Problem $4$ A $50mm$ cube of an orthotropic graphite reinforced epoxy is extended in the $1$ direction by $0\mathrm{.}5mm$ and is constrained against contractions in the $3$ direction: no strain in that direction. There is no constraint in the $2-$direction. What is the normal strain in the $2$ direction and the normal stresses along the $1$ and $3$ directions? The compliance matrix is given below.

$[S]=\left[\begin{array}{cccccc}6\mathrm{.}45& -1\mathrm{.}600& -1\mathrm{.}600& 0& 0& 0\\ -1\mathrm{.}600& 82\mathrm{.}6& -37\mathrm{.}9& 0& 0& 0\\ -1\mathrm{.}600& -37\mathrm{.}9& 82\mathrm{.}6& 0& 0& 0\\ 0& 0& 0& 312& 0& 0\\ 0& 0& 0& 0& 227& 0\\ 0& 0& 0& 0& 0& 227\end{array}\right](TPa{)}^{-1}$