Von Mises Yield Criterion - Mathematical Formulation

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.

Read more about this topic:  Von Mises Yield Criterion

Famous quotes containing the words mathematical and/or formulation:

    An accurate charting of the American woman’s progress through history might look more like a corkscrew tilted slightly to one side, its loops inching closer to the line of freedom with the passage of time—but like a mathematical curve approaching infinity, never touching its goal. . . . Each time, the spiral turns her back just short of the finish line.
    Susan Faludi (20th century)

    Art is an experience, not the formulation of a problem.
    Lindsay Anderson (b. 1923)