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.
Highlights
The material can undertake, etc), and it might well be that there exist correlations between them
The continuum limit description takes the form of a nonlinear theory for the displacement vector field πi that can be specified by an energy function or a constitutive relation
We have analyzed the nonlinear elastic response in materials with scale invariance from the low-energy perspective, using effective field theory and holographic methods. The advantage in these effective methods is that they are mainly based on how symmetries are realized and they can help to understand the nonlinear behaviour ‘universally’, that is, independently of the microscopic details of the material
Summary
We review the basic formalism to describe the elastic response under finite (“large”) deformations or applied stresses. The main obstacle is that, as in CFTs, scale-invariant solids are expected to lack a local Lagrangian description, the steps after (2.12) do not immediately apply (nor the identification of the ‘energy function’ with an effective Lagrangian) While this may seem unimportant regarding the response to static and homogeneous strain, it is crucial in order to possibly obtain nontrivial constraints in the nonlinear response (such as the correlations among various nonlinear parameters mentioned in the introduction) because this requires a knowledge of the full theory. We show how to extract stress-strain curves in (holographic models of) solids with manifest SI, we shall work out the equivalent of eq (2.17) for them, and find the constraints and relations among different nonlinear elasticity observables
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
