Questions on calc_Principal, elastoplastic tangent matrix, Newton's iteration

[cunyizju]

Hi, your repo is attactive to me. To test the UMAT's availability, I create a one-element example. During my debugging progress, the following bugs have been detected:

1. SUBROUTINE calc_Principal: the denominator cosTheta should add an ersatz parameter, e.g. 10e-6, to avoid infinity.
2. the elastoplastic tangent matrix:
   DDSDDE(:,:) = DDSDDE(:,:) - dyadMat(:,:)*denominatordLambda rather than DDSDDE(:,:) = DDSDDE(:,:) - dyadMat(:,:)/denominatordLambda
3. To obtain plastic state variables, Newton's iteration is used. However, it seems that the iteration is invalid, i.e., the value of 'eqStress - Flowstress' becomes much larger during the iteration, or one of the state variables becomes NaN.

Could you please provide some papers for theoretical reference, especially in the aspect of non-associated plasticity, continumm tangent stiffness and consistent tangent stiffness? It would be highly appreciated if you are interested in fixing the bugs.

Thanks a lot~

Best wishes, Bruce

[yossy11]

@cunyizju Thank you for helping me with my codes.

As you know, these subroutines are now under development, and I'm going to refine these codes till November(can't fix right now cuz busy working on other repos). I will really appreciate if you could review(if you have time) these codes after I fixed these bugs and useless codes.

Lastly, the papers I referenced are following:

F. Barlat, H. Aretz, J.W. Yoon, M.E. Karabin, J.C. Brem, R.E. Dick,
Linear transfomation-based anisotropic yield functions,
International Journal of Plasticity,
Volume 21, Issue 5,
2005,
Pages 1009-1039,
ISSN 0749-6419,

Mohsen Safaei, Myoung-Gyu Lee, Wim De Waele,
Evaluation of stress integration algorithms for elastic–plastic constitutive models based on associated and non-associated flow rules,
Computer Methods in Applied Mechanics and Engineering,
Volume 295,
2015,
Pages 414-445,
ISSN 0045-7825,

Best Regards

[cunyizju]

Thanks for providing the two paper. They provide me more insight into this problem. In fact, I have been rewriting Newton's iteration code according to

Cvitanić, V., Vlak, F., & Lozina, Ž. (2008). A finite element formulation based on non-associated plasticity for sheet metal forming. International Journal of Plasticity, 24(4), 646-687.

Thanks to your introduced work by Safaei, I notice that he also suggested that 'the continuum (standard) elasto-plastic tangent operator can generate spurious loading and unloading condition during the abrupt transition from elastic to plastic' in 2013, which puzzled me a lot in the recent two days. It seems that consistent tangent stiffness should be employed in fully implicit classical backward Euler algorithm. I would like to try that.

Safaei, M., Zang, S. L., Lee, M. G., & De Waele, W. (2013). Evaluation of anisotropic constitutive models: Mixed anisotropic hardening and non-associated flow rule approach. International Journal of Mechanical Sciences, 73, 53-68.

I am looking forward to the completeness of this repo and, certainly, feel honoured to have the opportunity to contribute.

Best wishes, Bruce