EXISTENCE AND UNIQUENESS OF AZIMUTHAL SHEAR SOLUTIONS IN COMPRESSIBLEISOTROPIC NONLINEAR ELASTICITY

The authors consider the two-point boundary-value problem resulting fr om the equations of nonlinear elastostatics for azimuthal shear of a B latz-Ko tube. Previous work on this problem by Simmonds and Wane inclu des a numerical study of these equations and indicates that smooth rad ial deformation solutions (no kinks) should exist regardless of the as pect ratio of the tube, provided that the dimensionless applied torque tau is small enough (tau <approximate to 0.72). The numerics of Simmo nds and Warne also indicated that the existence of smooth solutions fo r tau >approximate to 0.72 depends on the geometry of the tube, and th at for tau = root 3, no smooth solution exists. Motivated by this nume rical work, the authors prove via a topological shooting argument the existence and uniqueness of smooth solutions to this problem for tau l ess than or equal to tau(cr) = root 3/4 4/3 approximate to 0.69, and t he nonexistence of smooth solutions for tau = root 3.