Strain localization in reduced-order asymptotic homogenization

Abstract

A reduced-order asymptotic homogenization-based multiscale technique that can capture damage and inelastic effects in composite materials is proposed. This technique is based on a two-scale homogenization procedure where eigenstrain representation accounts for the inelastic response and the computational efforts are alleviated by a reduction-of-order technique. Macroscale stress is derived by calculating the influence tensors from analysis of a representative volume element. At microscale, the damage in the material is modeled using a framework based on continuum damage mechanics. To solve the problem of strain localization, a method of alteration of the stress–strain relation of microconstituents based on the dissipated fracture energy in a crack band is implemented. The issue of spurious postfailure artificial stiffness at macroscale is discussed and the effect of increasing the order to alleviate this problem is checked. Verification studies demonstrated that the proposed formulation predicts the macroscale response and also captures the damage- and plasticity-induced inelastic strains.