Multi-Scale Modeling for Combined Shock-Shear Initiation of Energetic Solids

Multi-scale interactions between initially planar deformation waves in heterogeneous energetic solids and macro-scale boundaries were computationally examined to characterize wave interaction structures and dissipative heating responsible for combustion initiation. The macro-scale response was described by a continuum theory that accounts for elastic and inelastic volumetric deformation in a thermodynamically consistent manner; the model equations were numerically integrated in terms of generalized curvilinear coordinates using a high-resolution shock-capturing technique. The mesoscale scale response was described by conservation principles and an elastic-viscoplastic constitutive theory to predict contact induced nonlinear deformation and thermomechanical fields within particles; the model equations were numerically integrated using a combined finite and discrete element technique. Predicted meso-scale fields were locally averaged and compared to independent predictions given by the macro-scale model. Wave-boundary interactions resulted in dispersed wave structures that are analogous to Mach stems in gas dynamics, with maximum dissipative heating rates occurring within the stem region along bounding surfaces away from the stagnation region. These maximum heating rates substantially increased the fraction of mass locally heated to elevated temperature. Bulk shear was shown to have a small effect on dissipative heating for the impact conditions investigated in this study. The dependence of wave structure, dissipative heating rate, and hot-spot mass fraction on initial wave strength was characterized. Macroand meso-scale predictions agreed well, provided that the averaging volume size was suitably chosen.