The representative unit cell (RUC) model of elastic heterogeneous solid with imperfectly bonded ellipsoidal inhomogeneities is developed. The periodic displacement solution has been obtained by combining the superposition principle, Papkovich-Neuber representation of displacement in terms of scalar harmonic potentials and expansion of these potentials in terms of periodic ellipsoidal harmonics. By accurate fulfilling the interface conditions, the RUC model boundary value problem is reduced to an infinite system of linear algebraic equations for the series expansion coefficients. The modified Rayleigh homogenization scheme has been extended to the elastic composite with ellipsoidal inhomogeneities and imperfect interface. The scheme takes into account volume content and elastic moduli of constituents, shape, size and arrangement of inhomogeneities, interaction between them and elastic stiffness of interface. Numerical algorithm of the method provides an accurate analysis of the RUC model for a whole range of the structure parameters. The reported numerical data illustrate convergence rate of the series solution and discover an effect of the volume content, elastic properties and arrangement of particles and interface stiffness on the stress field and macroscopic elastic moduli of the ellipsoidal particle composite.

建立了具有不完美结合的椭球不均匀性的弹性非均质固体的代表性晶胞（RUC）模型。通过组合叠加原理，就标量谐波势而言的位移的Papkovich-Neuber表示和就周期椭圆谐波而言的这些势的扩展，可以得到周期位移解。通过精确地满足界面条件，RUC模型边值问题被简化为级数展开系数的线性代数方程的无限系统。改进的瑞利均质化方案已扩展到具有椭圆形不均匀性和不完美界面的弹性复合材料。该方案考虑了成分的体积含量和弹性模量，形状，大小和不均匀性的排列，它们之间的相互作用和界面的弹性刚度。该方法的数值算法为整个结构参数范围提供了RUC模型的准确分析。所报道的数值数据说明了级数解的收敛速度，并发现了体积含量，颗粒的弹性特性和排列以及界面刚度对椭圆形颗粒复合材料的应力场和宏观弹性模量的影响。