Failure analysis of quasi-brittle materials involving multiple mechanisms on fractured surfaces

We present a variational formulation for the quasi-static boundary value problem of a structure with quasi-brittle materials, involving (i) unknown states of contact, (ii) deformation-dependent frictional forces, (iii) crack opening and closing with cohesive traction, and (iv) configuration change due to the initiation and the evolution of cracks, and propose a new finite cover method (FCM) capable of reflecting those multiple mechanisms in the failure analysis. The cover-division strategy is also introduced to judge the generation of cracks, and to locate and orient them within the framework of the FCM. A relevant numerical algorithm is designed to be consistent with the mathematical representation of the multiple mechanisms. Several numerical examples are presented to validate the proposed method and to demonstrate its promise and potential for evaluating the ultimate strength of quasi-brittle materials