a$)$ In general, how many components are required to specify elastic constant. If you multiply it by Kronecker delta, what would be its rank?

b$)$ Discuss the stress distribution in the vicinity of a crack. For an orientation directly ahead of crack tip, prove that ${}_x={}_y=(\sqrt[\phantom{2}]{\frac{a}{2r}})$ and ${}_{xy}=0.$

c$)$ Discuss the flow curves of Rigid ideal plastic, Ideal plastic with elastic region, and Strain hardening materials.

d$)$ How the Crack Opening Displacement $($COD$)$ is different from $K_{Ic}?$ Discuss its applicability.