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).

这项研究利用应变能密度函数的三阶展开和有限应变弹性理论来导出轴对称载荷条件下的孤立球形空隙的解析解。该解决方案已通过先前发表的针对不可压缩材料和静水压力的结果进行了验证。使用这种新解决方案和均质化方法，可以得出包含稀疏空隙分布的材料的有效线性和非线性特性。有效的非线性弹性特性通常显示出比线性弹性特性对空隙浓度更为敏感。