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.
Keywords
spherical elastic inhomogeneity, interface slip and
diffusion, deviatoric far-field load, relaxation time,
state-space equation, uniform stress state
