Torsion of compound cross-sections with imperfect interface

The Saint-Venant torsion problem of compound sections with imperfect interfaces is studied. Two kinds of an imperfect interface are considered: an imperfect interface which models a thin interphase of low shear modulus and an interface which models a thin interphase of high shear modulus. At the former kind, the tractions are continuous but the warping displacement undergoes a discontinuity; at the later kind the warping displacement is continuous but the shear traction undergoes a discontinuity. These imperfect interface conditions have been derived in a companion study [1]. The present paper is concerned with deriving benchmark solutions for the Saint-Venant torsion problem of compound sections with imperfect interfaces. Specifically, analytical solutions are given for a) a two-phase rectangular section, b) a two-phase section in the shape of a circular sector with an imperfect interface located along a circular arc, c) a two-phase circular sector with an imperfect interface along a radial line. The effect of imperfect bonding on the torsional rigidity of the compound bar is examined.