International Journal of Fracture

, Volume 177, Issue 2, pp 199–206 | Cite as

On the Compliance Contribution Tensor for a Concave Superspherical Pore

Letters in Fracture and Micromechanics


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.


Porous material effective properties non-ellipsoidal pores concave pores supersphere 


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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNew Mexico State UniversityLas CrucesUSA
  2. 2.LAEGO-ENSGVandoeuvre-l_es-Nancy CedexFrance

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