Shear stiffness of neo-Hookean materials with spherical voids

In this paper, the shear stiffness of neo-Hookean materials with spherical voids is investigated using a numerical homogenization approach. Three-dimensional representative volume element (RVE) models with non-overlapping identical randomly distributed spherical voids are generated to simulate the mechanical responses of the porous neo-Hookean materials. Pure shear deformations are simulated using the finite element method (FEM) and the numerical results show a clear linear relation between the nominal shear stress and the nominal shear strain. The effective shear stiffness of the porous neo-Hookean materials can then be computed by fitting the numerical data. It is further verified by more FEM simulations that the effective shear stiffness can be extended to predict the mechanical responses of the porous neo-Hookean materials subjected to any general isochoric deformations. It is also shown that the effective shear stiffness of the porous neo-Hookean materials can be well predicted as a function of the volume fraction of the voids using the classical three phase model originally proposed for linear elastic composites. Finally, RVE models with spherical voids of various sizes are created to study the effect of the size distribution of voids and the FEM results illustrate that it has negligible effect on the effective shear stiffness.