On the eigenstrain problem of a spherical inclusion with an imperfectly bonded interface

This article provides a comprehensive theoretical treatment of the eigenstrain problem of a spherical inclusion with an imperfectly bonded interface. Both tangential and normal discontinuities at the interface are considered and a linear interfacial condition, which assumes that the tangential and the normal displacement jumps are proportional to the associated tractions, is adopted. The solution to the corresponding eigenstrain problem is obtained by combining Eshelby’s solution for a perfectly bonded inclusion with Volterra’s solution for an equivalent Somigliana dislocation field which models the interfacial sliding and normal separation. For isotropic materials, the Burger’s vector of the equivalent Somigliana dislocation is exactly determined, the solution is explicitly presented and its uniqueness demonstrated. It is found that the stresses inside the inclusion are not uniform, except for some special cases.