Finite deformation of porous elastomers: a computational micromechanics approach

Abstract

The finite deformation of porous elastomers was studied by means of the numerical simulation of a representative volume element of the microstructure. The size and the discretization of the volume element were selected to obtain an exact response (to a few percent) of the plane-strain deformation of a material made up of a random and isotropic dispersion of circular cylindrical voids embedded in an incompressible neo-Hookean matrix. Three different loading modes (in-plane isotropic deformation, uniaxial elongation, and uniaxial traction) were simulated, and the corresponding stress—strain curves as well as the evolution of the microstructure with deformation were presented for materials with an initial porosity of 5, 10 and 20%. The numerical results were compared with the available homogenization models for the finite deformation of porous elastomers. It was found that the second-order estimate with field fluctuations of López-Pamiés and Ponte Castañeda led to very good approximations to the numerical results in most cases, and significant differences were only found under conditions of highly constrained deformation. The sources of these differences were discussed in the light of the changes in the microstructure provided by the numerical simulations.

Acknowledgments

This investigation was supported by the Spanish Ministry of Education and Science through grant MAT 2006-2602 and by the Comunidad de Madrid through the program ESTRUMAT-CM.