Past exam of the solid mechanics course of the University of Oxford / 2009 / 3 / i

At every point the deformation gradient attains the differentiable energy's minimum, so $DW(D\mathbf{y})=0$ and it is a natural state. By the strict Baker-Ericksen argument just proved, all its principal stretches are equal. In the radial formula this givesThus $r(R)=vR$ for one constant $v>0$ on the connected radial interval, andThe constancy is global through the annulus, not a separately chosen dilation at each point.