(Solved): Consider a differential (i.e. very small) element in a thick walled cylinder originally at (R,,Z) ...

Consider a differential (i.e. very small) element in a thick walled cylinder originally at $$(R,?,Z)$$ (i.e. in its unloaded state). This element moves to $$(r,?,z)$$ after loading. A general expression for deformation gradient in cylindrical coordinates is: $$\mathbf{F}=\left[\begin{array}{ccc}\frac{?r}{?R}& \frac{1}{R}\frac{?r}{??}& \frac{?r}{?Z}\\ r\frac{??}{?R}& \frac{r}{R}\frac{??}{??}& r\frac{??}{?Z}\\ \frac{?z}{?R}& \frac{1}{R}\frac{?z}{??}& \frac{?z}{?Z}\end{array}\right]$$ a) Find deformation gradient $$F$$ and Green strain $$E$$ for the following mapping of deformation for this element. $$r=aR,?=?,z=bZ$$ b) Interpret this deformation.