A quasi-static adhesive contact of a membrane with damage

Abstract

This work presents a quasi-static model for adhesive contact between an elastic membrane with damage and a rigid obstacle that lies beneath it. The model consists of an elliptic variational inequality for the membrane displacements, a nonlinear ordinary differential equation for the evolution of the adhesion field and a parabolic variational inequality for the damage field. By using regularity results from the theory of elliptic variational inequalities and a fixed point argument, the system is shown to have a unique weak solution.