoelastic body and a rigid obstacle, to the contact between two viscoelastic bodies and to a cracked viscoelastic body. We give classical and primal variational formulations for the problems. Penalized formulations are investigated by using an abstract existence and uniqueness result. Several estimates on the penalized solutions are established which allow to pass to the limit and to prove the existence of solutions for these dynamic unilateral contact problems with friction.