Analysis of 3D quasi-brittle solids failures by crack growth using the strong discontinuity approach with the boundary element method

Abstract

The continuum strong discontinuity approach (CSDA) is suitable for the analysis of material failures of quasi-brittle solids when constitutive damage models are applied to kinematic equations with displacement discontinuities. Its association with the implicit version of the boundary element method (BEM), using cells with embedded strong discontinuity, allows the analysis of material failures with crack growth. Such cells are mandatory for the domain discretization, which are restricted to the region where the crack is supposed to occur. They are introduced in the model as the analysis progresses, without the need to re-evaluate the pre-existing terms of the matrices, but only through their appropriate expansion. Discontinuity in the displacement field is quantified, after internal equilibrium verification, assuming a uniform displacement jump inside each cell. This work uses this methodology for the analysis of three-dimensional solids under external loads. An elastic-degrading isotropic constitutive model with an exponential softening law is considered, with the strong discontinuity regime imposed directly after the end of the elastic regime. This is the first time that such cells are applied for full three-dimensional mixed mode fracture problems, in the context of the boundary element method. The results presented in the numerical examples are in good agreement with the references.