SECONDARY DEFORMATIONS DUE TO AXIAL SHEAR OF THE ANNULAR REGION BETWEEN 2 ECCENTRICALLY PLACED CYLINDERS

Fosdick and Kao [1] extended a conjecture of Ericksen's [2] for non-li near fluids, to non-linear elastic solids, and showed that unless the material moduli of an isotropic elastic material satisfied certain spe cial relations, axial shearing of cylinders would be necessarily accom panied by secondary deformations if the cross-section were not a circl e or the annular region between two concentric circles. Further, they used the driving force as the small parameter for a perturbation analy sis and showed that the secondary deformation will occur at fourth ord er, much in common with what is known for non-linear fluids. Here, we show that if on the other hand the driving force is not small (of O(1) ), but the departure of the cylinder from circular symmetry is small, then secondary deformations appear at first order, the parameter for p erturbance being the divergence from circular symmetry.