$($a$)$ A solid cylinder of circular cross$-$section in forged axi$-$symmetrically to half its initial height. Calculate the three orthogonal true strains and the total effective $($von Mises$)$ strain. $(5$ points$)$

$($b$)$ If the cylinder is "Barreled" during forging, what are its causes, and how can it be reduced? Draw a diagram of the barreled cylinder to explain your arguments. $(5$ points$)$