Energetic structural materials (ESMs) constitute a new class of materials that provide dual functions of strength and energetic characteristics. ESMs are typically composed of micron-scale or nano-scale intermetallic mixtures or mixtures of metals and metal oxides, polymer binders, and structural reinforcements. Voids are included to produce a composite with favorable chemical reaction characteristics.

In this thesis, a continuum approach is used to simulate gas-gun or explosive loading experiments where a strong shock is induced in the ESM by an impacting plate. Algorithms are developed to obtain equations of state of mixtures. It is usually assumed that the shock loading increases the energy of the ESM and causes the ESM to reach the transition state. It is also assumed that the activation energy needed to reach the transition state is a function of the temperature of the mixture. In this thesis, it is proposed that the activation energy is a function of temperature and the stress state of the mixture. The incorporation of such an activation energy is selected in this thesis. Then, a multi-scale chemical reaction model for a heterogeneous mixture is introduced. This model incorporates reaction initiation, propagation, and extent of completed reaction in spatially heterogeneous distributions of reactants. A new model is proposed for the pore collapse of mixtures. This model is formulated by modifying the Carol, Holt, and Nesterenko spherically symmetric model to include mixtures and compressibility effects.

Uncertainties in the model result from assumptions in formulating the models for continuum relationships and chemical reactions in mixtures that are distributed heterogeneously in space and in numerical integration of the resulting equations. It is important to quantify these uncertainties. In this thesis, such an uncertainty quantification is investigated by systematically identifying the physical processes that occur during shock compression of ESMs which are then used to construct a hierarchical framework for uncertainty quantification.