Implementation and numerical verification of a non-linear homogenization method applied to hyperelastic composites

We present a 3D implementation and verification of a micromechanical model dedicated to highly compressible hyperelastic composites having a random microstructure. The model is based on the second-order method proposed by Ponte Castañeda and Tiberio [P. Ponte Castañeda, E., Tiberio, J. Mech. Phys. Solids 48 (2000) 1389–1411]. After recalling the basic principles of this non-linear homogenization technique, we describe its application to composites made up of an hyperelastic matrix and deformable (or rigid) spherical inclusions. The inclusions can be either particles or voids. Computational issues related to the implementation of the model are also presented. In order to provide a rigorous verification of the model for a large range of material contrasts, unit cell computations are performed for reinforced or porous hyperelastic materials. It is shown that in the two cases, the predictions of the model are in a good agreement with the reference finite elements solutions. Finally, voids shape effects on the macroscopic behavior of porous hyperelastic materials are analyzed.