Unit Cell Calculations Under Fully Characterized Stress States

Abstract

The available numerical methods for conducting finite element unit cell calculations under predefined stress states typically constrain the most general stress state to a single shear stress component superimposed on three normal stress components. This study represents an advancement in the field, expanding upon the current state of the art to enable the exploration of unit cell behavior under the most intricate stress states, encompassing three shear and three normal stress components [1]. The proposed methodology has been implemented within the commercial finite element software ABAQUS. Three-dimensional cubic unit cells, containing either a void or a particle at their center and subjected to various stress states, were analyzed. The results of these simulations demonstrate that the developed method offers both accuracy and computational efficiency. Moreover, simulations conducted on voided unit cells reveal that ductile failure demonstrates anisotropic behavior, with anisotropy becoming increasingly pronounced under the influence of shear loads.