A damage–friction interface model derived from micromechanical approach

The present paper deals with a micromechanical model of interface able to couple the damage (microcrack) evolution, the non-penetration conditions (Signorini equations) and the friction effect (Coulomb’s law). At a typical point of the interface, a representative volume element (RVE) is considered; it is characterized by the presence of two different materials and by a microcrack evolving along the material discontinuity. An innovative deductive approach based on a micromechanical analysis and on a homogenization procedure is proposed. In particular, the solution of the micromechanical problem on the RVE is determined considering three subproblems and properly superimposing their solutions. Then, a simplified approach is proposed by modeling the behavior of the material constituting the RVE in a very essential manner. Evolutionary laws for the crack growth are given and the equations governing the unilateral and friction phenomena are presented. The original proposed procedure is applied to derive an interface model for masonry structures considering the brick–mortar interaction. The solutions of three subproblems are determined adopting the finite element method on the specific RVE for different crack lengths; then, the solutions are interpolated by adopting a spline technique and properly superimposed. A numerical procedure based on the return-mapping algorithm and the classical backward-Euler integration scheme is presented for the specific considered evolutive problem. Some numerical tests, for monotonic and cyclic loadings are presented, remarking the ability of the proposed approach to reproduce the complex features of brick–mortar interfaces; comparisons between the results obtained adopting the original proposed model and the simplified model are performed.