  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 $\nu$.
