Black Rubber and the Non-linear Elastic Response of Scale Invariant Solids

TL;DR

This paper explores the nonlinear elastic behavior of scale invariant solids using holographic models, revealing how symmetry breaking affects elasticity bounds and drawing parallels to natural rubber.

Contribution

It introduces holographic models for scale invariant solids, analyzing their nonlinear stress-strain responses and elasticity limits, especially distinguishing manifest and spontaneously broken SI cases.

Findings

Elastic bounds differ significantly between SI cases.

Holographic models exhibit stress-strain curves similar to natural rubber.

Black rubber models show two power-law regimes at different strains.

Abstract

We discuss the nonlinear elastic response in scale invariant solids. Following previous work, we split the analysis into two basic options: according to whether scale invariance (SI) is a manifest or a spontaneously broken symmetry. In the latter case, one can employ effective field theory methods, whereas in the former we use holographic methods. We focus on a simple class of holographic models that exhibit elastic behaviour, and obtain their nonlinear stress-strain curves as well as an estimate of the elasticity bounds - the maximum possible deformation in the elastic (reversible) regime. The bounds differ substantially in the manifest or spontaneously broken SI cases, even when the same stress-strain curve is assumed in both cases. Additionally, the hyper-elastic subset of models (that allow for large deformations) is found to have stress-strain curves akin to natural rubber. The holographic instances in this category, which we dub black rubber, display richer stress-strain curves - with two different power-law regimes at different magnitudes of the strain.