Direct Mori-Tanaka calculations of strains in ellipsoidal inclusions with multiple orientations – Comments on the papers: Naili, G. et al. Comp Sci Tech, 187: 107942, 2020 (https://doi.org/10.1016/j.compscitech.2019.107942) and Jain, A. et al., Comp Sci Tech, 87: 86–93, 2013

Abstract

Recently, Naili et al. [1] compared the predictions of strains in inclusions by two methods viz. FE-MT and FE-Voigt for RVE containing 2D ellipsoidal inclusions. In this schemes, multiphase composite (composite having fibers with varying orientations) are homogenized by first homogenizing “pseudo-grains” consisting of fibers having same orientation and aspect ratio using full field Finite Element (FE) simulations. The second step of the homogenization was subsequently performed using the Mori-Tanaka (MT) formulation (the method designated as “FE-MT” homogenization) and the Voigt approximations (“FE-Voigt”). FE homogenization was chosen as the first step of homogenization to ensure that the comparison is “unbiased”. It is known that for uni-directional composites, the MT formulation and FE yield identical results for effective stiffness as well as the strains in the inclusions. Thus, the first step of homogenization could have been MT formulation with no or little change in the results. Further, Naili et al. show that MT-MT is equivalent to the full analytic MT formulation while MT-Voigt is equivalent to the pseudo-grain discretized formulation of the Mori Tanaka homogenization [2].