Capturing nanoscale effects by peridynamics

Molecular dynamic simulations inevitably demand large computational resources for structures of liner measures even as small as a few tens or hundreds of nanometers. Thus, a computationally efficient method to simulate larger structures and, at the same time, retain the properties and the mechanical response at the atomic scale is in demand. One such approach is peridynamics, which is a nonlocal extension of continuum mechanics. In this study, we investigate the possibility to efficiently reproduce results from molecular dynamic (MD) simulations by calibration of two parameters inherent in peridynamics: the length scale parameter and the interparticle bond strength. The free-ware LAMMPS supports both numerical approaches, and thus LAMMPS has been used as the common framework. Beams of single-crystal fcc copper of various sizes and under tension along the crystallographic [100]- and [110]-directions act as the modeling example. The force-displacement curves and the elastic-plastic transitions have been compared between the approaches. The conclusion is that proper calibration of the peridynamic two parameters to MD simulations results in proper reproduction of the molecular dynamic results. This in turn allows for geometrical upscaling or simulation of geometrically more complicated structures, without loss of features derived from the atomic scale but to a much lower computational cost.