Multiscale modelling of material failure using particles

Abstract

In this paper, we explore a prototypical model of material fragmentation – the penetration of a plate by a fast moving ball in two dimensions using both smooth particle applied mechanics (SPAM) and molecular dynamics (MD). Using a family of short-ranged pair potentials, we investigate the fracture as a function of impact velocity and plate strength. The MD provides data from which we make a direct comparison with SPAM simulations of the same system. The parameters for the SPAM simulations: equation of state, bulk and shear moduli, yield strength and tensile strength are obtained from the pair potentials and via non-equilibrium MD (tension test). By careful parameterisation of the SPAM model, we are able to observe qualitatively similar behaviour to that shown in the MD simulations of a single crystal (brittle) specimen; bending at low penetrator speed, cracking at higher speeds and eventually, complete penetration. The behaviour depends on the plate strength, which is directly related to details of the force law. For plates characterised as high strength, the agreement between MD and SPAM is evidently poor. We discuss the possible causes for this discrepancy. Nevertheless, SPAM, when used in conjunction with accurate atomistic simulation, is shown to be a highly promising tool for studying failure in materials.