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Code to plot von mises and tresca yield conditions

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dan
dan on 15 Nov 2019
Commented: Sharlin Shahid on 10 Feb 2021
Hello,
I am trying to figure out how to write a code to plot Von mises and Tresca yield condions at plane stress state. I am having trouble putting it all together in one code. Your help is much appreciated!!
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Sharlin Shahid
Sharlin Shahid on 10 Feb 2021
You can check how to plot von Mises and Hill48 yield surfaces to compare with experiments in this video:
https://youtu.be/JiCorn4u6TY

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Answers (1)

Unai San Miguel
Unai San Miguel on 17 Dec 2019
This plot can be generated
  1. with some analytic work, by getting the ellipse in parametric equations, generating points along that curve an plotting them with plot, and the same for the Tresca criterion, which is just a bunch of straight lines, or
  2. with brute force, defining functions for the left side of the equations and using contour to plot a single contour.
The latter approach has the advantage that one can plot any implicit function.
% Von Mises, s1^2 - s1s2 + s2^2 = Sy^2
% Non-dimensional variables x = s1 / Sy, y = s2 / Sy
vmc = @(x, y) x.^2 - x.*y + y.^2;
trc = @(x, y) 0.5 * max(cat(3, abs(x - y), abs(x), abs(y)), [], 3);
xx = linspace(-2, 2, 101);
yy = linspace(-2, 2, 101);
[X, Y] = ndgrid(xx, yy);
contour(X, Y, vmc(X, Y), [1 1])
hold on
contour(X, Y, trc(X, Y), [1 1]/2)
Note that the plot of the Tresca criterion is not going to be precise enough with this approach...
The trick of using contour to plot a single contour is in the documentation for the contour function, and the syntax for cat and |max| in their doc pages too.
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