Effective elastic properties of materials with high concentration of aligned spheroidal pores
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 \(C\ll 1\).
bounds for derivatives of five macroscopic moduli
elastic transversely isotropic porous materials
inhomogeneous stress boundary conditions
scientific article; zbMATH DE number 3930429