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                <term xml:lang="en">Concave pore</term>
                <term xml:lang="en"> Supersphere</term>
                <term xml:lang="en"> Effective properties</term>
                <term xml:lang="en"> Homogenization</term>
                <term xml:lang="en"> Cross-property connections</term>
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              <p>We calculate effective properties of a porous material with non-ellipsoidal concave pores. The pore shape is described by equation of a supersphere x(2p) + y(2p) + Z(2p) = 1 that is convex when p &gt; 0.5 and concave whenp &lt; 0.5. Compliance and resistivity contribution tensors for a superspherical pore are calculated using finite element method and approximated by analytical expressions for p &lt; 1. These tensors are used to evaluate effective elastic and conductive properties of a material with superspherical pores via non-interaction approximation, Mod-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.</p>
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