A numerical scheme for the study of poynting effect in wave propagation problems with finite boundaries

A second order effect, involving a change of length or an axial force, is present in hyperelastic cylindrical rods subjected to a finite twist. This second order effect leads to a coupling of torsional and longitudinal waves in such rods when they are subjected to finite deformations. In this paper, effects of such a coupling has been studied for cylindrical rods of finite length. The resulting finite deformation elastodynamic problem has been solved by a finite difference method which is a finite deformation elastodynamic problem has been solved by a finite difference method which is a MacCormack two-step variant of Lax-Wendroff second order accurate scheme. The accuracy of the numerical technique has been calibrated by comparing solutions with reported similarity solutions for semi-infinite rods. New results have been presented for finite rods and different loading conditions.