A Method for Tractable Dynamical Studies of Single and Double Shock Compression

A new multiscale simulation method is formulated for the study of shocked materials. The method combines molecular dynamics and the Euler equations for compressible flow. Treatment of the difficult problem of the spontaneous formation of multiple shock waves due to material instabilities is enabled with this approach. The method allows the molecular dynamics simulation of the system under dynamical shock conditions for orders of magnitude longer time periods than is possible using the popular nonequilibrium molecular dynamics approach. An example calculation is given for a model potential for silicon in which a computational speedup of ${10}^5$ is demonstrated. Results of these simulations are consistent with the recent experimental observation of an anomalously large elastic precursor on the nanosecond time scale.

Figure 1

Rayleigh lines on a hypothetical Hugoniot.

Figure 2

Flowchart for simulation of a shock to a chosen pressure or particle velocity boundary condition. Instabilities due to regions where $d^{2}p/d{v}^2<0$ along the Hugoniot can give rise to a discontinuity in the inset plot.

Figure 3

Comparison of calculated Hugoniots for the NEMD approach and the method presented in this Letter for roughly 10 ps runs. Note the ability to utilize much smaller computational cell sizes with the new method. Also included is one data point for a 5 ns simulation using this work which would be prohibitive with NEMD requiring a factor of ${10}^5$ increase in computational effort.