Necking and drawing in polymeric fibers under tension

A constitutive relation is proposed for the dependence of the tension in a thin polymeric fiber on the variation of the stretch ratio λ along the fiber axis. When this relation is placed in the equation of balance of forces, it yields a nonlinear second-order differential equation for λ whose equilibrium solutions (for a long fiber) are known in other contexts. The solutions describe necks, bulges, drawing configurations, and periodic striations. The assumption that motions resulting from gradual changes in tension or length are homotopies formed from these equilibrium solutions is compatible with many of the observed properties of tension-induced necking and drawing in fibers of such polymers as nylon and polyethylene.