Imagine a uniform wire of length ‘L’ suspended from the ceiling whose Young’s modulus of elasticity increases linearly from $Y_0$ at bottom to $Y_0+kL$  at the top. If ‘A’ is the area of cross-section and W be the load at its bottom then (neglect change in area of cross-section).

Tension is maximum at the top of the rope and equal to $W+\lambda Lg,where\lambda$  is linear density of the Rope 
 

The strain energy developed in the wire is $\frac{W^2}{2Ak}\ln [1+\frac{kL}{Y_0}]$  (if mass of rope is negligible compared to W)

Tension is maximum at the bottom of the rope and equal to W

Total elongation of the wire is $\frac{W}{Ak}\ln [1+\frac{kL}{Y_0}]$    (if mass of rope is negligible compared to W)