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Dear all,

Do you have any reference about the theory of plasticity? Especially about flow theory and von Mises yield criterion?

For example if I have an effective stress - plastic strain relationship, and I after yielding, I increase my strain again, how can I obtain the increment of the plastic strain and the stress deviator tensor?

Thanks a lot.



Dear Ray lau,

I have read your blog and I want to tell you about my some comments:

What kind of plasticity theory you want to use?

Well known that available the deformation plasticity theory and yielding theory. In case of Ilushin plasticity theory you must investigate the loading process and unloading process differently. But also well known that yielding theory have privelegous that defroamtion theory. How I understand  your problem on yielding theory. In this theory the strains velocities tensor and stress tensor relationships defined from associate yielding law. And there are not problem depended from strains increasement define the stress increasement. But well known that the mentionet relationships are nonlinear. And the mentioned increasements definition is problem. Also well known that the any nonlinear problem is the different problem. Also you have not signify you investigated material is istrop or not? If you have isotrop material than you can use the isotropy conditions (The general ways of strains velocities and stress are coincides).

I think you know the physical interpretation of Mises condition. By the Mises criterion we have the region where we have the plastic defroamtions, too. I want to note that the investigation of the elastic and plastic problems are hard problem of mechanical engineering. Do you know about full plasticity or no full plasticity?

Any problem with plasticity statement have the single character and it is necessary definite approach.

My personel web page vailable in: and you can send me your comments by e-mail.

I can note some literature but in Russian. If you have interests inform me.


Sedrak Vardanyan


  Try the book of Simo and Hughes, Computational Inelasticity, 1988.  It has exactly what you have asked about. 


Prof. Dr. Sanjay Govindjee
University of California, Berkeley



I am writing a UMAT for crystal plasticity. I am having convergence
problem in my UMAT. As far as FEM is concerned, I have tried many
options e.g. minimum time increment, maximum time increment, and
different options with *STEP but I could never reach the complete

Could anyone suggest any numerical method or procedure in UMAT
itself which I could use to get a convergent solution. I would like to
know how to go to the next step once specified number of iterations
have been completed (even if the solution for earlier time increment is
not complete..but sufficiently close and can be decided by me).




Ph.D. Student
School of Mechanical and Materials Engineering
Washington State University, Pullman


Hi Alankar,

UMAT sometimes can be very difficult to deal with. 

According to my expereince, when you saw a solution was not converging, most of time it was't because of (1) minimum time increment, (2) maximum time increment, (3) different options with *STEP, nor (4) number of iterations...

Try to do a single element test first before you implement to your model.



HY Shadow Huang

Postdoctoral Associate
Materials Science and Engineering
Massachusetts Institute of Technology

Thanks HY Shadow,

Yes I did try my UMAT for single element, and it works fine but when I try using it for bigger geometries, like 50 grains, sometimes it does not converge. It does converge sometimes, when I tune of my parameters in equations.

I wanted to fix this problem permanently, and wanted to set up some limit on number of iterations or convergence so that I runs completely.

Alankar Ph.D. Student School of Mechanical and Materials Engineering Washington State University, Pullman

Dear Ray Lau:

I am not aware on your mathematical background and so, I would like to warn that an excellent book on plasticity like Computational Inelasticity by Simo and Hughes could rapidly go beyond your current possibilities, making you to feel prematurely dissapointed and discouraged.

In that case, you could try by start reading the first two parts (about 50 pages) of a classical book: The Mathematical Theory of Plasticity, by R. Hill and then move forward to more advanced and modern books, like the one mentioned above, among many others.

Hope this help you in overcoming your problems.


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