Reduced order homogenization of composites with strength difference effects in elastoplasticity coupled to damage

Abstract

This paper addresses reduced order homogenization of composites with strength difference (SD) effects in elastoplasticity coupled to damage, while containing several well-known plasticity criteria as special cases. We extend two approaches for this purpose: 1. nonuniform transformation field analysis (NTFA by Michel and Suquet, 2003) and 2. a recent variant called cluster-based NTFA (CNTFA by Ri et al., 2021), and conduct a comparative study on them. For the NTFA approach, a space–time decomposition is done separately for volumetric and deviatoric inelastic strain fields. A coupled model is derived for the present case to govern the evolution of resulting reduced variables. For the CNTFA approach, a clustering analysis is additionally performed for a spatial decomposition of the micro-domain. Unlike the NTFA, the online analysis is formulated as a unified minimization problem, which does not require a major adaptation for the present case. For both approaches, localization rules are deduced from the superposition principle and then homogenized to obtain the effective responses. FE-based implementation is presented in detail for both approaches. Numerical results show that both approaches provide a striking acceleration rate against conventional FE computations. The CNTFA predictions are more accurate than the NTFA ones by involving clustered microscopic fields in the online analysis, thus resulting into a slightly increased memory requirement.