Effective elastic properties for a periodic bicontinuous porous medium

The effective elastic properties of a bicontinuous porous medium are calculated. The model geometry assumes a continuous solid phase consisting of an array of overlapping spheres on a simple cubic lattice. The interstitial spaces form a second continuous phase saturated with a compressible fluid. Following the approach of Nunan and Keller (J. Mech. Phys. Solids 32, 259-280, 1984), the anisotropic elasticity tensor C_ijkl is expressed in terms of three scalar parameters α, β and γ. Numerical computations are performed to evaluate these parameters as a function of volume fraction. The numerical computations are complemented by an asymptotic theory valid for small solid contact area. The variational results of Hashin and Shtrikman (J. Mech. Phys. Solids 10, 343-352, 1962b) are employed to estimate the elastic properties of isotropic polycrystals formed from randomly oriented grains of the anisotropic medium.