Constitutive modeling of neo-Hookean materials with spherical voids in finite deformation

In this paper, we present a new constitutive model to estimate the effective mechanical behaviors of the incompressible neo-Hookean materials with randomly distributed spherical voids under finite deformations. The volumetric multiplicative decomposition is employed to decompose the deformation gradient of a general finite deformation into the corresponding hydrostatic and isochoric part. By deriving and then superposing the strain energy density functions of the hydrostatic and isochoric deformation, we deduce the constitutive model of the porous neo-Hookean materials. The cubic units, which are randomly embedded with equal-sized spherical voids, are constructed as the representative volume element (RVE) models to numerically validate the proposed constitutive model. Various finite deformations are simulated and all the numerical results show that the proposed constitutive model can offer good estimates on the effective mechanical behaviors of the porous neo-Hookean materials. The constitutive model developed by Danielsson et al. (2004) is studied and compared with our model. The results suggest that our model can better capture the comprehensive mechanical behaviors of the porous neo-Hookean materials than the DPB model. The strain energy density function proposed is assessed to be strongly elliptic, which implies the macroscopic mechanical stability of the porous materials.