Structural evolution of granular systems: Theory

TL;DR

This paper develops a first-principles theoretical framework for understanding how the structure of planar granular systems evolves over time, focusing on cell order distribution and its dynamic behavior.

Contribution

It introduces a formalism for modeling the evolution of granular structures based on contact event rates, applicable to various system states and extendable to other structural features.

Findings

Convergence to steady state is exponential in most cases.

Approach to steady state is algebraic when only contact breaking occurs.

Dynamics are highly sensitive to contact event rates.

Abstract

A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of examples: dense systems undergoing progressive compaction; initial dilation of very dense systems; and the approach to steady state of general systems. It is shown that the convergence to steady state is exponential, except when contacts are only broken and no new contacts are made, in which case the approach is algebraic in time. Where no closed form solutions are possible, illustrative numerical solutions of the evolution are shown. These show that the dynamics are sensitive to the cell event rates, which are process dependent. The formalism can be extended to other structural characteristics, paving the way to a general theory of structural organisation of granular systems, parameterised by the contact event rates.