A finite element method for localized failure analysis

Abstract

A method is proposed which aims at enhancing the performance of general classes of elements in problems involving strain localization. The method exploits information concerning the process of localization which is readily available at the element level. A bifurcation analysis is used to determine the geometry of the localized deformation modes. When the onset of localization is detected, suitably defined shape functions are added to the element interpolation which closely reproduce the localized modes. The extra degrees of freedom representing the amplitudes of these modes are eliminated by static condensation. The proposed methodology can be applied to 2-D and 3-D problems involving arbitrary rate-independent material behavior. Numerical examples demonstrate the ability of the method to resolve the geometry of localized failure modes to the highest resolution allowed by the mesh. © 1987.