Pressure-dependent shear response of jammed packings of spherical particles

TL;DR

This paper investigates how the shear modulus of jammed spherical particle packings depends on pressure, revealing a complex interplay between geometrical family contributions and rearrangements, and introduces the concept of compression unjamming.

Contribution

It uncovers the linear decrease of shear modulus within geometrical families and explains the overall pressure dependence through a scaling function, also demonstrating compression unjamming.

Findings

Shear modulus decreases linearly within geometrical families.

Discontinuous jumps at geometrical transitions significantly affect average shear modulus.

Compression can unjam packings, leading to unjamming via isotropic compression.

Abstract

The mechanical response of packings of purely repulsive, spherical particles to athermal, quasistatic simple shear near jamming onset is highly nonlinear. Previous studies have shown that, at small pressure $p$, the ensemble-averaged static shear modulus $\langle G-G_0 \rangle$ scales with $p^\alpha$, where $\alpha \approx 1$, but above a characteristic pressure $p^{**}$, $\langle G-G_0 \rangle \sim p^\beta$, where $\beta \approx 0.5$. However, we find that the shear modulus $G^i$ for an individual packing typically decreases linearly with $p$ along a geometrical family where the contact network does not change. We resolve this discrepancy by showing that, while the shear modulus does decrease linearly within geometrical families, $\langle G \rangle$ also depends on a contribution from discontinuous jumps in $\langle G \rangle$ that occur at the transitions between geometrical families. For $p > p^{**}$, geometrical-family and rearrangement contributions to $\langle G \rangle$ are of opposite signs and remain comparable for all system sizes. $\langle G \rangle$ can be described by a scaling function that smoothly transitions between the two power-law exponents $\alpha$ and $\beta$. We also demonstrate the phenomenon of {\it compression unjamming}, where a jammed packing can unjam via isotropic compression.