Homogenization methods for porous elasto-plastic materials and composites

This thesis addresses the homogenization of porous materials or short fiber-reinforced composites (SFRC) in isothermal linear elasticity and elasto-plasticity with hardening. First, several homogenization methods are evaluated for elastic SFRCs. To ensure an unbiased assessment of these methods, only full-field finite element (FE) versions are developed and studied, excluding Eshelby-based mean-field models. The homogenization of unidirectional (UD) SFRC is performed using two computational models: representative volume elements (RVE) and unit cells, with their predictions compared. For the homogenization of misaligned porous SFRC, a model RVE, regarded as an aggregate of UD pseudo-grains (PG), is homogenized in two steps. In the first step, the effective response of the PGs is obtained via FE analysis of UD unit cells. In the second step, one of three homogenization schemes—Voigt, Reuss, or a FE-based version of the Mori-Tanaka (MT) model—is applied. The latter is equivalent to a direct MT homogenization of the RVE. A parametric study is conducted using various fiber volume fractions and orientation tensor components. Both the effective properties of RVEs and the mean strains within individual fibers are compared against reference results obtained from direct FE homogenization of actual RVEs.Another contribution of this thesis is the development of a predictive micromechanical approach for 3D porous materials, where the unreinforced or reinforced matrix phase exhibits elasto-plastic behavior with hardening. The cavities can take the form of spheres or long/short cylinders, while the fibers are modeled as either spherical or ellipsoidal inclusions.The approach is based on an alternative microstructure, consisting of elasto-plastic inhomogeneities embedded in a homogenized porous matrix phase, with volume fractions determined from a maximum packing argument. The effective properties of single hollow solids are calculated using an energy-based approach coupled with full-field FE analyses. Subsequently, the alternative microstructures are homogenized using mean-field (MF) models.For reinforced porous materials, a two-level method is adopted. The proposed approach is used at the lower level to obtain a fictitious homogenized matrix, into which reinforcements are embedded at the upper level. The present work focuses on monotonic and proportional loadings and applies the secant formulation of isotropic or transversely isotropic elasto-plasticity. However, no specific constitutive models are assumed or identified.The predictions were validated against reference full-field FE results for actual microstructures in both 3D and 2D plane strain or stress conditions, under arbitrary stress triaxialities, and good agreement was found in all cases.