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The FENE-P model replaces infinitely extensible Hookean polymers by finitely extensible nonlinear elastic springs with a mean-field closure. Finite extensibility regularizes the Oldroyd-B extensional catastrophe and produces shear thinning.

Let $a=\lambda \dot{\gamma }$. For simple shear, the steady conformation equation isIts nonzero components areSince $\mathbf{\tau }={\eta }_s\dot{\mathbf{\gamma }}+({\eta }_p/\lambda )(F\mathbf{C}-\mathbf{I})$,Thus the FENE-P model has