A long-standing area of research for computational shock physics has been the treatment of mixed materials. A mixed material volume is defined as a control volume space where two or more materials coexist as immiscible materials having separate densities and energies that have non-equilibrium stress and thermal states. In traditional computational shock physics framework, a mixture of materials can occupy a control volume having a common velocity corresponding to the mixture center of mass. In this work, this assumption is relaxed and separate densities, energies and velocities are used to characterize non-equilibrium material behavior. To accomplish this task, this work builds upon the original two-phase Baer and Nunziato model by extending the two-phase theory to N-phases. Specifically, this work is based on the development by Drumheller to derive a new N-phase mixture theory that incorporates deformation mechanics using the deformation gradient with a full stress tensor.

计算冲击物理学的一个长期研究领域是混合材料的处理。混合材料体积被定义为控制体积空间，其中两种或更多种材料作为具有不同密度和能量的不混溶材料共存，具有非平衡应力和热状态。在传统的计算冲击物理框架中，材料混合物可以占据一个控制体积，该体积具有对应于混合物质心的共同速度。在这项工作中，这一假设被放宽，并使用单独的密度、能量和速度来表征非平衡材料行为。为了完成这项任务，这项工作建立在原始的两相 Baer 和 Nunziato 模型的基础上，将两相理论扩展到 N 相。具体来说，