In this paper, we first review previous work on the antiplane shear of an elastic fiber composite containing fibermatrix interfaces that suffer nonlinear slip. We extend the theory to account for viscoelastic matrix response treating the solitary fiber problem and effective composite response along the way. The elastic and viscoelastic constitutive relations developed are used to analyze the pure torsion of a circular cylinder containing unidirectional fibers aligned parallel to the cylinder axis. The existence and character of singular surfaces, i.e., surfaces that separate regions of fully slipped material from a minimally slipped core are analyzed as well.

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