  A general formulation was developed to represent material models for
applications in dynamic loading. Numerical methods were devised to calculate
response to shock and ramp compression, and ramp decompression, generalizing
previous solutions for scalar equations of state. The numerical methods were
found to be flexible and robust, and matched analytic results to a high
accuracy. The basic ramp and shock solution methods were coupled to solve for
composite deformation paths, such as shock-induced impacts, and shock
interactions with a planar interface between different materials. These
calculations capture much of the physics of typical material dynamics
experiments, without requiring spatially-resolving simulations. Example
calculations were made of loading histories in metals, illustrating the effects
of plastic work on the temperatures induced in quasi-isentropic and
shock-release experiments, and the effect of a phase transition.
