Hi,
I want to generate a 3D plot of the yield function I am interested in (see attached, s is the deviatoric stress. The function can be found in the paper of Darrieulat and Piot, International journal of plasticity, vol. 12, nr. 5, pp. 575-610 (1996) ). I don't have a formulation of that function in principal stresses. To figure out, how to plot such a yield surface, I began to plot the von Mises cylinder. For the formulation in principal stresses this is simply done with three loops over different values for the principal stresses, checking the yield condition for that stress state and just plotting those pairs of sig1,sig2, sig3, which fulfill the yield condition (see "vonMisesprincipalstresses.m"). With this I get the intended von Mises cylinder (see figure vonMises_correct.jpg). So this is fine.
To enlarge the simulation to a general stress tensor, I thought of using six loops over the six stress components, checking again the von Mises yield criterion (now the formulation in general stresses), calculating the principal stresses for the stress tensors, that fulfill the yield condition and plotting them again in 3D principal stress space (see "vonMisesgeneralstresses.m"). The result should be the same as in "vonMisesprincipalstresses.m" but it is not a cylinder anymore (see figure vonMises_wrong.jpg). I got the warning message, that there are duplicate data points. So I think, that I don't cover the whole principal stress space. In my opinion, this could be the reason for the truncated form of the yield surface, but I don't know how to solve that problem. How should I generate the stress tensors? Does anyone know how to handle that problem?
Or is there any way to convert the formulation of my yield function from general stresses to principal stresses?
Any help would be appreciated. Thanks in advance!
Selina
I found the solution myself. The problem was the calculation of the principal stresses. Matlab always sorts the eigenvalues, so the first principal stress value is always the biggest one and the other principal stresses have decreasing values.
Instead of using 6 loops for stress components one can still loop also here over the 3 principal stresses and calculate the deviatoric stresses as usually. I attach the correct code for all who have the same problem.
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