Contact Changes of Sheared Systems: Scaling, Correlations, and Mechanisms

TL;DR

This study investigates contact changes in sheared 2D soft particle packings, revealing their statistical properties, scaling behaviors, and impact on material elasticity, with implications for understanding the mechanical response of amorphous solids.

Contribution

It provides a detailed analysis of contact change mechanisms, their scaling with system size and pressure, and their effects on shear modulus, supported by linear response predictions and correlation studies.

Findings

First contact changes often involve single particles, with different behaviors at low and high pressures.

Linear response accurately predicts strains at first contact changes.

The shear modulus remains well-behaved despite contact changes occurring at small strains.

Abstract

We probe the onset and effect of contact changes in 2D soft harmonic particle packings which are sheared quasistatically under controlled strain. First, we show that in the majority of cases, the first contact changes correspond to the creation or breaking of contacts on a single particle, with contact breaking overwhelmingly likely for low pressures and/or small systems, and contact making and breaking equally likely for large pressures and in the thermodynamic limit. The statistics of the corresponding strains are near-Poissonian. The mean characteristic strains exhibit scaling with the number of particles N and pressure P, and reveal the existence of finite size effects akin to those seen for linear response quantities. Second, we show that linear response accurately predicts the strains of the first contact changes, which allows us to study the scaling of the characteristic strains of making and breaking contacts separately. Both of these show finite size scaling, and we formulate scaling arguments that are consistent with the observed behavior. Third, we probe the effect of the first contact change on the shear modulus G, and show in detail how the variation of G remains smooth and bounded in the large system size limit: even though contact changes occur then at vanishingly small strains, their cumulative effect, even at a fixed value of the strain, are limited, so that effectively, linear response remains well-defined. Fourth, we explore multiple contact changes under shear, and find strong and surprising correlations between alternating making and breaking events. Fifth, we show that by making a link with extremal statistics, our data is consistent with a very slow crossover to self averaging with system size, so that the thermodynamic limit is reached much more slowly than expected based on finite size scaling of elastic quantities or contact breaking strains.