Multiscale modeling of impact through molecular dynamics and smooth particle hydrodynamics

We study the problem of a projectile impacting on a target at different length scales employing two widely used techniques — molecular dynamics (MD) simulations at atomistic scales and smooth particle hydrodynamics (SPH) at continuum scales. At the atomistic scale, the impact problem is modeled through a short-ranged pair potential whereas, at the continuum scale, the partial differential equations related to the different conservation equations are solved using SPH. SPH is parametrized in a manner that the equation of state and the elastic constants match those of the underlying MD simulations. We evaluate a number of recent improvements to the SPH framework – artificial viscosity, XSPH, Jaumann stress rotation, tensile instability, and mass initialization – by making a systematic comparison between an SPH model with varying degrees of these corrections, and a model based on MD, which acts as the pseudo experiment. We show that if all corrections are incorporated, the SPH results agree well with those from MD simulations. This has been ascertained by comparing the deformation response, the radial distribution function, and the shear strain.