Adaptive Multi‐scale Modeling Error Estimation for Composites

Abstract

Analysing composite materials through efficient higher-order homogenization techniques requires accurate simulations of highly heterogeneous domains. However the validity of the homogenization response in regions with highly localized variations is still questionable. A scale adaptation strategy is developed for a more accurate analysis of generally inelastic macrostructures, where a transition from a homogenized description to an explicit micro-structural resolution is pursued. The designated zones of interest are indicated through two different methods of error estimation. First for mesh refinement approaches, the discretization error is estimated using an indicator developed by Zienkiewicz-Zhu and studying L2 norm. Furthermore a second adaptation zone is identified based on a post-processing step on the homogenized solution and corresponds to regions with high strain-gradients, the gradient of the deformation gradient. In the designated sub-domains a micro-structure representation will replace the homogenized area. The introduced scale-adaptivity method returns an inexpensive and more accurate analysis of composite materials.