  The COMOFLO dynamic Monte Carlo algorithm is extended to enable the
simulation of steady-state extensional rheology of dense melts for the first
time ever. This significant advancement provides the ability to accurately
capture the extensional viscosity of entangled polymer melts from low
deformation rates, throughout the strain hardening regime, and into the region
of viscosity thinning To do so, the purely extensional flow field associated
with a four roll mill experiment is implemented in three dimensions. Periodic
boundary conditions exist in all directions to enable a uniform deformation
rate throughout the simulation domain. As expected, the extensional viscosity
is four times the zero shear viscosity at low deformation rates. As the
deformation rate increases, the extensional viscosity increases, plateaus, and
then decreases. The algorithm thus correctly captures the physics of polymer
melts in extensional flow in a fully a priori manner while providing
significant computational advantages over molecular dynamics methods. Because
the technique is applicable to polydisperse systems, the ability to predict in
an a priori manner both shear and elongational rheology for linear polymer
melts of arbitrary molecular weight distribution can now be considered a solved
problem.
