Interaction of harmonic plane waves with a mobile elastic phase boundary in anti-plane shear

This paper is concerned with the effect of sustained infinitesimal harmonic plane wave excitation of a phase boundary in a non-linearly elastic material that is subject to anti-plane shear deformation. The phase boundary is capable of motion that is here described by a harmonic travelling waveform. The reflected wave is also a harmonic plane wave, however the transmitted wave may be either in the form of a harmonic plane wave or a harmonic surface wave. The phase boundary motion is determined on the basis of a standard kinetic relation that involves a single mobility parameter. This gives phase boundary motion that is synchronized with the incident wave for the case of a transmitted plane wave, but is not synchronized with the incident plane wave for the case of a transmitted surface wave. A certain fraction of the energy provided by the incident wave is dissipated by phase boundary motion in a fashion that can be explicitly quantified. Special incident angles can suppress the reflected wave, suppress the transmitted wave or cause the dissipation to vanish.