Which theory is described as the distortion energy approach and is used to predict yielding under multi-axial loading?

• A. Distortion energy theory
• B. Maximum principal stress theory
• C. Rankine criterion
• D. Coulomb criterion

Answer: (A)

The distortion energy approach, commonly known as the von Mises yield criterion, is the way to predict yielding under multi-axial loading. It rests on the idea that yield occurs when the energy associated with shape change (distortion) reaches the same level as in simple uniaxial tension. In practice, you compute the von Mises equivalent stress from the three principal stresses, for example using the expression σ_vm = sqrt[ ((σ1−σ2)^2 + (σ2−σ3)^2 + (σ3−σ1)^2) / 2 ]. Yield is predicted when σ_vm equals the material’s uniaxial yield stress.

This approach captures how combined stresses interact to cause yielding, unlike criteria that rely only on the largest principal stress. It also explains why hydrostatic (equal in all directions) pressure doesn’t trigger yielding in metals, since the distortional energy is zero for a purely hydrostatic state. In short, using the distortion energy (von Mises) criterion provides a robust way to predict yielding under complex, multi-axial loading.