Localized Heating due to Stress Concentrations Induced in a Lossy Elastic Medium via the Scattering of Compressional Waves by a Rigid Spherical Inclusion

High-frequency mechanical excitation has been shown to generate heat within composite energetic materials and even induce reactions in single energetic crystals embedded within an elastic binder. To further the understanding of how wave scattering effects attributable to the presence of an energetic crystal can result in concentrated heating near the inclusion, an analytical model is presented. The stress and displacement solutions associated with the scattering of compressional plane waves by a spherical obstacle (Pao and Mow, 1963) are modified to account for the viscoelastic effects of the lossy media surrounding the inclusion (Gaunaurd and Uberall, 1978). The results from this solution are then utilized to estimate the spatial heat generation due to the harmonic straining of the material, and the temperature field of the system is predicted for a given duration of time. It is shown that for certain excitation and sample configurations, the elicited thermal response near the inclusion may approach, or even exceed, realistic decomposition temperatures of various energetic materials. Although this prediction indicates that viscoelastic heating of the binder may initiate the decomposition of the crystal even in the absence of defects such as initial voids or debonding between the crystal and binder, the thermal response resulting from this bulk heating phenomenon may be a precursor to dynamic events associated with such crystal-scale effects.