Von Mises stress

Von Mises stress, $\boldsymbol{\sigma\ _v}$ , is used to estimate yield criteria for ductile materials. It is calculated by combining stresses in two or three dimensions, with the result compared to the tensile strength of the material loaded in one dimension. Von Mises stress is also useful for calculating the fatigue strength.

Stress is a complicated six dimensional tensor quantity, Von Mises stress reduces this to one scalar number for the purposes of calculating yield criteria.

Von Mises stress in three dimensions;

$\sigma\ _v = \sqrt{\frac{(\sigma\ _1 - \sigma\ _2)^2 + (\sigma\ _2 - \sigma\ _3)^2 + (\sigma\ _3 - \sigma\ _1)^2 } {2}}$

where $\sigma\ _1,\sigma\ _2,\sigma\ _3$ are the principal stresses. In the case of plane stress, $\sigma\ _3$ is zero.

Finite element analysis results are typically presented as Von Mises stress.

Von Mises stress theory is also known as the Maximum Distortion Energy Theory and the Maxwell-Huber-Hencky-von Mises theory.

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See also