Faxen relations in solids - a generalized approach to particle motion in elasticity and viscoelasticity

Abstract

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.

11 pages, 4 figures

References in corpus (1)

• Impedance of a sphere oscillating in an elastic medium with and without slip

Cited by in corpus (5)

• Forces on rigid inclusions in elastic media and resulting matrix-mediated interactions
• Reversible magnetomechanical collapse: virtual touching and detachment of rigid inclusions in a soft elastic matrix
• Forces and torques on rigid inclusions in an elastic environment: resulting matrix-mediated interactions, displacements, and rotations
• Memory-based mediated interactions between rigid particulate inclusions in viscoelastic environments
• Force-induced elastic matrix-mediated interactions in the presence of a rigid wall