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How to deal with negetive plastic strain increment in FEA in an elasto - plastic problem

In case of elasto-plastic problem it is mentioned that unloading of an integration point should be started along the elastic moduli when the solution gives a negetive increment of the plastic strain at the integration point. If anyone could elaborate it a little more, it will be really helpful.


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DY hu's picture

The elastic-plastic relation computation can refer to the method of radial return.

Matt Lewis's picture


By plastic strain increment I assume you mean equivalent plastic strain increment.  The mathematical model known as elasto-plasticity is most often formulated in terms of an equivalent plastic strain rate that is directly proportional to the Euclidean norm of the plastic strain rate, a second order tensor.  As a result (because the constant of proportionality is always positive), the equivalent plastic strain rate is always nonnegative. 

If, in solving the equations for the equivalent plastic strain increment, you come up with a negative increment, it means that the response to the strain increment was elastic.  What that means is that the inner product of the strain increment with the normal to the the yield surface was less than zero, indicating unloading or motion of the stress toward the center of the yield surface.  The standard approach is to calculate a trial stress, which is done by assuming the entire strain increment is elastic.  In your case, that stress should lie inside the yield surface.  Does that help?


 Matt Lewis
Los Alamos, New Mexico

Thanks Matt for your elaborate reply. It was very helpful and made the confusions clear. Yes, by plastic strain increment I meant equivalent plastic strain increment and the problem is an elasto-viscoplastic problem. Actually I am using a formulation following the formulation mentioned by Fleck and Hutchinson where increment of equivalent plastic strain rate and displacement increment are considered as an independant degree of freedom. And the system of equations are decoupled so the displacement increment and the plastic strain rate increment can be solved independently. So, I guess that in this case I can simply make the plastic strain increment zero when the solution finds a negetive increment and update the stress and strains from the displacement increment ? And I am attaching the paper with this message.



faizan.iitm's picture


Sir , i m simmulating elastic-plastic analysisi of flat notch bar . i have the experimental data of froce and delection for flat notch bar and of round tensile bar of the same material .

1) could i use the plastic strain value of round bar int the elastic plastic analysis of notch bar , 

2) if i want to get plastic strain value of notch bar ,, which area of cross ssection  takeand what about the gauge lenght ?

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