On the Compliance Contribution Tensor for a Concave Superspherical Pore

This paper focuses on the effect of concavity of pores on elastic properties of porous materials. We consider a pore having a shape of a supersphere of unit radius (x)(2p) + (y)(2p) + (z)(2p) = 1 focusing mostly on the case p a parts per thousand currency sign 1. Using FEM analysis of Sevostianov et al (2008), we propose simple approximate formulae for components of the compliance contribution tensor of the supersphere. From these formulae, we identify the microstructural parameter describing its contribution into effective elastic properties. The derivation is illustrated by comparison of the results with the known ones for a spheroidal pore of the aspect ratio gamma.