Question

According to Von-Mises' distortion energy theory, the distortion energy under three dimensional stress state is represented by

• A. $\frac{1}{2E}[{\sigma }_1^2+{\sigma }_2^2+{\sigma }_3^2-2\mu ({\sigma }_1{\sigma }_2+{\sigma }_3{\sigma }_2+{\sigma }_1{\sigma }_3\left)\right]$
• B. $\frac{1-2\mu }{6E}[{\sigma }_1^2+{\sigma }_2^2+{\sigma }_3^2+2({\sigma }_1{\sigma }_2+{\sigma }_3{\sigma }_2+{\sigma }_1{\sigma }_3\left)\right]$
• C. $\frac{1+\mu }{3E}[{\sigma }_1^2+{\sigma }_2^2+{\sigma }_3^2-({\sigma }_1{\sigma }_2+{\sigma }_3{\sigma }_2+{\sigma }_1{\sigma }_3\left)\right]$
• D. $\frac{1}{3E}[{\sigma }_1^2+{\sigma }_2^2+{\sigma }_3^2-\mu ({\sigma }_1{\sigma }_2+{\sigma }_3{\sigma }_2+{\sigma }_1{\sigma }_3\left)\right]$

Answer 1

The correct option is C $\frac{1+\mu }{3E}[{\sigma }_1^2+{\sigma }_2^2+{\sigma }_3^2-({\sigma }_1{\sigma }_2+{\sigma }_3{\sigma }_2+{\sigma }_1{\sigma }_3\left)\right]$

No solution.