Effects of Non-local Stress on the Determination of Shear Banding Flow

Abstract

We analyze the steady planar shear flow of the modified Johnson-Segalman model, which has an added non-local term. We find that the new term allows for unambiguous selection of the stress at which two ``phases'' coexist, in contrast to the original model. For general differential constitutive models we show the singular nature of stress selection in terms of a saddle connection between fixed points in the equivalent dynamical system. The result means that stress selection is unique under most conditions for space non-local models Finally, illustrated by simple models, we show that stress selection generally depends on the form of the non-local terms (weak universality).