5. Summary of results

In this paragraph, we focus on the results of modeling A. For information purposes, the following curves represent the various comparisons between Code_Aster for the two types of loading mentioned. in the document (\(\mathrm{AD}\): With discharge; \(\mathrm{SD}\): Without discharge) and GEFDYN, the finite element software developed at laboratory MSSMat at Ecole Centrale Paris. The curves repeat the quantities tested previously in the previous section, namely \({\varepsilon }_{\mathrm{xy}}\) (Fig. 5.1), \({\epsilon }_{v}^{p}\) (Fig. 5.2) and \(({r}_{\text{ela}}^{d,c}+{r}_{\text{dev}}^{c})\) (Fig. 5.3).

Fig. 5.1 Deviatory stress as a function of distortion: comparison of Code_Aster and GEFDYN solutions.

Fig. 5.2 Plastic volume deformation as a function of shear stress: comparison between Code_Aster and GEFDYN solutions.

Fig. 5.3 Cyclic deviation radius as a function of loading times: comparison between Code_Aster and GEFDYN solutions.

The differences observed between GEFDYN and Code_Aster highlight a suspicious management by GEFDYN of the work hardening of cyclical deviatory circles in the imposed shear plane. While the model predicts elastic micro-discharge, GEFDYN proposes a complete work-hardening of the cyclic deviation circle until perfect plasticity, before defining a cyclic deviatory circle with elastic radius. The behavior of the Code_Aster respects the elastic character of this discharge and, at the outlet of this micro-discharge, resumes a work-hardening slope identical to that obtained previously.

The GEFDYN development team is aware of the discrepancies observed between the two calculation codes.