Semigroup well-posedness and exponential decay of a viscoelastic bilateral contact model with Tresca’s law and infinite memory

Abstract

In this article, we consider a dynamic contact for viscoelastic materials. The contact is bilateral, and the friction is modeled with Tresca’s friction law which provides a clear physical description of dry friction at the contact interface. The material is assumed to follow a nonlinear constitutive relation with history memory. Using the semigroup method, we establish the global well-posedness of the problem. Under suitable assumptions, the exponential stability of the system is established using an appropriate multiplier method.