Large-strain response of isotropic-hardening elastoplasticity with logarithmic rate: Swift effect in torsion

Recently, a new Eulerian rate-type isotropic-hardening elastoplasticity mod el has been established by utilizing the newly discovered logarithmic rate. It has been proved that this model is unique among all isotropic hardening elastoplastic models with all possible objective corotational stress rates and other known objective stress rates by virtue of the self- consistency criterion: the hypoelastic formulation intended for elastic behaviour must be exactly integrable to deliver a hyperelastic relation. The simple shear response of this model has been studied and shown to be reasonable for both the shear and normal stress components. The objective of this work is to f urther study the large deformation response of this model, in particular, t he second-order effects, including the well-known Swift effect, in torsion of thin-walled cylindrical tubes with free ends. An analytical perturbation solution is derived, and numerical results are presented by means of the R unge-Kutta method. It is shown that the prediction of this model for the sh ear stress is in good accord with experimental data, but the predicted axia l length change is negligibly small and much less than experimental data. T his suggests that the strain-induced anisotropy may be the main cause of th e Swift effect.