A kinetic theory of plastic flows in jammed materials

Amorphous jammed materials of diverse nature display complex flow properties intermediate between solid and liquid, as characterized by the existence of a yield stress. Furthermore flows in such systems usually exhibit spatial inhomogeneities, which cannot be reconciliated with classical rheological descriptions. We present a novel kinetic approach for the elasto-plastic flow dynamics of jammed materials, describing the spatio-temporal collective dynamics of the localized plastic events occuring during the flow [1]. This description yields a non-local constitutive law for the flow, introducing as a key dynamic quantity the local rate of plastic events. This quantity, interpreted as a local fluidity, is spatially correlated with a correlation length diverging in the quasistatic limit, i.e., close to yielding. In line with recent experimental [2] and numerical observations, we predict finite size effects in the flow behavior, as well as the absence of an intrinsic local flow curve.\\[4pt] [1] L. Bocquet, A. Colin, A. Ajdari, {\it Phys. Rev. Lett.} (2009) in press\\[0pt] [2] J. Goyon, A. Colin, G. Ovarlez, A. Ajdari, L. Bocquet, {\it Nature} {\bf 454} 84 (2008)