Dipole-based BEM formulation for three-dimensional cohesive crack propagation modelling

This study presents an alternative boundary element method (BEM) formulation for the cohesive crack propagation modelling in three-dimensional structures. The proposed formulation utilises an initial stress field for representing the mechanical behaviour along the fracture process zone, which leads to a set of self-equilibrated forces named as dipole. Cohesive laws govern the material nonlinear behaviour along the fracture process zone. The proposed dipole-based formulation demonstrates some advantages in comparison to classical BEM approaches in this field. Among them, it is worth citing the requirement of solely three integral equations per collocation point positioned at the fracture process zone. The effectiveness of the dipole-based formulation has been demonstrated by four applications. The results have been compared to numerical, experimental and analytical solutions available in the literature, in which excellent performance has been observed.