# Simplified von Mises equation - Principal stresses

## Description

RESTRICTIONS : σ₁₂ = σ₁₃ = σ₂₃ = 0

The von Mises yield criterion suggests that the yielding of materials begins when the second deviatoric stress invariant reaches a critical value. For this reason, it is sometimes called the -plasticity or flow theory. It is part of a plasticity theory that applies best to ductile materials, such as metals. Prior to yield, material response is assumed to be 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,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. The von Mises stress is used to predict yielding of materials under any loading condition from results of simple uniaxial tensile tests.

## Variables

σ_{v} | von Mises yield criterion (dimensionless) |

σ_{1} | stress tensor component (dimensionless) |

σ_{2} | stress tensor component (dimensionless) |

σ_{3} | stress tensor component (dimensionless) |