Unit cell calculations under fully characterized stress states

Abstract

The available numerical methods for performing finite element unit cell calculations under stress states evolving in a predefined manner restrict the most general stress state to a single shear stress component superimposed on three normal stress components. The present study builds on and extends state of the art such that the behavior of a unit cell under the most complex stress states, comprising three shear and three normal stress components, can be explored. The proposed method is implemented in the commercial finite element software Abaqus. Three-dimensional cubic unit cells containing either a void or a particle at the center and subjected to various stress states showed that the developed method is accurate and computationally efficient. Furthermore, simulations using voided unit cells demonstrate that ductile failure is an anisotropic process, with anisotropy intensifying in the presence of shear loads. That is, void growth and strain localization leading to ductile fracture are influenced by the relative ratios of all shear stress components as well as the stress triaxiality and the Lode parameter.