MEchanics GAthering -MEGA- Seminar: Shearing amorphous materials: revising mean-field descriptions

Amorphous materials, when submitted to an external deformation such as a constant shear, are known to exhibit a nonlinear response, signature of an out-of-equilibrium phase transition. This highly nontrivial behaviour depends in fact crucially on the intensity of the external driving, which triggers randomly local plastic rearrangements throughout the system, thus constantly updating its local disordered energy landscape. Linking on the one hand the collective behaviour of these local plastic events, and on the other hand the macroscopic nonlinear response, represents a challenging issue from the statistical physics point of view of driven disordered systems.

Several mean-field 'elasto-plastic' models have been developed, at a mesoscopic scale defined by the typical size of individual plastic events. These mean-field descriptions have proven to be rather successful in reproducing certain features observed in sheared disordered systems, but not all at once; moreover, a consistent picture connecting them is still missing. Here I will discuss the physical ingredients that are put in such mean-field models, in particular the assumptions underlying the effective stochastic process defining them. I will focus on the steady-state response of athermal systems, when the velocity of the deformation (i.e. shear rate) is controlled, discussing specifically the so-called `Hébraud-Lequeux’ model and its generalisations.

Related publications:
E. Agoritsas, E. Bertin, K. Martens, & J.-L. Barrat, Eur. Phys. J. E 38, 71 (2015).
E. Agoritsas & K. Martens, Soft Matter 13, 4653 (2017).
D. A. Matoz-Fernandez, E. Agoritsas, J.-L. Barrat, E. Bertin, & K. Martens, Phys. Rev. Lett. 118, 158105 (2017).