The stiffness of an elastic solid with an embedded,nominally spherical inclusion subjected to a small arbitrary motion

The article examines the problem of translation and rotation of a nominally (slightly deformed) spherical rigid inclusion embedded into an unbounded elastic medium. To the first order in the small parameter characterizing the boundary perturbation, explicit expressions are deduced for the induced displacement field as well as for the net force and net torque required to produce the applied translation and rotation.