An elasto-visco-plastic optimized behaviour to take into account the effects of memory and non radiality
by J.-M. Proix, EDF R&D / AMA
Most of behaviour laws do not allow to model the over-hardening due to non-radial load and can greatly minimize the amplitude of plastic deformation and stresses in comparison to the experimental results, with the risk of obtaining under-estimated results for fatigue with controlled deformation.
The Chaboche behavior model with memory effect and restoration has equations capable of describing the effect of non radiality. Integration of this law exists in Code_Aster: the VISCOCHAB model makes it possible to simulate this effect, but the algorithms have a lack of speed because they solve a system of 27 equations at each integration (therefore at each Gauss point at each step time, and at each iteration).
This is why this new model is proposed, VISC_MEMO_NRAD (VMIS_MEMO_NRAD in the absence of viscosity) which reduces the integration of behavior to the solving a single scalar equation. The performance comparison with the model VISCOCHAB highlights a interesting gain of robustness and speed for structure calculations and identifications of parameters. The results of both models are identical in all cases : one can observe on the following diagram (Torsion test called "Circular") the consistency of the results of VISCOCHAB and VISC_MEMO_NRAD (green and red curves) and the proper consideration of over-hardening due to non radiality. A behavior that does not model this gives much lower stress amplitudes (blue curve).
In terms of CPU performance, VISC_MEMO_NRAD is 4-26 times faster than implicit VISCOCHAB, depending on the number of time steps, itself 5-10 times faster than the explicit.
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References
[1]. « Multiaxial fatigue evaluation using discriminating strain paths » Nima Shamsaei, Ali Fatemi, Darrell F. Socie International Journal of Fatigue 33 (2011) 597–609