Mathematical Formulation
Mathematically the von Mises yield criterion is expressed as:
where is the yield stress of the material in pure shear. As shown later in this article, at the onset of yielding, the magnitude of the shear yield stress in pure shear is √3 times lower than the tensile yield stress in the case of simple tension. Thus, we have:
where is the yield strength of the material. If we set the von Mises stress equal to the yield strength and combine the above equations, the von Mises yield criterion and expressed as:
or
Substituting with terms of the stress tensor components
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.
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