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 ≤ 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 γ.
KeywordsPorous material effective properties non-ellipsoidal pores concave pores supersphere
Unable to display preview. Download preview PDF.
- Eshelby, J.D. (1961) Elastic inclusions and inhomogeneities. In: Progress in Solid Mechanics V.2 (eds. I. N. Sneddon, R. Hill), Norht-Holland, Amsterdam, 89-140.Google Scholar
- Grechka V., Vasconselos I., Kachanov M. (2006) The influence of crack shapes on the effective elasticity of fractured rocks. Geophysics 71: D153–D160Google Scholar
- Huet, C., Navi, P. and Roelfstra, P.E. (1991) A homogenization technique based on Hill’s modification theorem. In: Continuum Models and Discrete Systems, v.2 (ed. G. Maugin 135-143.Google Scholar
- Kachanov M., Sevostianov I. (2012) Rice’s internal variables formalism and its implications for the elastic and conductive properties of cracked materials, and for the attempts to relate strength to stiffness. J. Appl. Mech. 79: 031002–1-10Google Scholar
- Sevostianov, I. and Kachanov, M. (1998) On the relationship between microstructure of the cortical bone and its overall elastic properties, Int. J. Fracture, 92, 1998, pp. L3-L8.Google Scholar
- Sevostianov, I., Kováčik, J. and Simančík, F. (2006) Elastic and electric properties of closed-cell aluminum foams. Cross-property connection Materials Science Eng., A-420, 87-99.Google Scholar