%0 Journal Article %T Rheological properties vs Local Dynamics in model disordered materials at Low Temperature %A C. Fusco %A T. Albaret %A A. Tanguy %J Physics %D 2014 %I arXiv %X We study the rheological response at low temperature of a sheared model disordered material as a function of the bond rigidity. We find that the flow curves follow a Herschel-Bulkley law, whatever is the bond rigidity, with an exponent close to 0.5. Interestingly, the apparent viscosity can be related to a single relevant time scale $t_{rel}$, suggesting a strong connection between the local dynamics and the global mechanical behaviour. We propose a model based on the competition between the nucleation and the avalanche-like propagation of spatial strain heterogeneities. This model can explain the Herschel-Bulkley exponent on the basis of the size dependence of the heterogeneities on the shear rate. %U http://arxiv.org/abs/1403.7950v1