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A multiscale model is used to analyze the compaction processes in granular HMX beds composed of different particle sizes (coarse particles,  d=40  μm and microfine particles,  d=4  μm). The localization strategy of Gonthier is extended to include changes in thermal energy induced by compression. The variation in yield strength caused by solid-liquid phase change is also considered. Analysis of the steady-state wave structure indicates that the compaction behavior of a porous material is dependent on particle size. For solid volume fraction  φ s  &lt; 0.88 , the fine particle beds provide greater resistance to compaction than the coarse particle beds, and they propagate compaction waves that travel at faster speeds. When  φ s  &gt; 0.88 , the physical state of the compacted bed has become very similar for the two materials. For subsonic compaction waves, the evolution of the grain temperature shows that large particles lead to large hot spots and high temperature and coarse particles are more shock sensitive at low shock pressures. For supersonic compaction waves, compression induced changes in thermal energy play an important role in localization strategy. It increases the localization sphere center radius. The dissipated energy is deposited over a larger localization volume so that the grain temperature near the intergranular contact surface is reduced significantly. The localization center radius further increases because of the decrease in the yield strength caused by solid–liquid phase change. Consequently, the peak grain temperature is reduced further.

Multiscale Analysis of Particle Size-dependent Steady Compaction Waves in Granular Energetic Materials