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 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 effective field theory 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 behavior $\sigma (ϵ)\sim {ϵ}^{\nu }$, the maximum strain exhibits a sharp correlation with the exponent $\nu$.

• Received 12 September 2018

DOI:https://doi.org/10.1103/PhysRevD.100.065015

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society