a$)$ Explain the method to draw the Mohr's Circle of Strain.

b$)$ In case of state of stress on a principle plane in $3$D$,$ Prove that ${}^3-{}^2{I}_1+I_2-I_3=0.$ Where, $({}_x+{}_y+{}_z)=I_1,({}_x{}_y+{}_y{}_z+{}_z{}_x-{}_{xy}^2-{}_{yz}^2-{}_{zx}{?}_z)=I_2,({}_x{}_y{}_z+2{}_{xy}{}_{yz}{}_{zx}-,{}_x{}_{yz}^2-{}_y{}_{xz}^2-{}_z{}_{xy}^2)=I_3$ and $$ is normal principle stress.

c$)$ Prove that volume strain is equal to the first invariant of strain tensor.

d$)$ Explain the following terms:

Pure shear without rotation.

Pure rotation without shear.

Simple shear.de