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Drucker Prager Plasticity model

Hi All,

I am trying to code the Drucker prager plasticity model for the 2D plane strain case using consistent tangent modulus. I am using C++, therefore I would appreciate if anyone could share relevant materials which I could use and preferrably for the 2D case so it is not unnecessarily complicated.

 

I have already seen some codes written for the 3D case,however I am not sure if I am converting it to the 2D case right, as it does not work at the moment. For the consistent tangent modulus, I have to return a 3*3 matrix to the program for 2D with the coefficients for the x,y and xy directions. What I am doing currently is just selecting relevant members from the general 3D tangent matrix(6*6) and ignoring the z direction. Is that wrong?

 

Thank you!

Setareh

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It just occured to me: Is there a neat way, like transforming a 6*6 tangent matrix from 3D space to a 3*3 one for the 2D space by transformation matrices, so that I can do something like A^t . C . A to get a 3*3 tangent?

 

Thanks.

 

Dear Setareh,

Regarding your post, the following two items are noteworthy:

1. You can consult chapter 6 and 7 of 

E.A. de Souza Neto, D. Peric and D.R.J. Owen, Computational Methods for Plasticity: Theory and Applications, John Wiley and Sons, 2008.

The chapters mentioned above thoroughly discuss the plasticity models for infinitesimal deformations. The book is also very helpful for plasticity in finite deformations as well. The book also has FORTRAN codes for its samples and it is called HYPLAS. I think it should be available in the internet.

2. Remember that you can extract the elasticity tensor for plane strain problems from three dimensional case, but this is not the case for plane stress. Moreover, it can be algorithm dependent. Therefore you have to be very careful. Also do it this might drastically increase the computational time which is not favorable.

Mohsen

<p>Only for 2-D plane stress condition, you have to do special handling for driving out-of-plane stress to be zero if you 6*6 material matrix. For plane strain problems, it is OK that just using 6*6 3-D material matrix due to out-of-plane stress is not zero.&nbsp;</p>

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