Plane strain neck propagation (Q1082172)

Quasi-static neck propagation in polymers (cold drawing) is studied for the case of plane strain tension. For a \(J_ 2\)-deformation theory material (nonlinear elastic), jump conditions across the neck provide a simple steady-state solution. For a \(J_ 2\)-flow theory material a finite element solution characterizes the complete development of a neck in an initially smooth specimen. The numerical results include the overall load-deflection curve, details of deformation states, and the triaxial stress distribution. The solution algorithm is based on a convected coordinate description of the governing equations (Lagrangian in character) with both Newton equilibrium iterations and a stress integration algorithm to improve accuracy.