Rigidity transition of a highly compressible granular medium

TL;DR

This study investigates how large shape changes in highly deformable granular materials influence their rigidity, revealing a transition from a yielded to a solid state driven by density, shear amplitude, and friction effects.

Contribution

It introduces a model experimental system with highly compressible elastic rings to study rigidity transitions in disordered materials, highlighting the role of friction and geometry.

Findings

Rigidity transition from yielded to solid state with increased density or decreased shear amplitude.

Emergence of an effective attractive shear force between rings due to friction-geometry interplay.

Contact extent controls the rigidity transition when friction is sufficiently high.

Abstract

A wide range of disordered materials, from biological to geological assemblies, feature discrete elements undergoing large shape changes. How significant geometrical variations at the microscopic scale affect the response of the assembly, in particular rigidity transitions, is an ongoing challenge in soft matter physics. However, the lack of a model granular-like experimental system featuring large and versatile particle deformability impedes advances. Here, we explore the oscillatory shear response of a sponge-like granular assembly composed of highly compressible elastic rings. We highlight a progressive rigidity transition, switching from a yielded phase to a solid one by increasing density or decreasing shear amplitude. The rearranging yielded state consists of crystal clusters separated by melted regions; in contrast, the solid state remains amorphous and absorbs all imposed shear elastically. We rationalize this transition by uncovering an effective, attractive shear force between rings that emerges from a friction-geometry interplay. If friction is sufficiently high, the extent of the contacts between rings, captured analytically by elementary geometry, controls the rigidity transition.