Effect of randomly distributed voids on effective linear and nonlinear elastic properties of isotropic materials

Abstract

This study utilises a third-order expansion of the strain energy density function and finite strain elastic theory to derive an analytical solution for an isolated, spherical void subjected to axisymmetric loading conditions. The solution has been validated with previously published results for incompressible materials and hydrostatic loading. Using this new solution and a homogenisation methodology, the effective linear and nonlinear properties of a material containing a dilute distribution of voids are derived. The effective nonlinear elastic properties are shown to be typically much more sensitive to the concentration of voids than the linear elastic properties. The derived analytical expressions for effective material properties may be useful for the development and justification of new experimental methods for the evaluation of porosity and theoretical models describing the evolution of mechanical damage associated with void nucleation and growth (e.g. creep).