A Multi-Scale Model of Soft Imperfect Interface with Nonlocal Damage

The aim of this paper is to propose a model of bonded interface including nonlocal damage and unilateral conditions. The model is derived from the problem of a composite structure made by two adherents and a thin adhesive. The adhesive is damaged at microscopic level and is subjected to two regimes, one in traction and one in compression. The model of interface is derived by matched asymptotic expansions. In this paper, two cases corresponding to the two regimes are discussed. Moreover, this model can be considered as a model of contact with adhesion and unilateral constraint. At the end of the paper, a simple numerical example is presented to show the evolution of the model.