Finite elements for capturing localized failure

Abstract

In the paper, we examine the ability of different finite element enhancements to capture localized failure in elasto-plastic solids. Altogether seven variations of four noded elements are studied, from the standard bilinear quadrilateral up to recent mixed strain-displacement expansions. The weak form of localization determines whether an element is capable to reproduce discontinuous bifurcation for elasto-plastic material properties which exhibit a singularity of the localization tensor in the element domain. Both, discontinuous tensile splitting and shear banding are examined in square and quadrilateral element, geometries within the frame of associated and non-associated elasto-plastic Rankine-and Drucker-Prager descriptions. Aside from spectral studies of discontinuous bifurcation on the element level, the effect of progressive failure computations is examined with the help of two boundary value problems.