Automatic cells generation algorithms for two-dimensional physically non-linear BEM analysis

Abstract

The integral equations used by the boundary element method (BEM) in physically non-linear analysis of solid mechanics present a remaining domain integral term, involving the inelastic field. The most direct way to treat this term is by the introduction of internal cells. However, this procedure represent a drawback in the BEM context, since not only the boundary is being discretized. On the other hand, an opportunity to develop algorithms that optimize such analyses emerges from the fact that only the inelastic regions of the domain need to be divided into cells. In this way, this paper presents new methodologies to progressively generate two-dimensional cells, with triangular or quadrilateral geometries, following the growth of the dissipative region. Moreover, a unified constitutive modeling framework is used in order that different material behaviors can be addressed by a unique computational structure. Numerical examples considering elastoplatic and isotropic damage constitutive models are presented.