Problem $2$

The strain tensor for a material element is given as:

$lon=\left[\begin{array}{ccc}3{10}^{-5}& 1{10}^{-5}& 0\\ 1{10}^{-5}& -3{10}^{-5}& 0\\ 0& 0& 0\end{array}\right]$

The material is isotropic linear elastic with Lam$$ constant $=80$GPa, Shear modulus $=80$GPa. It has a tensile strength of $10$ MPa $,$ a compressive strength of $-10$ MPa $,$ and a shear strength of $5$ MPa $.$ Will the material fail under any orientation? If so$,$ determine the plane of failure.