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.

在以预定义方式演变的应力状态下执行有限元单元计算的可用数值方法将最一般的应力状态限制为叠加在三个法向应力分量上的单个剪切应力分量。本研究建立在现有技术的基础上并对其进行了扩展，从而可以探索在最复杂的应力状态下的晶胞行为，包括三个剪切和三个法向应力分量。所提出的方法在商业有限元软件 Abaqus 中实现。三维立方晶胞在中心包含空隙或颗粒并受到各种应力状态，表明所开发的方法是准确且计算高效的。此外，使用空隙单元进行的模拟表明，延性破坏是一个各向异性的过程，在存在剪切载荷的情况下各向异性会加剧。也就是说，导致韧性断裂的空隙生长和应变局部化受所有剪切应力分量的相对比率以及应力三轴性和 Lode 参数的影响。