A cauchy-stress based solution for a necking elastic constitutive model under large deformation

Abstract

A finite element based method for solution of large-deformation hyperelastic constitutive models is developed, which solves the Cauchy-stress balance equation using a single rotation of stress from principal directions to a fixed co-ordinate system. Features of the method include stress computation by central differencing of the hyperelastic energy function, mixed integration-order incompressibility enforcement, and an iterative solution method that employs notional `small strain¿ stiffness. The method is applied to an interesting and difficult elastic model that replicates polymer `necking¿; the method is shown to give good agreement with published results from a well-established finite element package, and with published experimental results. It is shown that details of the manner in which incompressibility is enforced affects whether key experimental phenomena are clearly resolved.