Traditional equivalent inclusion method provides unreliable predictions of the stress concentrations of two spherical inhomogeneities with small separation distance. This paper determines the stress and strain fields of multiple ellipsoidal/elliptical inhomogeneities by equivalent inhomogeneous inclusion method. Equivalent inhomogeneous inclusion method is an inverse of equivalent inclusion method and substitutes the subdomains of matrix with known strains by equivalent inhomogeneous inclusions. The stress and strain fields of multiple inhomogeneities are decomposed into the superposition of matrix under applied load and each solitary inhomogeneous inclusion with polynomial eigenstrains by the iteration of equivalent inhomogeneous inclusion method. Multiple circular and spherical inhomogeneities are respectively used as examples and examined by the finite element method. The stress concentrations of multiple inhomogeneities with small separation distances are well predicted by equivalent inhomogeneous inclusion method and the accuracies improve with the increase of eigenstrain orders. Equivalent inhomogeneous inclusion method gives more accurate stress predictions than equivalent inclusion method in the problem of two spherical inhomogeneities.

传统的等效夹杂方法无法可靠地预测两个球面不均匀性以及较小的分离距离的应力集中。本文通过等效不均匀夹杂法确定了多个椭圆形/椭圆形不均匀性的应力场和应变场。等效不均匀包含方法是等效包含方法的逆方法，它用等效不均匀包含替换已知应变的矩阵子域。通过等价非均质包含方法的迭代，将多个非均质的应力场和应变场分解为外加载荷作用下的矩阵叠加，以及每个具有多项式特征应变的孤立非均质包含。多个圆形和球形不均匀性分别用作示例，并通过有限元方法进行了检验。用等效的非均质夹杂方法可以很好地预测具有较小分隔距离的多个非均质应力集中，并且随着本征应变阶数的增加，精度会提高。在两个球面不均匀性的问题上，等效的非均质夹杂法比等效的夹杂法能提供更准确的应力预测。