Continuum mechanics of shear stress growth

One good way to explore fluid microstructure experimentally is to suddenly subject the fluid to a large steady shearing deformation, and to then observe the evolving stress response. If the steady shear rate is high enough, the shear stress and also the normal stress differences can, overshoot, and then, they can even undershoot. We call such responses nonlinear, and this experiment shear stress growth. This work discusses exact analytical solutions for interpreting measured nonlinear shear stress growth responses from the Oldroyd 8-constant constitutive framework. Specifically, we explore the effect of η∞ on stress growth material functions using the special case of the corotational Jeffreys fluid. Using the Johnson-Segalman fluid, we also explore the effect of non-affine deformation. Lastly, we explore the role played by three nonlinear Oldroyd parameters (µ0, ν1, ν2).One good way to explore fluid microstructure experimentally is to suddenly subject the fluid to a large steady shearing deformation, and to then observe the evolving stress response. If the steady shear rate is high enough, the shear stress and also the normal stress differences can, overshoot, and then, they can even undershoot. We call such responses nonlinear, and this experiment shear stress growth. This work discusses exact analytical solutions for interpreting measured nonlinear shear stress growth responses from the Oldroyd 8-constant constitutive framework. Specifically, we explore the effect of η∞ on stress growth material functions using the special case of the corotational Jeffreys fluid. Using the Johnson-Segalman fluid, we also explore the effect of non-affine deformation. Lastly, we explore the role played by three nonlinear Oldroyd parameters (µ0, ν1, ν2).