Cohesive crack growth modelling based on an alternative nonlinear BEM formulation

Abstract

Fracture mechanics and crack propagation problems have been widely studied by the scientific community in recent years, because crack growth phenomenon can explain the failure of structures. In order to model accurately the structural behaviour of complex engineering structures numerical techniques are required. In this regard, the boundary element method (BEM) has been widely used to solve complex engineering problems, especially those where its mesh dimension reduction includes advantages on the modelling. This paper addresses the analysis of crack propagation in quasi-brittle materials using an alternative BEM formulation. In this type of problem, the damaged zone ahead the crack tip is modelled based on the fictitious crack model. Therefore, the residual resistance of the damaged zone is represented by cohesive stresses, which tends to close the crack faces. The alternative BEM formulation proposed aims at modelling the cohesive stresses using the domain term of the direct integral representation. This term is degenerated, in order to be non null only at the fictitious crack path. As a result of the domain term manipulation, appears a dipole of stresses, which will govern the cohesive stresses. It leads a nonlinear formulation, where the cohesive stresses are determined according the crack opening displacement. Linear, bi-linear and exponential cohesive laws are used to model the residual resistance of the cohesive zone. The results achieved by the proposed formulation are compared with experimental and numerical ones available in literature, in order to validate and prove its robustness and accuracy.