Faxén relations in solids - A generalized approach to particle motion in elasticity and viscoelasticity

A movable inclusion in an elastic material oscillates as a rigid body with six degrees of freedom. Displacement/rotation and force/moment tensors which express the motion of the inclusion in terms of the displacement and force at arbitrary exterior points are introduced. Using reciprocity arguments two general identities are derived relating these tensors. Applications of the identities to spherical particles provide several new results, including simple expressions for the force and moment on the particle due to plane wave excitation.