On elastic interactions between spherical inclusions by the equivalent inclusion method

In this work three-dimensional stress distributions around interacting spherical inclusions embedded in an isotropic elastic matrix are investigated. The stress distributions around the interacting inclusions are computed by using Eshelby’s equivalent inclusion method (EIM) with constant, linear, or quadratic eigenstrains. A Taylor series expansion is employed to find the approximate solution of the EIM consistency equations. The effect of the location of a point around which a Taylor expansion is carried out on the accuracy of the EIM solution is also investigated. In addition to the EIM, finite element computations are performed to establish the robustness and accuracy of the analytical method. After validating the EIM approach, the effect of the distribution pattern of the inclusions on the radial interface stresses around several interacting inclusions is examined.