Dynamic constraints predict the relaxation of granular materials

TL;DR

This paper investigates how dynamic constraints influence the relaxation behavior of granular materials under cyclic shear, revealing a non-monotonic relationship between relaxation time and friction through simulations and theory.

Contribution

It introduces the concept of dynamic constraints to explain re-entrant relaxation dynamics in granular packs, unifying frictionless and frictional system behaviors.

Findings

Relaxation time varies non-monotonically with friction.

Dynamic constraints cause re-entrant relaxation behavior.

Theoretical framework applies to complex systems with time-dependent constraints.

Abstract

Granular materials such as sand, powders, and food grains are ubiquitous in civil engineering, geoscience, agriculture, and medicine. While the influence of friction between the grains on the static structure of these systems is well understood, its impact on the dynamics is an open problem. Here we use particle-based simulations of a granular pack under cyclic shear and discover that the relaxation time of the system is a non-monotonic function of friction. By introducing the concept of dynamic constraints, we reveal that this re-entrant dynamics is due to the competition between increasing frictional coupling and a concurrent change in the structure of the granular pack. Our theoretical approach, which unifies the dynamics of friction-less systems with frictional ones, is applicable to other systems that have a complex free energy landscape and a dynamics which involves time-dependent constraints, thus setting the stage for a description of the dynamic behavior of a large class of complex systems.