Yield surface

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 first principal invariant ( I 1 {displaystyle I_{1}}  ) of the Cauchy stress ( σ {displaystyle {oldsymbol {sigma }}}  ), and the second and third principal invariants ( J 2 , J 3 {displaystyle J_{2},J_{3}}  ) of the deviatoric part ( s {displaystyle {oldsymbol {s}}}  ) of the Cauchy stress are defined as:There are several different yield surfaces known in engineering, and those most popular are listed below.