MULTIPLE HELICAL PERVERSIONS OF FINITE, INTRISTICALLY CURVED RODS

Author:

DOMOKOS G.1,HEALEY T. J.2

Affiliation:

1. Department of Mechanics, Materials and Structures and Center for Applied Mathematics and Computational Physics, Budapest University of Technology and Economics, H-1521 Budapest, Hungary

2. Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853-1503, USA

Abstract

We investigate mechanical spatial equilibria of slender elastic rods with intristic curvature. Our work is, to some extent, motivated by papers [Goriely & Tabor, 1998; Goriely & McMillen 2002]. There such rods of infinite length were recently studied to quantify the behavior of botanical filaments. In particular, an adequate explanation for the existence of helical perversions (the transition between helical segments of opposite handedness) is provided in [Goriely & Tabor, 1998]. However, this theory fails to describe multiple perversions, which can be observed in Nature. In contrast we formulate a two-point boundary-value problem describing rods of finite length with initial curvature and clamped ends. We identify trivial solutions as straight configurations and also k-covered circles, rigorously establish the existence of local bifurcations, and then compute global solutions via the Parallel Hybrid Algorithm [Domokos & Szeberényi, 2004] to find spatially complex equilibria characterized by multiple perversions. Based on computational results and the White–Fuller theorem [White, 1969; Fuller, 1971; Calugareanu, 1961] we describe a heuristic global picture of the bifurcation diagram, which can serve as an explanation for the evolution of physically observable tendril shapes.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

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