A kinetic theory of plastic flow in soft glassy materials

A kinetic model for the elasto-plastic dynamics of a flowing jammed material is proposed, which takes the form of a non-local – Boltzmann-like – kinetic equation for the stress distribution function. Coarse-graining this equation 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 quasi-static limit, i.e. close to yielding. We predict finite size effects in the flow behavior, as well as the absence of an intrinsic local flow curves. These features are supported by recent experimental and numerical observations.