page_title: Yield surface
section_title: von Mises yield surface
hierarchical_section_title: Yield surface / Examples of yield surfaces / von Mises yield surface
context_page_description: A yield surface is a five-dimensional surface in the six-dimensional space of stresses. The yield surface is usually convex and the state of stress of inside the yield surface is elastic. When the stress state lies on the surface the material is said to have reached its yield point and the material is said to have become plastic. Further deformation of the material causes the stress state to remain on the yield surface, even though the shape and size of the surface may change as the plastic deformation evolves. This is because stress states that lie outside the yield surface are non-permissible in rate-independent plasticity, though not in some models of viscoplasticity.
  The yield surface is usually expressed in terms of a three-dimensional principal stress space, a two- or three-dimensional space spanned by stress invariants or a version of the three-dimensional Haigh–Westergaard stress space. Thus we may write the equation of the yield surface in the forms:
  where are the principal stresses.
  where is the first principal invariant of the Cauchy stress and are the second and third principal invariants of the deviatoric part of the Cauchy stress.
context_section_description: The von Mises yield criterion is expressed in the principal stresses as
  where  is the yield strength in uniaxial tension.
  Figure 3 shows the von Mises yield surface in the three-dimensional space of principal stresses. It is a circular cylinder of infinite length with its axis inclined at equal angles to the three principal stresses. Figure 4 shows the von Mises yield surface in two-dimensional space compared with Tresca–Guest criterion.  A cross section of the von Mises cylinder on the plane of  produces the elliptical shape of the yield surface.
caption: Figure 4: Comparison of Tresca–Guest and Huber–Mises–Hencky criteria in 2D space (
    
      
        
          
            σ
            
              1
            
          
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            σ
            
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      {\displaystyle \sigma _{1},\sigma _{2}}
    
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