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We study the rheological response at low temperature of a sheared modeldisordered material as a function of the bond rigidity. We find that the flowcurves follow a Herschel-Bulkley law, whatever is the bond rigidity, with anexponent close to 0.5. Interestingly, the apparent viscosity can be related toa single relevant time scale $t_{rel}$, suggesting a strong connection betweenthe local dynamics and the global mechanical behaviour. We propose a modelbased on the competition between the nucleation and the avalanche-likepropagation of spatial strain heterogeneities. This model can explain theHerschel-Bulkley exponent on the basis of the size dependence of theheterogeneities on the shear rate.

Rheological properties vs Local Dynamics in model disordered materials at Low Temperature