Stress Averaging for a Beam Network for Use in a Hierarchical Multiscale Framework

Abstract

Abstract : An efficient procedure for obtaining the average stress within a representative volume element (RVE) composed of beam elements is developed and validated. A model composed of a network of elastic beam elements is taken as the lower length scale in a hierarchical modeling framework for dynamic analyses. An efficient procedure for attaining the static equilibrium configuration of the RVE is presented. An algorithm for determining the average stress within the RVE based on the virtual work principle is assessed by comparison with either the total elastic energy within the RVE or the summation of surfaces forces over the RVE boundary. The results from the virtual work stress computation algorithm are in good agreement with the more direct calculations, including those with inelastic deformation, indicating that it is appropriate for analysis of a lower length scale model in a hierarchical modeling framework.