On stress relaxation timescales for dense binary particulate systems

Abstract

We study contact stress relaxation timescales, especially the temporal correlation involved in dense binary particulate systems, which o ers insight into the intriguing relationship between the contact stresses and the contact time of particle interactions under non-equilibrium state. The contact time (also referred to as contact age) of a pair of particles is de ned by the duration between current time and the instant when the contact was formed. The interspecies inter-particles contact stresses are derived from Liouville's theorem. We apply particle dynamics methods (e.g. molecular dynamics, discrete element method) to simulate 3D dense binary particulate systems with periodic boundary conditions. External perturbation is exerted on the system to balance the dissipation of energy due to the viscoelastic collisions. The contact stresses, Reynolds stresses, and the probability density function of the contact time of particles are predicted at di erent volume fraction of particles. The obtained stress-strain rate data are used to examine the constitutive relation of macroscopic materials. The study targets the impact of the short-term and the long-term contact/collision on the contact stress relaxation. The simulation results reveal distinct e ects of the short-term and the long-term contact/collision on the contact stresses, which have been treated by only an averaged expression of particle interactions in discrete element methods before.