Homogenization using modified Mori-Tanaka and TFA framework for elastoplastic-viscoelastic-viscoplastic composites: Theory and numerical validation

Abstract

This study proposes a micromechanical model based on a modified multi-scale mean field approach that predicts the overall behavior of long fiber reinforced elastoplastic and viscoelastic-viscoplastic composites. The homogenization method adopted is the Mori-Tanaka scheme combined with the Transformation Field Analysis. Moreover, motivated by the distribution of local fields observed in finite element based homogenization analyses, the proposed approach is extended and introduces a special type of coating between the fibers and the matrix. This extension permits to deal with the overestimation of the global stress-strain response using the classical Mori-Tanaka method. Specifically, the coating has the same initial behavior as the matrix, but the inelastic strain fields are amplified compared to those in the matrix during loading. The constitutive equations governing the proposed approach are provided and the numerical implementation, utilizing the “return mapping algorithm” scheme, is explained in detail. The effectiveness of this new method is demonstrated through extensive numerical validation tests, including non-monotonic and non-proportional loading at different strain rates. The reference solution consists of the full field computation using finite element simulations on the studied Representative Volume Element (RVE).