Von Mises Stress (Distortion Energy Theory)

Von Mises stress is a stress criterion used to determine whether a material will yield or not. It is particularly widely used for metals and ductile materials (materials that exhibit the same properties in all directions). The von Mises theory is based on the concept of distortion energy and is also commonly referred to as the "distortion energy theory" or "maximum distortion energy theory".

The concept of von Mises stress was first proposed by Maksymilian Huber in 1904. However, it attracted significant attention when Richard von Mises independently reintroduced it in 1913 in a more comprehensive form. Both researchers provided only a mathematical equation; it was Heinrich Hencky who developed the concept of "von Mises stress" with a meaningful physical interpretation.

Von Mises argues that to determine whether a material has yielded, one must consider only the deviatoric stresses (not the total stresses, which include hydrostatic and deviatoric components).

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• Hydrostatic Stress
• • Hydrostatic stress is a state of stress or pressure that acts equally in all directions on a material.
  • This pressure causes a change in volume but does not produce any shape change (distortion).
  • Mathematically, hydrostatic stress is defined as follows.

This stress changes only the volume of the material. Plastic deformation

• Deviatoric Stress
• • Deviatoric stress is the component of stress that causes shape change (distortion) in the material.
  • These stresses are the primary cause of yielding in materials.