Von Mises yield criterion

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In continuum mechanics, the maximum distortion energy criterion (also von Mises yield criterion^[1]) states that yielding of a ductile material begins when the second invariant of deviatoric stress ${\displaystyle J_{2}}$ reaches a critical value.^[2] It is a part of plasticity theory that mostly applies to ductile materials, such as some metals. Prior to yield, material response can be assumed to be of a linear elastic, nonlinear elastic, or viscoelastic behavior.

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

Because the von Mises yield criterion is independent of the first stress invariant, ${\displaystyle I_{1}}$, it is applicable for the analysis of plastic deformation for ductile materials such as metals, as onset of yield for these materials does not depend on the hydrostatic component of the stress tensor.

Although it has been believed it was formulated by James Clerk Maxwell in 1865, Maxwell only described the general conditions in a letter to William Thomson (Lord Kelvin).^[3] Richard Edler von Mises rigorously formulated it in 1913.^[2][4] Tytus Maksymilian Huber (1904), in a paper written in Polish, anticipated to some extent this criterion by properly relying on the distortion strain energy, not on the total strain energy as his predecessors.^[5][6][7] Heinrich Hencky formulated the same criterion as von Mises independently in 1924.^[8] For the above reasons this criterion is also referred to as the "Maxwell–Huber–Hencky–von Mises theory".