A new one-dimensional, unsteady continuum model is numerically solved to predict dynamic compaction and localized heating of an initially stress-free granular reactive solid (HMX) having non-uniform porosity. The material loading response is dependent on its strain history as the stress necessary for inelastic compaction (crush-up) increases with initial porosity. A high-resolution numerical method is combined with a parallel computing strategy to accurately and efficiently solve the hyperbolic model equations. Numerical predictions indicate that significant localized heating results from inelastic compaction of materials having densely packed regions adjacent to highly porous regions. A grain surface heat flux of 189 MW/m~2 is predicted for a piston impact speed of 100 m / s for a material having a spatial variation in initial solid volume fraction within the range Φ_(fp) ≡ 0.655 ≤ Φ_0(x) ≤ 0.999, where Φ_(fp) is the free-pour value. The grain surface temperature rise within the compaction wave structure is estimated to be in excess of 400 K based on an energy localization analysis. This temperature rise is sufficient to initiate HMX combustion, and is consistent with experimental observations which indicate prompt combustion initiation due to dynamic compaction of granular HMX having comparable porosity variations.
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