According to the Distortion Energy Theory, failure will not occur when (Symbols have the usual meaning)

- 1
  
  ${[\frac{{(σ_{1} - σ_{2})}^{2} + {(σ_{2} - σ_{3})}^{2} + {(σ_{3} - σ_{1})}^{2}}{2}]}^{\frac{1}{2}} \leq σ_{0}$
- 2
  
  ${[{(σ_{1} - σ_{2})}^{2} + 4 τ^{2}]}^{\frac{1}{2}} \leq σ_{0}$
- 3
  
  ${[({σ_{1}}^{2} + {σ^{2}}_{2} + {σ_{3}}^{2}) - \frac{1}{m} (σ_{1} σ_{2} + σ_{2} σ_{3} + σ_{3} σ_{1})]}^{\frac{1}{2}} \leq σ_{0}$
- 4
  
  $\frac{{(σ_{1} + σ_{2})}^{2} + {[{(σ_{1} - σ_{2})}^{2} + 4 τ^{2}]}^{\frac{1}{2}}}{2} \leq σ_{0}$

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