# Stress analysis: Von mises stress

## Introduction

Von Mises stress is usually used to analyze the yield point of a metal part under the action of complex loads. The stress value indicates the load per unit area at which material will yield or fracture. it helps engineers to check whether their design will withstand a given load condition.

## von Mises yield criterion

It is also known as the Maximum Distortion Energy. Its formula can be written as follows,

##

J

_{2}= k^{2}^{Where k is the yield stress of the material in pure shear.}

^{}

##
^{Use of Von Mises stress}

^{The stress value can be used, }

- To check whether the design will fail or work.
- T know how much deformation will happen.
- To choose the right material that can withstand the load.

The concept was first invented by Maksymilian Huber but became famous only when Richard von Mises in 1913 proposed it again. The main motto is to formulate a criterion for especially ductile metals that works for any complex 3-D loading situation, independent of the addition of normal and shear stresses.

## Distortion energy failure theory

It states that when material tries to yield, the distortion strain energy per unit volume (at the point of failure) equals or exceeds the distortion strain energy per unit volume when yielding occurs in the tension test specimen.

It can be expressed as,

Ïƒ

_{v}≥ Ïƒ_{y}_{}

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