Mathematical properties of a delamination model

In this paper, some mathematical properties of a delamination model are studied. The laminate is schematized as two plates connected by a very special interface material. An interface constitutive model, based on the adhesion theory is introduced. The proposed model is governed by a functional which is neither smooth nor convex. The fundamental properties of this nonsmooth model are presented. Then, a regularized interface model is constructed. The existence of a solution for the delamination problem obtained adopting the regularized interface model is proved. It is shown that this solution converges to a solution of the nonsmooth initial delamination problem when the regularization parameters tend to 0. The lack of convexity of the functional governing both the nonsmooth and the regularized problems makes this proof not straightforward.