# Archive ouverte HAL – How collective asperity detachments nucleate slip at frictional interfaces

### Tom W. J. de GeusMarko Popović 1 Wencheng JiAlberto Rosso 2 Matthieu Wyart 3

#### Tom W. J. de Geus, Marko Popović, Wencheng Ji, Alberto Rosso, Matthieu Wyart. How collective asperity detachments nucleate slip at frictional interfaces. Proceedings of the National Academy of Sciences of the United States of America , National Academy of Sciences, 2019. ⟨hal-02395574⟩

Sliding at a quasi-statically loaded frictional interface occurs via macroscopic slip events, which nucleate locally before propagating as rupture fronts very similar to fracture. We introduce a novel microscopic model of a frictional interface that includes asperity-level disorder, elastic interaction between local slip events and inertia. For a perfectly flat and homogeneously loaded interface, we find that slip is nucleated by avalanches of asperity detachments of extension larger than a critical radius $A_c$ governed by a Griffith criterion. We find that after slip, the density of asperities at a local distance to yielding $x_\sigma$ presents a pseudo-gap $P(x_\sigma) \sim (x_\sigma)^\theta$, where $\theta$ is a non-universal exponent that depends on the statistics of the disorder. This result makes a link between friction and the plasticity of amorphous materials where a pseudo-gap is also present. For friction, we find that a consequence is that stick-slip is an extremely slowly decaying finite size effect, while the slip nucleation radius $A_c$ diverges as a $\theta$-dependent power law of the system size. We discuss how these predictions can be tested experimentally.

• 1. MPI-PKS - Max Planck Institute for the Physics of Complex Systems
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 3. EPFL - Ecole Polytechnique Fédérale de Lausanne