Mises yield criterion is written as: or Substituting with the Cauchy stress tensor components, we get , where is called deviatoric stress. This equation defines the yield surface as a circular cylinder (See Figure) whose yield curve, or intersection with the deviatoric plane, is a circle with radius , or . This implies that the yield condition is independent of hydrostatic stresses. Reduced von Mises equation for different stress conditions Uniaxial (1D) stress In the case of uniaxial stress or simple tension, , the von Mises criterion simply reduces to , which means the material starts to yield when reaches the yield strength of the material , in agreement with the definition of tensile (or compressive) yield strength. Multi-axial (2D or 3D) stress An equivalent tensile stress or equivalent von-Mises stress, is used to predict yielding of materials under multiaxial loading conditions using results from simple uniaxial tensile tests. Thus, we define where are components of stress deviator tensor : . In this case, yielding occurs when the equivalent stress, , reaches the yield strength of the material in simple tension, . As an example, the stress state of a steel beam in compression differs from the stress state of a steel axle under torsion, even if both specimens are of the same material. In view of the stress tensor, which fully describes the stress state, this difference manifests in six degrees of freedom, because the stress tensor has six independent components. Therefore, it is difficult to tell which of the two specimens is closer to the yield point or has even reached it. However, by means of the von Mises yield criterion, which depends solely on the value of the scalar von Mises stress, i.e., one degree of freedom, this comparison is straightforward: A larger von Mises value implies that the material is closer to the yield point. In the case of pure shear stress, , while all other , von Mises criterion becomes: . This means that, at the onset of yielding, the magnitude of the shear stress in pure shear is times lower than the yield stress in the case of simple tension. The von Mises yield criterion for pure shear stress, expressed in principal stresses, is In the case of principal plane stress, and , the von Mises criterion becomes: This equation represents an ellipse in the plane . Summary Physical interpretation of the von Mises