A Homogenization Scheme for Nonlinear Viscoelastic Behaviors of Particulate Reinforced Composites

Abstract

The present study introduces a micromechanical model for predicting nonlinear viscoelastic responses of composite systems reinforced with solid spherical micro particles. The composite microstructures are simplified with uniformly distributed cubic particles over an infinite medium. The representative volume element (RVE) consists of a single particle embedded in the cubic matrix. One eighth unit-cell model with four particle and polymer subcells is generated. The solid spherical particle is modeled as linear elastic, while the polymer follows nonlinear viscoelastic material responses. The homogenized micromechanical relation is developed in terms of the average strains and stresses and satisfies traction continuity and displacement compatibility at the subcells' interfaces. The micromechanical model provides three-dimensional (3D) effective properties of homogeneous materials, while recognizing important micro-structural aspects and parameters of the heterogeneous medium. The micromechanical formulation is generalized to include an explicit time-scale for modeling time-dependent behavior and is designed to be compatible with general displacement based finite element (FE) analyses. Due to the nonlinear and time-dependent response in the polymeric matrix, the linearized micromechanical relations will often deviate from the nonlinear constitutive equations. Thus, the stress-strain correction scheme is formulated to satisfy both micromechanical and nonlinear constitutive relations. Experimental data and analytical models available in the literature are used to verify the capability of the above micromechanical model in predicting the overall nonlinear behaviors. Comparisons with detail unit-cell FE model are also presented.