  The motivation of this work is to produce an integrated formulation for
material response due to detonation wave loading. Here, we focus on
elastoplastic structural response. In particular, we are interested to capture
miscible and immiscible behaviour within condensed-phase explosives arising
from the co-existence of a reactive carrier mixture of miscible materials, and
several material interfaces due to the presence of immiscible impurities such
as particles or cavities. The dynamic and thermodynamic evolution of the
explosive is communicated to one or more inert confiners through their shared
interfaces, which may undergo severe topological change. We also wish to
consider elastic and plastic structural response of the confiners, rather than
make a hydrodynamic assumption for their behaviour. Previous work by these
authors has met these requirements by means of the simultaneous solution of
appropriate systems of equations for the behaviour of the condensed-phase
explosive and the elastoplastic behaviour of the confiners. In the present
work, we employ a single system of partial differential equations (PDEs)
proposed by Peshkov and Romenski, which is able to account for different states
of matter by means of generalising the concept of distortion tensors beyond
solids. We amalgamate that formulation with a single system of PDEs which meets
the requirement of co-existing miscible and immiscible explosive mixtures. We
present the mathematical derivation and construct appropriate algorithms for
its solution. The resulting model is validated against exact solutions for
several use-cases, including mechanically- and thermally-induced, inviscid and
viscous detonations. Results indicate that the model can accurately simulate a
very broad range of problems involving the nonlinear interaction between
reactive and inert materials within a single framework.
