An analysis of professor J.F. Bell's research on the finite twist and extension of thin-walled polycrystalline cylindrical tubes

Professor J. F. Bell's empirical result regarding the rotation factor in the polar decomposition of the deformation gradient for the finite twist-extension of a thin-walled polycrystalline cylindrical metal tube is examined. The correct expression for the rotation is derived and used to show how Bell's result should be interpreted. Some implications for his incremental plasticity equations are also discussed. In particular, they are shown to satisfy appropriate invariance requirements when cast in terms of the variables actually measured by Bell in his experiments. Further consequences of his equations consistent with his data are also derived. Finally, it is shown that his theory furnishes a consistent constitutive statement about the response of isotropic solids provided that the Cauchy stress is constrained to be symmetric.