Particle modeling of dynamic fragmentation-I: theoretical considerations

This paper series adopts particle modeling (PM) to simulation of dynamic fracture phenomena in homogeneous and heterogeneous materials, such as encountered in comminution processes in the mining industry. This first paper is concerned with the setup of a lattice-type particle model having the same functional form as the molecular dynamics (MD) model (i.e., the Lennard–Jones potential), yet on centimeter length scales. We formulate four conditions to determine four key parameters of the PM model (also of the Lennard–Jones type) from a given MD model. This leads to a number of properties and trends of resulting Young’s modulus in function of these four parameters. We also investigate the effect of volume, at fixed lattice spacing, on the resulting Young modulus. As an application, we use our model to revisit the dynamic fragmentation of a copper plate with a skew slit [J. Phys. Chem. Solids, 50(12) (1989) 1245].