Summary: We present a theory and propose a numerical algorithm for the solution of dissipative problems involving a class of composite materials which are assembled using an adhesive element. We consider the interface between two different components which undergo a unilateral adhesive contact. The generalized forces associated with the mathematical model are obtained from non-convex super potentials by forming their local subdifferentials. The complementary equation is derived by the introduction of a pseudo-potential of dissipation and the application of the hypothesis of normal dissipation. In order to circumvent the non-differentiability of these potentials, we make use of a regularization process. A Galerkin finite element method together with an explicit finite difference method are applied to obtain solutions of two-dimensional problems.