### Homogenous Numerical Models for Porous Hyperelastic Materials

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#### Abstract

In this work, a general micromechanics framework for the development of constitutive models of the large-strain deformation of porous elastomeric materials is developped. The framework is applicable to any type of isotropic hyperelastic matrix material which obeys pointwise incompressibility: such as the Neo–Hookean, Mooney–Rivlin and Ogden model. The strain energy density function depends on the properties of the incompressible hyperelastic matrix material, the initial level of porosity, and the macroscopic deformation. The constitutive model is used to predict the stress–strain behavior of the pore-containing matrix as a function of initial porosity and macroscopic loading conditions. As an example, a constitutive model is analytically developed for a porous Neo–Hookean material. The stress is observed to depend on the material properties of the elastomers matrix, the initial void volume fraction (porosity) and the applied state of strain. Constitutive model predictions compared well with those obtained from a numerical three-dimensional micromechanical cell model for a range of initial void volume fractions and tensile load cases. The applicability of the model to compressive loading situations is discussed, such as uniaxial compression. *Copyright © 2015 Praise Worthy Prize - All rights reserved.*

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