Abstract
We extend the stability analysis of the configurations under finite strain using Effective Field Theory (EFT) methods done in [L. Alberte, M. Baggioli, V. C. Castillo, and O. Pujolas, Phys. Rev. D 100, 065015 (2019)]. At finite strain the medium is anisotropic and so fluctuations in different directions behave differently. We recompute the bounds by including the instabilities that may occur in all possible directions. Qualitatively, the main conclusions of [Phys. Rev. D 100, 065015 (2019)] remain unchanged: Nontrivial bounds and correlations between different nonlinear observables can be obtained using EFT methods. Quantitatively, the bounds become more stringent---especially so for materials with power-law stress strain curves ($\ensuremath{\sigma}\ensuremath{\sim}{ϵ}^{\ensuremath{\nu}}$) characterized with a small exponent $\ensuremath{\nu}$.
Highlights
We extend the stability analysis of the configurations under finite strain using Effective Field Theory (EFT) methods done in [L
In Appendix A of [1], we computed the effective action for the phonon fluctuations πI [see Eqs. (A2) and (A3)]
The angle dependence disappears in the linear limit c2i ðθ; ε → 0Þ since the background becomes isotropic again
Summary
We extend the stability analysis of the configurations under finite strain using Effective Field Theory (EFT) methods done in [L. Rev. D 100, 065015 (2019)] remain unchanged: Nontrivial bounds and correlations between different nonlinear observables can be obtained using EFT methods. The nonlinear strain-dependent speed of propagation of the phonon fluctuations depends crucially on the angle of propagation θ, which in [1] was considered to be only θ 1⁄4 0 (longitudinal modes) and θ 1⁄4 π=2 (transverse modes).
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