On end rotation for open rods undergoing large deformations

G.H.M. van der Heijden, M.A. Peletier & R. Planqué

We give a careful discussion of end rotation in elastic rods, focusing on ambiguities that arise if arbitrarily large deformations are allowed. By introducing a closure and restricting to a class of deformations we show that a rigorous treatment of end rotation can be obtained. The results underpin various non-rigorous discussions in the literature and serve to promote the variational analysis of boundary-value problems for rods undergoing large deformations. As an example we discuss the application to the model of a rod lying on the surface of a cylinder.

keywords: rod theory, end rotation, twist, writhe, large deformations

Quarterly of Applied Mathematics 65, 385-402 (2007)