Molecular dynamics simulations of head-on low-velocity collisions between particles

The particle contact model is important for powder simulations. Although several contact models have been proposed, their validity has not yet been well established. Therefore, we perform molecular dynamics (MD) simulations to clarify the particle interaction. We simulate head-on collisions of two particles with impact velocities less than a few percent of the sound velocity to investigate the dependence of the interparticle force and the coefficient of restitution on the impact velocity and particle radius. In this study, we treat particles with a radius of 10-100 nm and perform simulations with up to 0.2 billion atoms. We find that the interparticle force exhibits hysteresis between the loading and unloading phases. Larger impact velocities result in strong hysteresis and plastic deformation. For all impact velocities and particle radii, the coefficient of restitution is smaller than that given by the Johnson-Kendall-Robert theory, which is a contact model that gives the force between elastic spherical particles. A contact model of inelastic particles cannot reproduce our MD simulations. In particular, the coefficient of restitution is significantly reduced when the impact velocity exceeds a certain value. This significant energy dissipation cannot be explained even by the contact models including plastic deformation. We also find that the coefficient of restitution increases with increasing particle radius. We also find that the previous contact models including plastic deformation cannot explain the strong energy dissipation obtained in our MD simulations, although they agree with the MD results for very low impact velocities. Accordingly, we have constructed a new dissipative contact model in which the dissipative force increases with the stress generated by collisions. The new stress-dependent model successfully reproduces our MD results over a wider range of impact velocities than the conventional models do. In addition, we proposed another, simpler, dissipative contact model that can also reproduce the MD results.