Non-linear elasticity, yielding and entropy in amorphous solids

TL;DR

This paper explores the complex mechanical and thermodynamic behavior of amorphous solids under shear using effective field and gravitational theories, revealing correlations supported by simulations and linking soft matter physics with gravity concepts.

Contribution

It introduces a novel theoretical framework connecting non-linear elasticity, yielding, and entropy in amorphous solids with gravitational theories, supported by simulation evidence.

Findings

Correlations between non-linear elastic exponent and yielding properties.

Qualitative agreement between theory and granular matter simulations.

Potential unified understanding of solid rheology and black hole physics.

Abstract

The holographic duality has proven successful in linking seemingly unrelated problems in physics.Recently, intriguing correspondences between the physics of soft matter and gravity are emerging,including strong similarities between the rheology of amorphous solids, effective field theories for elasticity and the physics of black holes. However, direct comparisons between theoretical predictions and experimental/simulation observations remain limited. Here, we study the effects of non-linear elasticity on the mechanical and thermodynamic properties of amorphous materials responding to shear, using effective field and gravitational theories. The predicted correlations among the non-linear elastic exponent, the yielding strain/stress and the entropy change due to shear are supported qualitatively by simulations of granular matter models. Our approach opens a path towards understanding complex mechanical responses of amorphous solids, such as mixed effects of shear softening and shear hardening, and offers the possibility to study the rheology of solid states and black holes in a unified framework.