Which criterion is commonly identified with Von Mises theory, using distortion energy to predict yielding?

• A. Distortion energy theory
• B. Maximum shear stress theory
• C. Von Mises criterion
• D. Hydrostatic criterion

Answer: (C)

Distortion energy governs when ductile metals yield under complex loading. The Von Mises criterion embodies this idea by using an equivalent stress derived from the deviatoric (distortion) part of the stress, not the hydrostatic (pressure) part. Yielding occurs when this equivalent von Mises stress reaches the yield strength in simple uniaxial tension. In practice, the equivalent stress is computed from the principal stresses as sigma_eq = sqrt(((sigma1 - sigma2)^2 + (sigma2 - sigma3)^2 + (sigma3 - sigma1)^2)/2). This reflects energy associated with shape change, so uniform pressure doesn’t by itself cause yielding under this criterion.

The phrase distortion energy theory is essentially describing the same concept, but the widely used and recognized name for it is the Von Mises criterion. Other options describe different ideas: the maximum shear stress theory (Tresca) uses the largest shear stress to predict yielding, and a hydrostatic criterion would predict yield based on pressure alone. Therefore, the criterion tied to distortion energy and yielding under multi-axial states is the Von Mises criterion.