

Alejandro Kolton (Centro Atómico Bariloche, Bariloche)
Driven dynamics in random media: domain walls and vortex lattices
The outofequilibrium driven dynamics of elastic manifolds or interacting particle systems in random media is characterized by the occurrence of different flow regimes or dynamical phases as a function of the drive. To understand such regimes, it is crucial to know, roughly speaking, whether the flow in each regime is strictly “elastic” or “plastic”. The first corresponds to the case of a transported object that has such an integrity that its topological order is maintained. A paradigmatic example of such “elastic flow” are uniformly driven magnetic domain walls in weakly disordered thin film ferromagnets, whose universal emergent dynamical behavior can be described by minimal models of interfaces in random media, and tackled by powerful analytical and numerical techniques. On the other hand, systems such as vortex lattices in superconductors were shown to clearly display “plastic flow regimes”, much more difficult to describe than their elastic counterpart. Although both systems display a depinning transition from a static to a moving phase, the fate of the universality found for purely elastic systems in systems that can tear during its motion is, to my view, an important open question. In this talk I will describe theoretical and experimental results for both systems, and bring to discussion the similarities and differences of their depinning transitions with the analogous yielding phenomenon of driven amorphous materials.

JeanLouis Barrat (Université Grenoble Alpes, Grenoble)
Elastoplastic models of flow in amorphous solids

Stéphane Santucci (ENS Lyon)
Critical depinning of interfaces  Case study of interfacial cracks and imbibition fronts
In last years, numerous efforts have been devoted to the development of model experimental systems in which the structure and the dynamics of an interface propagating in a disordered medium can be directly observed and followed with high precision – both spatially and temporally.
I will present two relevant examples of such experimental efforts: On one hand, I will describe the crackling dynamics of a fracture front along a weak heterogeneous interface, and on the other hand, I will discuss the intermittent dynamics of a viscous wetting fluid interface invading a disordered medium.
I will show that the avalanche front dynamics of those two very different physical systems can be well described in the framework of a critical depinning transition. Nevertheless, I will focus on some specific observations, which appear in strong contrast with theoretical/numerical predictions.

Vivien Lecomte (Universités Paris Diderot et Pierre et Marie Curie, Paris)

Pierfrancesco Urbani (CEA Saclay)

Jérôme Weiss (ISTerre, CNRS/Univ. Grenoble Alpes, Grenoble)
Coulomb’s failure of quasibrittle materials interpreted as a depinning transition, and the problem of the size effect on strength
The larger the structures, the lower their mechanical strength. Already discussed by da Vinci and Mariotte several centuries ago, size effects on strength remain of crucial importance in modern engineering for the elaboration of safety regulations in structural design, or the extrapolation of laboratory results to geophysical field scales. Under tensile loading, statistical size effects are traditionally modeled with a weakest link approach. One of its prominent results is a prediction of vanishing strength at large scales that can be quantified in the framework of extreme value statistics. Despite a frequent use outside its range of validity, this approach remains the dominant tool in the field of statistical size effects. Here we focus on Coulomb’s compressive failure, which concerns a wide range of geophysical and geotechnical situations. We show on historical and recent experimental data that weakest link predictions are not obeyed. In particular, the mechanical strength saturates at a nonzero value towards large scales. Accounting explicitly for the elastic interactions between defects during the damage process, we build a formal analogy of this failure process with the depinning transition of an elastic manifold. This critical transition interpretation naturally entails finitesize scaling laws for the mean strength and its associated variability. Theoretical predictions are in remarkable agreement with measurements reported for various materials such as rocks, ice, coal, or concrete. Interestingly, these finitesize scaling laws seem also relevant for the yield strength of granular media under multiaxial compression, thus raising the intriguing question of the comparison between yielding and depinning.

Alberto Rosso (Université Paris Sud, Orsay)
Scaling description of the yielding transition in soft amorphous solids at zero temperature
Yield stress solids flow if a sufficiently large shear stress is applied. Although such materials are ubiquitous and relevant for industry, there is no accepted microscopic description of how they yield. Here we propose a scaling description of the yielding transition which relates the flow curve, the statistics of the avalanches of plasticity observed at threshold, and the density of local zones that are about to yield. Our description shares some similarity with the depinning transition that occurs when an elastic manifold is driven through a random potential, but also presents some striking differences. Numerical simulations on a simple elastoplastic model find good agreement with our predictions.