Elasticity bounds from Effective Field Theory

TL;DR

This paper uses effective field theory to derive bounds on the elastic properties of hyperelastic materials, linking nonlinear stress-strain behavior to fundamental physical limits on strain and stress.

Contribution

It introduces a novel EFT approach to constrain elastic bounds in hyperelastic materials based on their nonlinear stress-strain relations.

Findings

Bounds on maximum strain and stress derived from EFT principles.

Maximum strain correlates sharply with the power-law exponent of stress-strain relations.

Effective field theory constrains the nonlinear elastic behavior of materials.

Abstract

Phonons in solid materials can be understood as the Goldstone bosons of the spontaneously broken spacetime symmetries. As such their low energy dynamics are greatly constrained and can be captured by standard effective field theory (EFT) methods. In particular, knowledge of the nonlinear stress-strain curves completely fixes the full effective Lagrangian at leading order in derivatives. We attempt to illustrate the potential of effective methods focusing on the so-called hyperelastic materials, which allow large elastic deformations. We find that the self-consistency of the EFT imposes a number of bounds on physical quantities, mainly on the maximum strain and maximum stress that can be supported by the medium. In particular, for stress-strain relations that at large deformations are characterized by a power-law behaviour $\sigma(\varepsilon)\sim \varepsilon^\nu$, the maximum strain exhibits a sharp correlation with the exponent $\nu$.