Multiscale modelling for equations of state

When modelling the shock response of a material it is imperative to have a physically-based equation of state. These can be expensive and difficult to measure. Existing formulations can also be somewhat lacking if strength considerations need to be included. Modifications to materials are difficult to account for quickly within a program of work. An hierarchical approach is suggested that overcomes these obstacles and also takes into account the different approaches needed for different materials. We find good predictions for simple crystals using quantum mechanics codes. Further up the hierarchy of length scales it is seen that molecular dynamics and molecular mechanics is useful in determining pressure-volume-energy relations for polymers and organic macromolecules. A simplified mean field approach using atomistic parameters can give analytic functionality and serves as a bridge between the lower length scales and the thermodynamic length scales. Composite models can be formulated from models of the constituents. The approach provides results that can be implemented into hydrocodes in tabulated form and then validated from a few experimental points. The tools with which to carry out this hierarchical approach are readily available in the literature and in commercially-available software.