Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Drach B., Tsukrov I., Gross T., Dietrich S., Weidenmann K., Piat R., Böhlke T. (2011) Numerical modeling of carbon/carbon composites with nanotextured matrix and 3D pores of irregular shapes. Int. J. Sol. Structures 48: 2447–2457
Eshelby J.D. (1957) The determination of the elastic field on an ellipsoidal inclusion and related problems. Proc. Roy. Soc. L., A 241: 376–392
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.
Grechka V., Vasconselos I., Kachanov M. (2006) The influence of crack shapes on the effective elasticity of fractured rocks. Geophysics 71: D153–D160
Hill R. (1963) Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids 11: 357–372
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.
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: 031002–1-10
Kachanov M., Tsukrov I., Shafiro B. (1994) Effective moduli of solids with cavities of various shapes. Appl. Mech. Rev. 47: S151–S174
Mear M.E., Sevostianov I., Kachanov M. (2007) Elastic compliances of non-flat cracks. Int. J. Sol. Structures 44: 6412–6427
Onaka S. (2001) Averaged Eshelby tensor and elastic strain energyof a superspherical inclusion with uniform eigenstrains. Phil. Mag. Let. 81: 265–272
Onaka S. (2012) Superspheres: intermediate shapes between spheres and polyhedral. Symmetry 4: 336–343
Onaka S., Fujii T., Kato M. (2007) Elastic strain energy due to misfit strains in a polyhedralprecipitate composed of low-index planes. Acta Mater. 55: 669–673
Prokopiev O., Sevostianov I. (2006) On the possibility of approximation of irregular porous microstructure by isolated spheroidal pores. Int. J. Fracture 139: 129–136
Prokopiev O., Sevostianov I. (2007) Modeling of porous rock: digitization and finite elements versus approximate schemes accounting for pore shapes. Int. J. Fracture 143: 369–375
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.
Sevostianov I., Kachanov M. (2002) On the elastic compliances of irregularly shaped cracks. Int. J. Fracture 114: 245–257
Sevostianov I., Kachanov M. (2007) Relations between compliances of inhomogeneities having the same shape but different elastic constants. Int. J. Eng. Sciences 45: 797–806
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.
Sevostianov I., Kachanov M., Zohdi T. (2008) On computation of the compliance and stiffness contribution tensors of inhomogeneities. Int. J. Sol. Structures 45: 4375–4383
Tsukrov I., Novak J. (2002) Effective elastic properties of solids with defects of irregular shape. Int. J. Solids Struct. 39: 1539–1555
Tsukrov I., Novak J. (2004) Effective elastic properties of solids with two-dimensional inclusions of irregular shape. Int. J. Solids Struct. 41, 2004: 6905–6924
Zimmerman R.W. (1986) Compressibility of two-dimensional cavities of various shapes. J. Appl. Mech. 53: 500–504
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sevostianov, I., Giraud, A. On the Compliance Contribution Tensor for a Concave Superspherical Pore. Int J Fract 177, 199–206 (2012). https://doi.org/10.1007/s10704-012-9754-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-012-9754-7