Critical dynamics at the yielding transition and creep behavior of amorphous systems : mesoscopic modeling

Abstract : Amorphous systems deep blow the glass transition, as well as colloidal glasses at high packing fractions,concentrated emulsions, foam systems, etc. exhibit divergent microscopic relaxation time scales and flowonly upon a large enough external loading. This dynamical phase transition of amorphous systems fromthe apparent solid state to the apparent liquid state mediated by the external loading, is called theyielding 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 thetarget of the elasto-plastic model description, a formulation of the elasto-plastic model, slightly differentfrom the conventional ones used in the literature, is introduced for incorporating both the shear ratecontrol and the stress control protocols. It is also shown that the mean-field Hebraud-Lequeux model canbe 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 shearrate dependence of the avalanche statistics close to criticality. A crossover from a non mean-field behaviorto an apparent mean-field behavior with respect to an increasing shear rate is evidenced. Scaling laws in thezero shear rate limit, support the idea that the yielding transition belongs to a non mean-field universalityclass of a dynamical phase transition. The dependence of the symmetry of the average shape of the stressdrops on the stress drop duration, the system size and the shear rate, leads to the interpretation that stressdrops at finite shear rates result from the superposition of individual avalanches possessing a cooperativelength and time scale.By studying the macroscopic stress fluctuation, the cooperative length scale l_c is identified as thecrossover size below which the scaling relation with the system size 1/L^d implied by the central limittheorem breaks down. Further a saturation time scale T_c can be defined in the analysis of the timeseries of macroscopic plastic strain rate. Below this time scale one observes the manifestation of Browniandynamics. The saturation time for systems of sizes smaller than the cooperative length l_c scales withthe system size as a power law T_c~(l_c)^z, which can be interpreted as the scaling relation between thecooperative 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 aswell as the mean-field Hébraud-Lequeux model) are shown to be capable to reproduce the response ofthe macroscopic shear rate to an imposed stress slightly above the yielding point in qualitatively goodagreement with several experiments. Within the mesoscopic modeling approach, the results reveal thatthe creep behavior depends strongly on the initial condition of the amorphous system submitted to creepexperiments.
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Submitted on : Friday, September 22, 2017 - 4:45:06 PM
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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. ⟨NNT : 2016GREAY066⟩. ⟨tel-01592136⟩



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