Three dimensional cells with embedded strong discontinuity for material failure analysis by the boundary element method

Abstract

The Boundary Element Method (BEM) associated with the Continuum Strong Discontinuity Approach (CSDA) can be used as a non-geometric alternative for the modelling of crack growth in physically non-linear three-dimensional problems of solid mechanics. This work makes use of the refereed approach through the implementation of volumetric hexahedral cells with embedded discontinuity that enables the evaluation of discontinuous jumps in the displacement field along a crack discontinuity surface. This is made with an internal equilibrium verification, using a regularized isotropic damage constitutive model. Although this formulation has been extensively studied for two-dimensional problems over the past few years, this is the first time that a three-dimensional extension is presented. The strong discontinuity regime in the cells were imposed directly after the end of the elastic regime, as a typical behaviour of the fracture process of brittle materials. These cells are needed only at the specific region of the solid domain where the cracks propagation is supposed to occur, while the remaining non-discretized regions of domains are considered to work in elastic regime. Some simple numerical examples shows the feasibility of such methodology.