Critical Dynamics at the Yielding Transition and Creep Behavior of Amorphous Systems : Mesoscopic Modeling

Abstract : Amorphous systems deep below the glass transition, as well as colloidal glasses at high packing fractions, concentrated emulsions, foam systems, etc. exhibit divergent microscopic relaxation time scales and flow only upon a large enough external loading. This dynamical phase transition of amorphous systems from the apparent solid state to the apparent liquid state mediated by the external loading, is called the yielding transition. This transition is studied throughout this thesis by a mesoscopic modeling approach, specifically versions of the so-called elasto-plastic model. After introducing a general background of the glass transition and experimental systems, that are the target of the elasto-plastic model description, a formulation of the elasto-plastic model, slightly different from the conventional ones used in the literature, is introduced for incorporating both the shear rate control and the stress control protocols. It is also shown that the mean-field Hebraud-Lequeux model can be derived from the spatially resolved elasto-plastic model by assuming some approximations. Using the shear rate control protocol, the yielding transition is firstly probed by studying the shear rate dependence of the avalanche statistics close to criticality. A crossover from a non mean-field behavior to an apparent mean-field behavior with respect to an increasing shear rate is evidenced. Scaling laws in the zero shear rate limit, support the idea that the yielding transition belongs to a non mean-field universality class of a dynamical phase transition. The dependence of the symmetry of the average shape of the stress drops on the stress drop duration, the system size and the shear rate, leads to the interpretation that stress drops at finite shear rates result from the superposition of individual avalanches possessing a cooperative length and time scale. By studying the macroscopic stress fluctuation, the cooperative length scale ξc is identified as the crossover size below which the scaling relation with the system size ∼ 1/L^d implied by the central limit theorem breaks down. Further a saturation time scale can be defined in the analysis of the time series of macroscopic plastic strain rate. Below this time scale one observes the manifestation of Brownian dynamics. The saturation time for systems of sizes smaller than the cooperative length scales with the system size as a power law, which can be interpreted as the scaling relation between the cooperative time and the cooperative length of individual avalanches. Further using the stress controlled protocol, the yielding transition is studied by simulating typical creep experiments of the amorphous systems. The mesoscopic models (the elasto-plastic model as well as the meanfield Hébraud-Lequeux model) are shown to be capable to reproduce the response of the macroscopic shear rate to an imposed stress slightly above the yielding point in qualitatively good agreement with several experiments. Within the mesoscopic modeling approach, the results reveal that the creep behavior depends strongly on the initial condition of the amorphous system submitted to creep experiments.
Complete list of metadatas

https://tel.archives-ouvertes.fr/tel-01570010
Contributor : Chen Liu <>
Submitted on : Friday, July 28, 2017 - 9:41:03 AM
Last modification on : Tuesday, September 11, 2018 - 9:24:02 AM

Identifiers

  • HAL Id : tel-01570010, version 1

Collections

Citation

Chen Liu. Critical Dynamics at the Yielding Transition and Creep Behavior of Amorphous Systems : Mesoscopic Modeling. Soft Condensed Matter [cond-mat.soft]. Université Grenoble Alpes, 2016. English. ⟨tel-01570010⟩

Share

Metrics

Record views

136

Files downloads

163