Inclusion problem with dislocation-like imperfect interface

The exact solution to spherical inclusion problem with imperfect interface is presented. Using the dislocation-like imperfect interface model, a spherical inclusion embedded in an infinitely extended body with uniform stress at infinite is considered. Based on the direct method developed by Luré to solve symmetrically loaded sphere problems, spherical harmonic functions are introduced to express the displacement components. With the dislocation-like boundary conditions, the displacements fields inside and outside the inclusion are obtained in explicit form, respectively. Then the stress field in the whole domain is concluded relevantly.