A NOTE ON THE FINITE EXTENSION AND TORSION OF A CIRCULAR CYLINDER OF COMPRESSIBLE ELASTIC ISOTROPIC MATERIAL

A circular compressible cylinder is given a finite extension increasing its length in the ratio λ: 1 and then a twist ψ per unit length so that plane sections perpendicular to the axis remain plane sections. The strain-energy function has a completely general form in terms of the three invariants of strain and the solution is developed as a power series in ψ. The ratio of the radii of the strained and unstrained cylinder and the longitudinal forces required to maintain the extension and twist are found in series as far as the terms in ψ2, whilst the axial couple necessary to produce the twist is given as far as the term in ψ3. The special case in which the longitudinal force is zero is also considered and the resulting extension ratio λ is evaluated in this case for a given ψ.