  Elastic stress concentration at tips of long slender objects moving in
viscoelastic fluids has been observed in numerical simulations, but despite the
prevalence of flagellated motion in complex fluids in many biological
functions, the physics of stress accumulation near tips has not been analyzed.
Here we theoretically investigate elastic stress development at tips of slender
objects by computing the leading order viscoelastic correction to the
equilibrium viscous flow around long cylinders, using the weak-coupling limit.
In this limit nonlinearities in the fluid are retained allowing us to study the
biologically relevant parameter regime of high Weissenberg number. We calculate
a stretch rate from the viscous flow around cylinders to predict when large
elastic stress develops at tips, find thresholds for large stress development
depending on orientation, and calculate greater stress accumulation near tips
of cylinders oriented parallel to motion over perpendicular.
