Hierarchical model reduction at multiple scales

Abstract

Abstract A hierarchical model reduction approach aimed at reducing computational complexity of non‐linear homogenization at multiple scales is developed. The method consists of the following salient features: (1) formulation of non‐linear unit cell problems at multiple scales in terms of eigendeformation modes that a priori satisfy equilibrium equations at multiple scales and thus eliminating the need for costly solution of discretized non‐linear equilibrium, (2) the ability to control the discretization of the eigendeformation modes at multiple scales to maintain desired accuracy, and (3) hierarchical solution strategy that requires sequential solution of single‐scale problems. A two‐scale formulation is verified against an one‐dimensional model problem for which an analytical solution can be obtained and a three‐scale formulation is validated against tube crash experiments. Copyright © 2009 John Wiley & Sons, Ltd.