Developing space-time dependent boundary conditions for composite RVEs at high strain-rates

Abstract

This paper examines the effectiveness of periodic boundary conditions (PBCs), when applied to heterogeneous representative volume elements (RVEs) subjected to high strain-rate loading conditions. Even for a periodic multi-phase microstructure, the local stress and strain responses in the RVE under conditions of high strain-rate is not periodic. Stress waves propagate in the microstructure and interact with heterogeneities, resulting in reflection and transmission at the interfaces. To mitigate the limitations of PBCs, space and time dependent boundary conditions (STBCs), derived from analytical solutions to the 1D wave propagation problem, are proposed in this paper. This results in significant increase in the efficiency of the RVE analysis since it is not necessary to include larger RVEs. The paper introduces analytical solutions of the longitudinal and shear wave equations for elastic two-phase materials under time-dependent boundary conditions. Subsequently a 3D composite RVE problem, is solved to investigate the efficacy of STBCs. Results show that STBCs significantly improve the accuracy over PBCs for the same RVE. From this analysis, a strain-rate ≥105s−1 is considered to be suitable transition point from periodic to space-time dependent boundary conditions for heterogeneous elastic composites.