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

TL;DR

This paper investigates how adding a non-local term to the Johnson-Segalman model influences shear banding, demonstrating that it enables unique stress selection and highlighting the dependence of stress selection on non-local term forms.

Contribution

It introduces a modified Johnson-Segalman model with a non-local term that unambiguously determines shear stress in flow coexistence, advancing understanding of stress selection mechanisms.

Findings

Non-local term enables unique stress selection in shear flow.

Stress selection depends on the form of non-local terms.

Stress selection is generally singular and model-dependent.

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).