The fracture failure modelling of three-dimensional structures composed of quasi-brittle materials subjected to different loading velocities rates by the dipole-based BEM approach

This study presents a numerical formulation for representing the fracture-failure of three dimensional structures composed of quasi-brittle materials. In addition to the nonlinear nature of quasi-brittle fracture, the formulation accounts the mechanical effects of different loading velocities rates. Therefore, these developments enable the modelling of viscous-cohesive fracture processes. The Boundary Element Method (BEM) describes the mechanical fields by the dipole-based approach, which has been extended to the three dimensional problems herein. This BEM approach is effective in crack growth modelling because only one crack surface requires discretisation. The classical cohesive crack approach models the material resistance at the energy dissipation zone surrounding the crack front. Besides, a time dependent function updates the cohesive crack approach and incorporates the viscous behaviour by modifying the tensile material strength and the material fracture energy as a function of the loading velocity rate. Three applications demonstrate the adequate performance of the proposed formulation, in which the results obtained have been compared against analytical and experimental responses available in the literature.