Dynamic Contact Problem with Normal Damped Response, Friction and Adhesion

Abstract

This work considers a mathematical model describing a dynamic frictional contact between a viscoelastic body and an adhesive foundation. The contact is modeled with normal damped response condition associated with a new version of Coulomb’s law of dry friction with adhesion introducing a new term which gives a better transition from adhesion to friction. We present a variational formulation of the problem which is given as a system coupling an evolution inequality of the second order for the displacement and a differential equation of the first order for the bonding field. We establish the existence and uniqueness of the weak solution. The proof is based on parabolic variational inequalities of the second kind, differential equations and fixed point theorem.