Second-order effects in the torsion of elastic materials with voids

This paper applies the technique of successive approximation to the nonlinear theory of elastic materials with voids, as developed by Nunziato and Cowin [2]. The complete set of equations for the first and second order approximation is derived. The torsion problem within the second-order theory is studied. It is shown that the solution can be expressed in terms of solutions of some two-dimensional problems. The theory is applied to study the torsion of a circular cylinder. It is shown that an infinitesimal twist produces a second-order volume fraction field which is proportional to the square of the amount of torsion. © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.