# Maximum von Mises Stress Criterion

The maximum von Mises stress criterion is based on the von Mises-Hencky theory, also known as the Shear-energy theory or the Maximum distortion energy theory.

## Pure Shear

In terms of the principal stresses σ1, σ2, σ3, the von Mises stress is expressed as:

σvonMises= {[( σ1 - σ2 )2 + ( σ2 - σ3 )2 + ( σ1 - σ3 )2 ] / 2}1/2

The theory states that a ductile material starts to yield at a location when the von Mises stress becomes equal to the stress limit. In most cases, the yield strength is used as the stress limit. However, the software allows you to use the ultimate tensile or set your own stress limit.

σvonMises >= σlimit

Yield strength is a temperature-dependent property. This specified value of the yield strength should consider the temperature of the component. The factor of safety at a location is calculated from:

Factor of Safety (FOS) = σlimit / σvonMises

In the case of pure shear, σ12 = σ21 ≠ 0 , while other σ12 = 0 , the von Mises criterion stress is expressed as: σ12 max = σyield / √3 = 0.5777 σyield .

This means that, at the onset of yielding, the maximum shear stress in pure shear is √3 times lower than the yield stress in the case of simple tension.

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