Short fiber reinforced composites: Unbiased full-field evaluation of various homogenization methods in elasticity

Abstract This paper deals with the evaluation of several homogenization methods for short fiber-reinforced composites (SFRC) in isothermal linear elasticity. In order to have an unbiased assessment, only full-field finite element (FE) versions of the methods are developed and studied, no analytical mean-field models are considered. Firstly, the FE homogenization of unidirectional (UD) SFRC is performed using two computational models: representative volume elements (RVE) and unit cells, and comparing their predictions. Secondly, for the homogenization of misaligned SFRC, a model RVE seen as an aggregate of UD pseudo-grains (PG) is homogenized in two steps. In the first step, the effective response of PGs is obtained by FE analysis on UD unit cells. The second step is performed with one of three homogenization schemes: Voigt, Reuss and a FE-based version of the Mori-Tanaka (MT) model. The latter is equivalent to a direct MT homogenization of the RVE. The actual SFRC microstructure is 3D, but because of limited computer resources, the current article is restricted to 2D analyses, which nevertheless provide some guidance. A parametric study is conducted using several fiber volume fractions and orientation tensor components. Both the effective properties of RVEs and the mean strains inside individual fibers are assessed against reference results obtained by direct FE homogenization of the actual RVEs.