Evolution of enduring contacts and stress relaxation in a dense granular medium

Particle contacts in a granular material are formed at different times and have different contact ages, the differences between current time and the times when the contacts were formed. The probability distribution of the contact ages is one of the important statistical properties of particle interactions. The rate of the probability relaxation is proved to be closely related to the stress evolution in the dense granular system. While all particle contacts contribute to the stress, the major contribution is from the contacts with long contact ages compared to the binary collision time of the particles in a dense and slow granular flow, in which particle inertia can be neglected. There is a spectrum of relaxation times in the probability distribution of contact ages. These relaxation times result in different time scales of stress relaxation. As an example, the relations among stress, strain, and the strain rate are studied for a dense granular material undergoing an oscillatory simple shear. The interaction of the time scales determines the fluidlike or solidlike behavior of the material.