Análise de degradação material, bifurcação e transição entre descontinuidades fracas e fortes através do método dos elementos de contorno

Abstract

The implicit formulation of the boundary element method is applied to bidimensional problems of material failure involving, sequentially, inelastic dissipation with softening in continuous media, bifurcation and transition between weak and strong discontinuities. The bifurcation condition is dened by the singularity of the localization tensor, also known, for historical reasons, as acoustic tensor. The weak discontinuities are associated to strain localization bands of nite width, which become increasingly narrow until to collapse in a surface with discontinuous displacement eld, called strong discontinuity surface. Continuum constitutive models are adopted to represent the material behaviour in all of these steps, taking into account the adaptations that come from the strong discontinuity analysis for the post-bifurcationphases. The methodology is generic enough to treat any type of material instability and, according with the constitutive model adopted, the discontinuities may represent slip lines in geomechanics, shear bands in ductile materials or cracks in brittle (or quasi-brittle) materials. However, in this thesis, only the last case was considered, from the adoption of an isotropic damage model. The crack propagationacross the solid domain is done by an automatic cells generation algorithm and, in this context, the fracture process zone in the crack tip became totally represented by the cells in the continuum damage regime and the cells with weak discontinuities.