  As a stiff polymer tumbles in shear flow, it experiences compressive viscous
forces that can cause it to buckle and undergo a sequence of morphological
transitions with increasing flow strength. We use numerical simulations to
uncover the effects of these transitions on the steady shear rheology of a
dilute suspension of stiff polymers. Our results agree with classic scalings
for Brownian rods in relatively weak flows but depart from them above the
buckling threshold. Signatures of elastoviscous buckling include enhanced shear
thinning and an increase in the magnitude of normal stress differences. We
discuss our findings in the light of past work on rigid Brownian rods and
non-Brownian elastic fibers and highlight the subtle role of thermal
fluctuations in triggering instabilities.
