Stress-controlled weakly periodic boundary conditions: Axial stress under varying orientations

The accuracy of multiscale modeling approaches for the analysis of heterogeneous materials hinges on the representativeness of the micromodel. One of the issues that affects this representativeness is the application of appropriate boundary conditions. Periodic boundary conditions are the most common choice. However, when localization takes place, periodic boundary conditions tend to overconstrain the microscopic problem. Weakly periodic boundary conditions have been proposed to overcome this effect. In this study, the effectiveness of weakly periodic boundary conditions in restoring transverse isotropy of representative volume elements (RVE) for a fiber-reinforced composite with elastoplastic matrix is investigated. The formulation of weakly periodic boundary conditions is extended to allow for force-controlled simulations where a uniaxial stress can be applied. A series of simulations is performed where the orientation of applied stress is gradually varied and the influence of this orientation on the averaged response is examined. An original method is presented to test the correlation between the ultimate principal stress and average localization angle of shear bands within an RVE. It is concluded that weakly periodic boundary conditions alleviate anisotropy in the RVE response but do not remove it.