$1.$ You are given a solid circular polycarbonate bar with a radius of $4$ mm and a length of $50$ mm $.$ The elastic modulus $($Young$\text{'}$s Modulus$)$ is reported as $2\mathrm{.}6$ GPa $,$ Poisson's ratio is $\backslash ($ v$=0\mathrm{.}46\backslash ),$ the yield stress is $46$ MPa $.$

a$.$ Calculate the stress and strain tensors if the bar is loaded axially in compression with a load of $2$ kN $.$

b$.$ Will the bar yield?

c$.$ Which criterion did you use to make this determination?