In the case of plane stress, where the in-plane principal strains are given by (epsilon_{1}) and (epsilon_{2}),

Question:

In the case of plane stress, where the in-plane principal strains are given by $\epsilon_{1}$ and $\epsilon_{2}$, show that the third principal strain can be obtained from
\[\epsilon_{3}=\frac{-u\left(\epsilon_{1}+\epsilon_{2}\right)}{(1-u)}\]

where $u$ is Poisson's ratio for the material.

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