Eulerian Finite Volume Method for High Deformation Multi-Material Hydrodynamics

A finite volume method for high-strain rate multi-material hydrodynamics on unstructured meshes is presented. Thermodynamically consistent hyper-elastic constitutive laws are used to model solid materials. Plastic deformations are modeled using the plastic deformation rate tensor. This involves adding source terms in the deformation gradient equations, leading to mathematically stiff equations. An Implicit-Explicit (IMEX) Runge-Kutta time integrator is used to handle this stiffness by selectively treating these plastic sources implicitly. This relaxes the severe time step restrictions imposed by plasticity, while enhancing accuracy of the time-integration. Furthermore, each material has its own thermodynamic state (pressure, temperature, deformation gradients), which provides a more accurate representation of the underlying physics, rather than enforcing equilibrium between materials with widely different material properties. As a result, the proposed method will enable accurate solutions to high strain-rate solid dynamics problems in several key multi-physics scenarios. Several test cases are provided to validate our approach.