An alternative BEM formulation, based on dipoles of stresses and tangent operator technique, applied to cohesive crack growth modelling

Fracture mechanics has been widely studied by the scientific community in recent years because it can consistently explain the failure of structures. The simulation of the failure process of complex engineering structures requires numerical techniques coupled with robust theories. The boundary element method (BEM) has been widely used to solve such complex engineering problems, particularly those problems in which the BEM mesh dimension reduction provides modelling advantages. This paper presents an alternative BEM formulation applied to cohesive crack propagation analysis. In this type of problem, the process zone ahead of the crack tip is simulated using the fictitious crack model. Therefore, the residual resistance of the fracture process zone is represented by cohesive stresses. The proposed BEM formulation models the cohesive stresses using the domain term of the direct integral representation. This term is modified to be non-null only at the fictitious crack path. As a result of this domain term manipulation, a dipole of stresses appears that will govern the cohesive stresses. The nonlinear problem is solved using a tangent operator, which incorporates the nonlinear cohesive laws into the algebraic BEM equations. The results from the proposed formulation are compared with experimental and numerical results to validate and prove the formulation’s robustness and accuracy.