Molecular dynamics of shock fronts and their transitions in Lennard-Jonesium and Tin

We develop a Continuous Hugoniot Method for the efficient simulation of shock wave fronts with molecular dynamics. This approach achieves a significantly improved efficiency in the generation of a dense sampling of steady-state shock front states, and allows for the study of shocks as a function of a continuous shock strength parameter, $v_p$. This is, to our knowledge, the first attempt to map out the Hugoniot in a continuous fashion. We first apply this method to shocks in single-crystal Lennard-Jonesium along the <100> direction. Excellent agreement is found with both the published Lennard-Jones Hugoniot and results of conventional simulation methods. We next present a continuous numerical Hugoniot for shocks in tin which agrees to within 6% with experimental data. We study the strong shock to elastic-plastic shock transition in tin and find that it is a continuous transition consistent with a transcritical bifurcation.