Constant-stress Hugoniostat method for following the dynamical evolution of shocked matter

We present an alternative equilibrium molecular dynamics method-the uniaxial constant-stress Hugoniostat-for following the dynamical evolution of condensed matter subjected to shock waves. It is a natural extension of the recently developed uniaxial constant-volume Hugoniostat [ Maillet , Phys. Rev. E 63, 016121 (2001) ]. Integral feedback is employed to reach the Hugoniot (final) state of the shock process by controlling both the normal component of the stress tensor and internal energy. The finite strain rate imposed on the system is closely related to that inherent in the front of a shock wave. The method can easily identify phase transitions along the Hugoniot shock states, even those that exhibit multiple wave structures. As an example of the method, we have simulated the Hugoniot of a Lennard-Jones crystal shocked along the <110> direction. The results agree well with multi-million-atom nonequilibrium molecular-dynamics simulations.