A 3D multiscale cohesive zone model for quasi-brittle materials accounting for friction, damage and interlocking

A three-dimensional (3D) two-scale Cohesive Zone Model (CZM), which is based on a multiplane approach and couples damage with friction and interlocking, is presented for analysing crack propagation in quasi-brittle materials along structural interfaces where formation of cracks is expected. The main idea of the 3D multiplane formulation herein exploited is to describe the asperities of the interface in the form of periodic patterns of inclined planes, denominated Representative Interface Elements (RIE). The interaction within each plane of the RIE is governed by the interface formulation proposed by Alfano and Sacco in earlier work. After reporting details of the formulation and of its algorithmic implementation, the sensitivity of the macroscopic mechanical response to the specific selection of the RIE is analysed and reported with a general numerical assessment of the 3D interface mechanical response to monotonic and cyclic loading histories. A fundamental issue addressed in this paper is the identification of optimal RIE patterns with a minimum number of planes capable of providing isotropic in-plane behaviour in response to confined slip tests.