Find the deformation gradient in terms of gx2- if the

Question

An initially straight beam AB is bent into a circular arc A'B' as shown in the figure. The deformation is specified as

Where g(X₂) is a simple function of X₂.

(a) Find the deformation gradient in terms of g(X₂).

(b) If the volume of the beam does not change, find g(X₂).

(c) Using g(X₂) in (b), find U, Q, and V.