Detailed program

Alejandro Kolton (Centro Atómico Bariloche, Bariloche)

Driven dynamics in random media: domain walls and vortex lattices

The out-of-equilibrium 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.


Jean-Louis 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)

Motion of interfaces with an internal degree of freedom
We examine the dynamics of an interface subjected to a pinning potential, in situations where the position of the interface is coupled to an internal degree of freedom (e.g. a spin phase for magnetic domain walls, or a momentum for inertial strings). Focusing on rigid walls, we investigate the depinning transition, which displays unsuspected features when compared to standard cases: at zero temperature, there exists a bistable regime for low forces, with a 1/log depinining law at the transition. For weak pinning, there occurs a succession of bistable transitions corresponding to different modes of the phase evolution, separated by topological transitions. At finite temperature, the force-velocity characteristics is non-monotonous, as an effect of the zero-temperature topological transitions, as we show, borrowing methods from stochastic dynamical systems. We open perspectives on the effects of internal degrees of freedom on the motion of extended interfaces.


Pierfrancesco Urbani (CEA Saclay)

Following the evolution of glassy states under shear-strain in infinite dimension
I will discuss a mean field approach to glasses based on the exact solution of structural glass models in the limit of infinite dimension. Remarkably the theory predicts a novel critical point, the Gardner transition, where standard elasticity breaks down and the elastic response becomes intermittent. The Gardner transition is generically found when a glass is perturbed in some ways: cooling, compressing or straining it. Upon straining the system, the Gardner transition signs the onset of marginal stability.
It turns out that the yielding point is deep in the Gardner phase. I will describe what is the scenario for the yielding transition that emerges from these findings.


Jérôme Weiss (ISTerre, CNRS/Univ. Grenoble Alpes, Grenoble)

Coulomb’s failure of quasi-brittle 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 non-zero 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 finite-size 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 finite-size 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 elasto-plastic model find good agreement with our predictions.


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