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Statistics of stress avalanches in deformed amorphous solids : insight from elastoplastic models
Elastoplastic models [1] describe the deformation of amorphous solids through a simple lattice based implementation of the scenario identified in numerous experiments and simulations [2] : irreversible ”shear transformations”, take place in localized regions in the stressed material, and the corresponding stress release is transferred elastically to the surrounding medium. As a result of this supplementary load, new transformations may occur in cascade, resulting in a so called ”avalanche” behaviour, with critical features (diverging size and power law distributions) in the limit of large systems and low strain rates. This critical behaviour has interesting similarities, but also deep differences, with other systems exhibiting avalanche behaviour, such as elastic lines pinned by disorder. Elastoplastic models, with less severe size and time limitations than molecular dynamics simulations, are particularly useful to study these critical features. I will present numerical results obtained from simple elastoplastic models for this dynamical phase transition towards a flowing solid. I will show how the critical behavior progressively crosses over to mean field as the strain rate increases [3]. I will also discuss, using molecular dynamics [4] and finite element [5] based calculations, how the critical scalings are affected by the inclusion of inertia in the microscopic dynamics.
[1] ”A mesoscopic model for the rheology of soft amorphous solids, with application to microchannel flows.” A. Nicolas, J-L. Barrat, Faraday Discussions 167, 567 (2013)
[2] ”Modeling the mechanics of amorphous solids at different length scale and time scale.”, D. Rodney, A. Tanguy, D. Vandembroucq, Modelling and simulation in materials science and engineering, 19, 083001 (2011)
[3] ”Driving Rate Dependence of Avalanche Statistics and Shapes at the Yielding Transition ” C. Liu, E. Ferrero, F. Puosi, J-L. Barrat, K. Martens, Phys. Rev. Letters, 116, 065501 (2016)
[4] "Effects of Inertia on the Steady-Shear Rheology of Disordered Solids", A. Nicolas, J. Rottler, J-L Barrat, Phys. Rev. Letters, 116, 058303 (2016)
[5] ”Role of inertia in the rheology of amorphous systems : A finite-element-based elastoplastic model” K. Karimi, J-L. Barrat, Phys. Rev E 96, 022904 (2016) ; "Inertia and universality of avalanche statistics : the case of amorphous solids" K. Karimi, E. Ferrero, J-L. Barrat, Phys Rev E, in press.