Problem $4$:

An elastic material is subjected to thermoelastic loading in a rigid die $($shown below$).$ The mechanical properties of the material are given as: elastic modulus, $E,$ Poisson's ratio, $v,$

and coefficient of thermal expansion, $.$ The sample of material fits snuggle inside the die and is initially cube$-$shaped $($i$.$e$.,LLL)$ and subjected to a temperature change of $T.$ Determine the state of stress of the material as well as its change in volume.

$2$