Development of a one-dimensional moving window CAC framework to model long-time shock wave propagation

We develop a long-time moving window framework using the Concurrent Atomistic-Continuum (CAC) method to model shock wave propagation and interaction along a one-dimensional monoatomic chain. The moving window formulation follows a propagating shock wave allowing us to model shock propagation much longer than conventional non-equilibrium MD (NEMD) simulations. Additionally, the framework significantly decreases the required domain size and thus reduces the overall computational cost. The method uses CAC to divide the domain into an inner refined region containing the shock wave flanked on either end by coarse-grained regions which incorporate continuum shock conditions. We first perform verification studies to ensure that the system is properly coupled and can reproduce the correct phonon dispersion relation. Next, we update the governing equation to allow waves to pass between the atomistic and coarse-grained regions. Currently, we are implementing a scheme to simultaneously refine the continuum region as well as coarsen the atomistic region at the speed at which the shock wave moves. This will allow us to simulate long-time shock wave propagation and eventually model microstructural shock interactions with dislocations and/or other materials. Such research is necessary because while existing concurrent schemes have been very successful in modeling material defects and their motion, they have not yet been extended to model shock wave propagation through a material.