A master equation for force distributions in soft particle packings - Irreversible mechanical responses to isotropic compression and decompression

TL;DR

This paper develops and validates a master equation model that captures the irreversible force distribution changes in soft particle packings under cyclic quasi-static deformations, aligning well with molecular dynamics simulations.

Contribution

It introduces a detailed master equation framework for force distributions that accounts for contact opening and closing, advancing understanding of irreversible behaviors in soft particle systems.

Findings

Master equation accurately reproduces irreversible responses

Irreversibility decreases with higher area fraction

Irreversibility diminishes over multiple cycles

Abstract

Mechanical responses of soft particle packings to quasi-static deformations are determined by the microscopic restructuring of force-chain networks, where complex non-affine displacements of constituent particles cause the irreversible macroscopic behavior. Recently, we have proposed a master equation for the probability distribution functions of contact forces and interparticle gaps [K. Saitoh et al., Soft Matter 11, 1253 (2015)], where mutual exchanges of contacts and interparticle gaps, i.e. opening and closing contacts, are also involved in the stochastic description with the aid of Delaunay triangulations. We describe full details of the master equation and numerically investigate irreversible mechanical responses of soft particle packings to cyclic loading. The irreversibility observed in molecular dynamics simulations is well reproduced by the master equation if the system undergoes quasi-static deformations. We also confirm that the degree of irreversible responses is a decreasing function of the area fraction and the number of cycles.