The ellipsoidal inhomogeneity with transversely isotropic incoherent interface is considered in the conductivity and elasticity context. The general imperfect interface is modeled by the first order approximation of thin transversely isotropic interphase layer. This model expands the Gurtin et al. (1998) theory of curved deformable interfaces in solids with a nanometer-scale microstructure to the incoherent interfaces between the dissimilar elastic materials and provides a certain insight into the interface moduli. The rigorous analytical solution to the conductivity and elasticity problems has been obtained by the multipole expansion method in terms of ellipsoidal solid harmonics. An accurate fulfillment of the imperfect interface conditions reduces the model boundary value problem to the linear algebraic system for multipole strengths. These results apply equally to the inhomogeneities with anisotropic interphases and nano level incoherent interfaces. The obtained solutions are valid for the non-uniform far loading and are readily incorporated in the many-particle (finite cluster or representative unit cell) model of heterogeneous solid with anisotropic incoherent interface. The tensors of effective conductivity and elastic stiffness of composite with ellipsoidal inhomogeneities are evaluated using Maxwell homogenization scheme. The obtained accurate numerical data indicate that the effective properties of composite may vary widely due to shape of inhomogeneities and the interface anisotropy ratio. Taking the incoherency of interface into account may increase reliability of predicting the behavior of nanostructured solids.

在电导率和弹性方面考虑了具有横向各向同性非相干界面的椭球不均匀性。一般的不完美界面由薄横向各向同性界面层的一阶近似建模。该模型扩展了 Gurtin 等人。(1998) 具有纳米级微观结构的固体中弯曲变形界面与不同弹性材料之间的非相干界面的理论，并提供了对界面模量的一定了解。电导率和弹性问题的严格解析解已经通过椭球固体谐波的多极展开方法获得。不完美界面条件的准确满足将模型边界值问题简化为多极强度的线性代数系统。这些结果同样适用于具有各向异性界面和纳米级非相干界面的不均匀性。获得的解决方案对于非均匀远载荷是有效的，并且很容易合并到具有各向异性非相干界面的异质固体的多粒子（有限簇或代表性晶胞）模型中。使用麦克斯韦均匀化方案评估具有椭圆体不均匀性的复合材料的有效电导率和弹性刚度的张量。获得的精确数值数据表明，由于不均匀的形状和界面各向异性比，复合材料的有效性能可能会有很大差异。考虑界面的不连贯性可能会增加预测纳米结构固体行为的可靠性。