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In this work we develop a theoretical framework for the localization of flowin the steadily flowing regime of sheared disordered solids with inertialdynamics on a microscopic scale. To this aim we perform rheology studies atfixed shear rate on a 3D model of dense disordered solid. Our particle basedsimulations reveal the existence of heterogeneous shear-profiles in thestationary flow under homogeneous driving conditions. To rationalize thisresult, we propose a continuum model that couples the dynamics of the localflow to the evolution of a kinetic temperature field. A linear stabilityanalysis of this theory predicts the minimum system size necessary for the flowinstability to develop. This prediction as well as the velocity profilesobtained from this continuum model are in good agreement with the results fromthe particle based simulations.

Permanent shear localization in dense disordered materials due to microscopic inertia