$1.$ a$)$ Using Hook's law, derive the equation to calculate the energy required to induce plastic deformation

at zero plastic strain. This equation must include yield strength.

b$)$ With reference to Table $1,$ calculate the strain and energy required to induced yielding for Dual Phase

steel $600$ and TRIP $800.$

c$)$ Material A has twice the Young's modulus when compared to Material B and assuming both

materials have similar yield strength. Compare in terms of elastic energy when both materials are

under two different stages of loading. One is under constant stress and the other under constant strain.