Nonlinear Homogenization of Finitely Deformed Viscoelastic-Viscoplastic Composites Using Mechanics of Structure Genome
The objective of this paper is to develop a micromechanics approach to homogenizing finitely deformed viscoelastic-viscoplastic composites using the mechanics of structure genome. The incremental constitutive relation for glassy polymers, formulated in the spatial configuration, is implemented in the present approach.This involves (1) pulling-back the constitutive model to the material configuration and (2)choosing the deformation gradient tensor and the first Piola–Kirchhoff stress tensor as the strain and the stress measures during homogenization, respectively. An Euler–Newton predictor–corrector method is developed for homogenization. Each step involves formulating a variational statement using the mechanics of structure genome, discretizing the statement in a finite-dimensional space, and solving the problem using an Euler/multilevel Newton method. The present approach is demonstrated by homogenizing fiber- and particle-reinforced composites undergoing uniaxial, biaxial, or shear deformation, at different stain rates.