Writhing instabilities of twisted rods: from infinite to finite length

S. Neukirch, G.H.M. van der Heijden & J.M.T. Thompson

We use three different approaches to describe the static spatial configurations of a twisted rod as well as its stability during rigid loading experiments. The first approach considers the rod as infinite in length and predicts an instability causing a jump to self-contact at a certain point of the experiment. Semi-finite corrections, taken into account as a second approach, reveal some possible experiments in which the configuration of a very long rod will be stable throughout. Finally, in a third approach, we consider a rod of real finite length and we show that another type of instability may occur, leading to possible hysteresis behaviour. As we go from infinite to finite length, we compare the different information given by the three approaches on the possible equilibrium configurations of the rod and their stability. These finite size effects studied here in a 1D elasticity problem could help us guess what are the stability features of other more complicated (2D elastic shells for example) problems for which only the infinite length approach is understood.

keywords: stability and bifurcations, buckling, finite deflections, elastic material, beams and columns

J. Mech. Phys. Solids 50, 1175-1191 (2002)