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# Yield surface of a material model

Wed, 2014-04-30 08:15 - Mirkhalaf

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## Theoretical and Applied Mechanics - StackExchange

Try asking the question in the dedicated stackExchange site:

http://area51.stackexchange.com/proposals/67726/theoretical-and-applied-...

See the discussion here for more information on it:

http://imechanica.org/node/16427

## Hello, If you have the

Hello,

If you have the equation of the yield surface, you can just plot it in Matlab. I have done this for a 2D yield surface(my following description works for 3D also). A brute force method works. Just try lots of points and if they are on the yield surface within some tolerance epsilon, then you plot the point. If it is not close enough to the yield surface you don't plot the point. If you plot enough points eventually you will have a complete depiction of the yield surface. Finite element software is not required to do this.

regards,

Louie

## Dear Louie, Thank you for

Dear Louie,

Thank you for your reply to my question. The thing is I am not using an explixit yield function for the FEM implementation. That is why, I am trying the capture the yield surface using FEM simulations. I guess, since the material model is isotropic, having axisymmetric simualtions (both tensile and compressive) and plane strain simuations (both tensile and compressive) and pure shear simulations will provide enough yiled points to draw the yield surface. What do you think?

Thanks again.

Regards,

Mohsen

## perhaps if I could see the constitutive model it would help

Hi Mohsen,

It would be helpful to see the constitutive model you are using. However, it seems like you must have some sort of criteria for a state of stress being on the yield surface or not. Even if this is an algorithmic criteria rather than an explicit formula, you still can algorithmically detect if a stress state is on the surface or not. (At least I'm assuming this is true.) I'm not sure why you would have to resort to a finite element analysis. If you have a sufficiently large grid at a sufficiently small spacing in principal stress space you should be able to detect which principal stress points (sigma 1, sigma 2, sigma 3) are on the surface. Maybe I'm not understanding your situation correctly, but I'd be willing to look at the model if you wish.

I hope this helps.

regards,

Louie

## Elasto-viscoplastic model without explicit yield criteria

Dear Louie,

Thanks again. An elasto-viscoplastic model

was developed based on single model Leonov model. This model is described in:

http://mate.tue.nl/mate/pdfs/20.pdf

The only way I can think of to plot the

yield surface of the model is to conduct some numerical examples in different

stress states. I was wondering if you, considering the model, could let me know

if you have any other idea. I appreciate your concern.

Regads,

Mohsen