Effective elastic properties of materials with high concentration of aligned spheroidal pores (Q1067818)

A model of elastic transversely isotropic porous materials is presented. It may have applications with cancellous bone. The arrangement of aligned spheroidal pores is obtained through a homological transformation from Hashin's composite-sphere model. The volume fraction C of the matrix is assumed small. Two extremal variational principles of the theory of elasticity yield some inequalities or bounds for the derivatives with respect to C at \(C=0\) of five macroscopic moduli. By using inhomogeneous stress boundary conditions for a hollow spheroidal element, the bounds are considerably improved. They coincide with the upper bounds for spherical pores. The bounds for the derivatives with respect to C at \(C=0\) of five moduli, obtained from a kinematically admissible displacement, are of a simple form and can be used for an approximation to five macroscopic moduli for \(C\ll 1\).