In the present work, solutions are recapitulated according to the theory of elasticity for the deformations of an adhesive spherical inhomogeneity in an infinite matrix under remote uniform axial and axial-symmetrical radial tension. Stress fields in the inhomogeneity and at the interface in the matrix are provided, too. It is shown that the sphere is deformed to a spheroid under any of the loading cases considered. Due to the axial-symmetric setup of the problem, the deformation is fully described by the two displacement values at line segments on the principal axes of the spheroid. The displacements depend on the applied remote load and on two traction fields at the inhomogeneity-matrix interface. For any combination of inhomogeneity and matrix stiffness, the condition of compatibility of deformations yields a system of two linear equations with the two magnitudes of the tractions as unknowns. Thus, the problem is reduced to a formulation for solving a twofold statically indetermined structure. The system is solved and the exact solution of the general spherical inhomogeneity problem with differing stiffness in terms of Young’s moduli and Poisson’s ratios of inclusion and matrix is presented.

在目前的工作中，根据弹性理论概括了在远距离均匀的轴向和轴向对称径向张力下，无限基质中胶粘剂球形不均匀性变形的解决方案。还提供了非均匀性和基体界面处的应力场。结果表明，在任何考虑的载荷情况下，球体都变形为球体。由于该问题的轴对称设置，变形由椭球体主轴线段上的两个位移值完全描述。位移取决于所施加的远程载荷以及不均匀性-矩阵界面上的两个牵引场。对于不均匀性和基体刚度的任何组合，形变的相容性条件产生了一个由两个线性方程组成的系统，两个牵引力的大小未知。因此，该问题被简化为用于解决双重静态确定的结构的公式。对该系统进行了求解，并给出了根据杨氏模量和包含体与基体的泊松比之不同刚度的一般球形非均匀性问题的精确解。