Von Mises yield criterion

The von Mises yield criterion suggests that the yielding of materials begins when the second deviatoric stress invariant ${\displaystyle J_{2}}$ reaches a critical value. It is part of a plasticity theory that applies best to ductile materials, such as metals. Prior to yield, material response can be assumed to be anything i.e. nonlinear elastic, viscoelastic or simply linear elastic.

In materials science and engineering the von Mises yield criterion can be also formulated in terms of the von Mises stress or equivalent tensile stress, ${\displaystyle \sigma _{v}}$, a scalar stress value that can be computed from the Cauchy stress tensor. In this case, a material is said to start yielding when its von Mises stress reaches a critical value known as the yield strength, ${\displaystyle \sigma _{y}}$. The von Mises stress is used to predict yielding of materials under any loading condition from results of simple uniaxial tensile tests. The von Mises stress satisfies the property that two stress states with equal distortion energy have equal von Mises stress.

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