Análise de sólidos tridimensionais parcialmente frágeis utilizando modelo de dano e células com descontinuidade incorporada, por meio do método dos elementos de contorno

Abstract

The Boundary Element Method (BEM), associated with the Continuous Strong Discontinuity Approach (CSDA), has been shown to be a successful alternative in the analysis of material failures of solids in plane state problems, with non-geometric representation. In this work, the use of the methodology is extended to the analysis of three-dimensional solids. Hexahedral cells with embedded strong discontinuity are used to discretize the region of the domain where energy dissipation effects occur. Cells can be placed along the entire failure trajectory from the beginning of the analysis, or they can be introduced into the system progressively during the analysis, in order to describe the development of a crack trajectory. The use of cells with embedded discontinuity enables the compatibility of continuous constitutive models, equipped with a softening law, with kinematics with discontinuity in the strain field or in the displacement field. Starting from the elastic regime, the evolution of material failure is contemplated through the transition to the inelastic regime with a continuous damage model, with possible bifurcation and transition between weak and strong discontinuities. This evolution, not necessarily passing through all regimes, is typically the behavior observed in quasi-brittle materials. The bifurcation condition, defined by the singularity of the localization tensor, is evaluated numerically. The computational implementations were developed using the collaborative platform INSANE. The numerical analysis of three-dimensional models allowed the evaluation of the use of the methodology regarding the potential, limitations, and challenges in practical problems of failure analysis of quasi-brittle solids.