Problem $4.$

Consider the stress field:

$(x)=\left[\begin{array}{ccc}1& 0& \frac{1}{2}(x_1^2+x_2^2)\\ 0& 1& 4\\ x_2^2& x_1+2& x_3\end{array}\right]$

a$)$ Find the principal stresses and principal directions of stress at the point $(2,2,1).$

b$)$ Find the maximum shear stress at this point.