Non-smooth solutions in the azimuthal shear of an anisotropic nonlinearly elastic material

In the context of nonlinear anisotropic elasticity the model plane-strain problem of azimuthal shear of a circular cylindrical tube is considered. In particular, the effect of anisotropy associated with preferred material directions on the emergence and disappearance of non-uniqueness of solution is examined. The non-smooth character of the global energy-minimizing solution of the boundary-value problem in which the inner boundary is fixed and the outer boundary is subject to a prescribed shear traction is highlighted and illustrated graphically.