# Criticality in the approach to failure in granular materials and amorphous solids

### Jie Lin 1 Thomas Gueudré 2 Alberto Rosso 3 Matthieu Wyart 4

#### Physical Review Letters, American Physical Society, 2015, 115, pp.168001

Failure of amorphous solids is fundamental to various phenomena, including landslides and earthquakes. Recent experiments indicate that highly plastic regions form elongated structures that are especially apparent near the maximal shear stress $\Sigma_{\max}$ where failure occurs. This observation suggested that $\Sigma_{\max}$ acts as a critical point where the length scale of those structures diverges, possibly causing macroscopic transient shear bands. Here we argue instead that the entire solid phase ($\Sigma<\Sigma_{\max}$) is critical, that plasticity always involves system-spanning events, and that their magnitude diverges at $\Sigma_{\max}$ independently of the presence of shear bands. We relate the statistics and fractal properties of these rearrangements to an exponent $\theta$ that captures the stability of the material, which is observed to vary continuously with stress, and we confirm our predictions in elastoplastic models.

• 1. Center for Soft Matter Research
• 2. DISAT - Department of Applied Science and Technology
• 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 4. Institute of Theoretical Physics