The von Mises criterion, named after Richard von Mises (the engineer brother of economist Ludwig), is one of two techniques commonly used to determine whether or not a structure or element of a structure subject to applied forces will fail.

As in the Tresca criterion, you first need to calculate the principal stresses. In this case, there's no need to rank them from highest to lowest, but the math is a bit more complicated.

In two dimensions, given the known yield point of the material (σyp) and the principal stresses σ1 and σ2, the criterion is σyp ≥ (σ12 + σ22 - σ1σ2)½.

In three dimensions, the equation becomes: σyp ≥ [((σ12 - σ22) + (σ22 - σ32) - (σ32 - σ12)) / 2]½.

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