A progressive cells activation algorithm for physically non-linear BEM analysis
Rodrigo G. Peixoto, Gabriel O. Ribeiro, Roque L. S. Pitangueira
Journal of the Brazilian Society of Mechanical Sciences and Engineering , v. 40:112 , 2018
Resumo (em inglês)
A drawback of the boundary element method (BEM) to analyse solid non-linear problems is the necessity to discretize, not only the boundaries, but also the domain in internal cells. Such discretization is required to evaluate the domain integrals involving the inelastic (initial) fields and represents a loss of one of the most remarkable features of the BEM, which is the reduction of the problem’s dimension by one order. However, only regions where the dissipative effects take place need to be divided in cells, allowing optimization of the non-linear solution algorithms. In this paper, one of these optimization attempts is present in which the cells are progressively activated, augmenting the corresponding matrices, as the inelastic region develop and grow. In addition, the implicit formulation of the BEM with a unified constitutive modelling framework is used in order that different material behaviours may be addressed by a single numerical structure. Three numerical examples are presented: two involving ductile material behaviour, modelled with the elastoplastic von Mises associative constitutive model, and another to simulate quasi-brittle behaviour by an isotropic damage constitutive model.