Non-linear dynamic intertwining of rods with self-contact

Author Posting. © Elsevier B.V., 2007. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in International Journal of Non-Linear Mechanics 43 (2008): 65-73, doi:10.1016/j.ijnonlinmec.2007.10.004.Twisted marine cables on the sea floor can form highly contorted three-dimensional loops that resemble tangles. Such tangles or ‘hockles’ are topologically equivalent to the plectomenes that form in supercoiled DNA molecules. The dynamic evolution of these intertwined loops is studied herein using a computational rod model that explicitly accounts for dynamic self-contact. Numerical solutions are presented for an illustrative example of a long rod subjected to increasing twist at one end. The solutions reveal the dynamic evolution of the rod from an initially straight state, through a buckled state in the approximate form of a helix, through the dynamic collapse of this helix into a near-planar loop with one site of self-contact, and the subsequent intertwining of this loop with multiple sites of self-contact. This evolution is controlled by the dynamic conversion of torsional strain energy to bending strain energy or, alternatively by the dynamic conversion of twist (Tw) to writhe (Wr).The authors (NCP and SG) gratefully acknowledge the research support provided by the U.S. Office of Naval Research (grant N00014-00-1-0001), the Lawrence Livermore 25 National Laboratories (grant B 531085), and the U. S. National Science Foundation (grants CMS 0439574 and CMS 0510266)