Code to plot von mises and tresca yield conditions

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!!

[Erivelton Gualter]

I will make your life easier:

https://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer

[KALYAN ACHARJYA]

Can you share more details?

[dan]

My apologies, I want to plot the yield criterion for Tresca and Von-Mises in sigma1-sigma2 stress space using matlab . I really appreciate your help.

[Star Strider]

Not all of us are familiar with economics (that may be what you are referring to). Providing a sufficiently detailed description or reference would be apporopriate.

[Stephan]

I suspect the question refers to mechanical stress.

https://en.m.wikipedia.org/wiki/Yield_surface?wprov=sfla1

[Sharlin Shahid]

You can check how to plot von Mises and Hill48 yield surfaces to compare with experiments in this video:

https://youtu.be/JiCorn4u6TY

Answer 1

[Unai San Miguel]

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.

[Sahil Bharti]

Hi,

contour(X, Y, vmc(X, Y), [1 1])

What is the use of [1 1 ], in this expression ?

Thanks

[Unai San Miguel]

It is the way to plot only the contour with value 1, See this in the documentation.