Is it possible , theta = k/G(r), where k is a constant and shear modulus which is a function of r.
For the case of uniform torsion with no warping restraint, the rate of twist remains constant along the axis of the bar. So theta* (rate of twist) = T/ G(r)*J where T is the torsional stress resultant at any section along the axis and J is the torsional constant at that section.
For a prismatic bar, J is constant, so effectively, theta*=K/G(r) where K=T/J is constant along the axial coordinate.
The only change expected in the case of torsion of inhomogeneous isotropic bars is that the shear stress is sensitive to the variation assumed for G. So the max shear stress may not occur at the outer radius of the bar.
For more info, check out the attached paper.
Theta=T/(G*J)
Where T is the moment of torsion, G is the shear modulus and J is the torsion constant for the section.
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