Evaluation of the effective elastic and conductive properties of a material containing concave pores

We calculate effective properties of a porous material with non-ellipsoidal concave pores. The pore shape is described by equation of a supersphere x2p+y2p+z2p=1 that is convex when p > 0.5 and concave whenp < 0.5. Compliance and resistivity contribution tensors for a superspherical pore are calculated using finite element method and approximated by analytical expressions for p < 1. These tensors are used to evaluate effective elastic and conductive properties of a material with superspherical pores via non-interaction approximation, Mori-Tanaka scheme and Maxwell scheme. We show that the geometrical parameters entering expressions for the elastic moduli and conductivity are the same and establish cross-property connection for such materials. These connections coincide with ones for a material with spherical pores.