Origin of Rigidity in Dry Granular Solids

TL;DR

This paper proposes a new theoretical framework explaining shear rigidity in dry granular solids as a force-space symmetry breaking, contrasting with traditional density-based mechanisms, and validates it with experimental shear-jammed states.

Contribution

It introduces a force-space symmetry breaking perspective for shear rigidity in granular materials, challenging traditional density-based paradigms.

Findings

Shear rigidity in granular solids arises from force-space symmetry breaking.

Shear-jammed states exhibit persistent non-uniform force-space density modulations.

Theoretical predictions align with experimental observations of shear-jammed states.

Abstract

Solids are distinguished from fluids by their ability to resist shear. In traditional solids, the resistance to shear is associated with the emergence of broken translational symmetry as exhibited by a non-uniform density pattern. In this work, we focus on the emergence of shear-rigidity in a class of solids where this paradigm is challenged. Dry granular materials have no energetically or entropically preferred density modulations. We show that, in contrast to traditional solids, the emergence of shear rigidity in these granular solids is a collective process, which is controlled solely by boundary forces, the constraints of force and torque balance, and the positivity of the contact forces. We develop a theoretical framework based on these constraints, which connects rigidity to broken translational symmetry in the space of forces, not positions of grains. We apply our theory to experimentally generated shear-jammed (SJ) states and show that these states are indeed characterized by a persistent, non-uniform density modulation in force space, which emerges at the shear-jamming transition.