Effects of nonlocal stress on the determination of shear banding flow

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