Generalized continuum mixture theory for multi-material shock physics

Abstract

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.