question_answer

If \[{{\sigma }_{y}}\] is the yield strength of a particular material, then the distortion energy theory is expressed as:

A) \[{{({{\sigma }_{1}}-{{\sigma }_{2}})}^{2}}+{{({{\sigma }_{2}}-{{\sigma }_{3}})}^{2}}+{{({{\sigma }_{3}}-\sigma )}^{2}}=2s_{y}^{2}\]

B) \[({{\sigma }_{1}}^{2}+{{\sigma }_{2}}+{{\sigma }_{3}})-2v({{\sigma }_{1}}{{\sigma }_{2}}+{{\sigma }_{2}}{{\sigma }_{3}}+{{\sigma }_{3}}{{\sigma }_{1}})=\sigma _{y}^{2}\]

C) \[({{\sigma }_{1}}+{{\sigma }_{2}}^{2})+{{({{\sigma }_{2}}-{{\sigma }_{3}})}^{2}}+{{({{\sigma }_{3}}-{{\sigma }_{1}})}^{2}}=3{{\sigma }_{y}}^{2}\]

D) \[(1-2v){{({{\sigma }_{1}}+{{\sigma }_{2}}+{{\sigma }_{3}})}^{2}}=2(1+v){{\sigma }_{y}}\]