Analytically derived space time-based boundary condition (STBC) to account for stress wave propagation in a heterogeneous micromechanical model at hypervelocity impact

Abstract

Recent years have seen a surge in research on material and structural response of composites using the homogenization based hierarchical modeling method. The microstructural representative volume element (RVE) is a small micro-region for which the volume average of variables is the same as those for the entire body. Representations of the microstructure are used for micromechanical simulations in determination of effective material properties by homogenization. Conventionally, periodic boundary conditions (PBC) are applied on the RVE boundary. However, when the heterogeneous microstructure is under very high strain rate loading conditions (105s−1−107s−1), periodic boundary conditions (PBC) do not accurately represent the effect of stress wave propagation. Improper boundary conditions can lead to significant error in homogenized material properties. In order to increase the accuracy of the homogenization model, this study introduces a new space-time dependent boundary condition (STBC) for a 3D microscopic RVE subjected to high strain rate deformation in explicit FEM simulation by using the characteristics method of traveling waves. The advantages of the STBC are discussed in comparison with time-dependent averaged results of examples using PBC. The proposed STBC offers significant advantages over conventional PBC in the RVE-based analysis of heterogeneous materials.