A constitutive model has been developed to model the shock response of single crystal aluminum from peak pressures ranging from 2-110 GPa. This model couples a description of higher-order thermoelasticity with a dislocation-based viscoplastic formulation, both of which are formulated for single crystals. The constitutive model has been implemented using two numerical methods: a plane wave method that tracks the propagating wave front; and an extended one-dimensional, finite-difference method that can be used to model spatio-temporal evolution of wave propagation in anisotropic materials. The constitutive model, as well as these numerical methods, are used to simulate shock wave propagation in single crystals, polycrystals, and pre-textured polycrystals. Model predictions are compared with extensive existing experimental data and are then used to quantify the influence of the initial material state on the subsequent shock response. A coarse-grained model is then proposed to capture orientation-dependent deformation heterogeneity, and is shown to replicate salient features predicted by direct finite-difference simulation of polycrystals in the weak shock regime. The work in this thesis establishes a general framework that can be used to quantify the influence of initial material state on subsequent shock behavior not only for aluminum single crystals, but for other face-centered cubic and lower symmetry crystalline metals as well.

The research presented in this dissertation presents a methodology to experimentally predict and simulate the mechanical behavior of polymers under high strain rate deformation. Specifically, the interplay between the effects of temperature and strain rate on polymer behavior is examined and then used as a tool to help recreate the high rate mechanical response of several different polymers: ranging from rubbers to amorphous polymers to composites. Multiple literature reviews are conducted and presented in this thesis, e.g. experimental mechanics test methods, high rate behavior, time-temperature equivalence, constitutive modeling, and temperature measurement methods. In accordance with mechanical theory, an experimental and analytical protocol in rate- and temperature- dependence was applied to a range of PVC materials ranging in plasticizer contents. Further to this, these PVC materials were modeled with a rubbery model describing the network stress seen in polymer behavior, and an amorphous polymer model to describe PVC low to high rate responses to deformation. This modeling develops insights in the adiabatic nature of high rate response. Time-temperature equivalence, and the temperature rise during adiabatic deformation, are studied and exploited in order to implement a proposed experimental method which simulates the high rate deformation of polymeric materials. The development of an experimental methodology to simulate and predict high rate behavior is presented, applied, and expanded to a range of materials: amorphous polymers (e.g. PVC 20wt% plasticizer, PMMA, PC) and composites (e.g. polymer bonded explosive simulant). The work also presents and highlights the fact that micro to nano-scale imaging may be used in parallel with the simulation method in order to better understand high rate behavior. Furthermore, in result of the studies conducted in this body of work, several novel techniques were developed, or improved upon, and applied to the current research (e.g. additions to time-temperature equivalence, temperature measurement methods at high, moderate, and low strain rates, and a method for measuring the high rate behavior of soft materials).