I am running a fairly large shell element model and the stress graphic shows considerable negative von Mises stresses. How is this possible or is it just the graphic that has a problem?

The values at the nodes should always be non-negative. But the contour plot for values between nodes is calculated using the elements' shape functions which, if they're quadratic, allow negative values. It's partly a graphics problem (quadratic interpolation may not be the best choice for von Mises) and partly discretization error. If you refine the mesh, the negative values should move towards positive as they become more accurate.

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