A spherical elastic inhomogeneity with interface slip and diffusion under a deviatoric far-field load

Abstract

We study the problem of a spherical elastic inhomogeneity with simultaneous interface slip and diffusion embedded in an infinite elastic matrix subjected to a uniform deviatoric far-field load. The inhomogeneity and the matrix have separate elastic properties. Using the representations for displacements and tractions given by Christensen and Lo (1979), the original boundary value problem is ultimately reduced to a state-space equation which is then solved analytically. The field variables in the inhomogeneity and the matrix decay with two relaxation times. As time approaches infinity, the stresses inside the spherical inhomogeneity are completely relaxed to zero. Our solution recovers existing solutions in the literature when the inhomogeneity is rigid or when the inhomogeneity and the matrix have the same elastic properties. The internal spatially uniform and time-decaying stress field inside the spherical inhomogeneity is achieved when the radius of the spherical inhomogeneity is appropriately designed corresponding to interface diffusion and drag parameters.