An improved multiaxial stress-strain correction model for elastic fe postprocessing

In this paper, the model of Köttgen, Barkey and Socie, which corrects the elastic stress and strain tensor histories at notches of a metallic specimen under non-proportional loading, is improved. It can be used in connection with any multiaxial a-e-law of incremental plasticity. For the correction model, we introduce a constraint for the strain components that goes back to the work of Hoffmann and Seeger. Parameter identification for the improved model is performed by Automatic Differentiation and an established least squares algorithm. The results agree accurately both with transient FE computations and notch strain measurements. The essential thing from the physical point of view is, that our improved version of Köttgens model together with Jiangs model and appropriate parameters is in fact able to reproduce the complex transient and highly nonlinear elastoplasticity effects accurately, based on a few linear elastic FE unit load cases, avoiding full transient nonlinear elastoplastic FE computations. (As a pointwise postprocessing it is clearly much faster than elastoplastic FE.) The results for the circular loading path are not completely satisfactory; they could be improved by the use of Dörings constitutive law, which takes out-of-phase phenomena better into account.