Fracture failure representation of quasi-brittle materials using a three-dimensional dipole BEM formulation including loading rate effects

Resumo

This study presents an alternative boundary element method (BEM) formulation for the cohesive crack propagation modelling in three-dimensional structures, including loading rates problems. Therefore, these developments enable the modelling of viscous-cohesive fracture processes. An initial stress field for representing the mechanical behaviour along the fracture process zone is proposed, which leads to a set of self equilibrated forces named as dipole. The proposed dipole-based formulation demonstrates some advantages in comparison to classical BEM approaches in this field. Among them, it is worth citing the discretisation of only one crack surface and the requirement of solely three integral equations per source point at the crack surface. Then, in addition to the accuracy, the proposed formulation is efficient in terms of computational effort, which is a bottle neck in three-dimensional problems. Cohesive laws govern the material nonlinear behaviour along the fracture process zone. The mechanical effects of loading rate over the material resistance at the FPZ are properly handled by a time dependent function, which modifies the tensile material strength and the material fracture energy as a function of the loading velocity rate. Some applications are introduced to demonstrate the adequate performance of the proposed formulation, in which the results obtained have been compared against experimental responses available in the literature.