The effect of viscoplastic deformation of the energetic material HMX on the mechanical, thermal, and ignition response of a two-phase (HMX and Estane) polymer bonded explosive (PBX) is analyzed. Specific attention is given to the high strain rate response of the material during the first passage of the stress wave when impacted by a constant velocity piston. PBX microstructures are subjected to impact loading from a constant velocity piston traveling at a rate of 50 to 200 m/s using a 2D cohesive finite element (CFEM) framework. The initial focus is to fully quantify the effect that viscoplastic HMX has on the behavior of a PBX composite, a thorough thermo-mechanical analysis is performed. The thermal response of the PBX specimens having viscoplastic HMX is characterized by a significant reduction in average heating, peak temperature rise, and the number or amount of material experiencing localized heating (hotspots). This reduction in heating is found to be accomplished through the mechanism of greatly reducing the density of fracture in the PBX. The second focus of this work is to evaluate the ignition sensitivity of these materials to determine the effect, if any, of the viscoplastic HMX. Viscoplastic HMX is shown to increase the minimum load duration, mean load duration, and range of critical load durations required for ignition. A 3D crystal plasticity framework is employed to quantify the potential heterogeneities in the stress and temperature field resulting from the inherent crystalline anisotropy of the HMX grains. It is found that in a densely packed HMX, the heterogeneities due to material anisotropy can contribute to increased stress gradients and localized temperature rise. Finally, the 2D framework is used to study a hypothetical composite containing HMX grains suspended in an aluminum matrix. This investigation focuses not on the feasibility of producing such a composite, but on determining whether such an arrangement would be advantageous from a mechanical and ignition sensitivity standpoint. Results indicate that this hypothetical composite would be considerably less sensitive than a similar PBX.