Saint-Venant torsion of a two-phase circumferentially symmetric compound bar

This work is concerned with the Saint-Venant torsion problem of a two-phase circumferentially symmetric compound prismatic bar. By generalizing a method originally proposed by Packham and Shail, we demonstrate that for a particular two-phase configuration, simply or multiply connected, which is invariant with phase interchange, the solutions can be constructed from solutions of two analogous problems with constant material properties. An effective shear modulus is derived in analytic form, which is approximately the harmonic mean of the component shear moduli. We also show that the effective torsional shear modulus is homogeneous for arbitrary configurations.