2007/01/06 by Sachin Goyal, Noel C. Perkins, N. C. Perkins +1 · 74 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Materials and Mechanics #Bending #Classical mechanics #Computer science #Elastic energy #Fluid Dynamics Simulations and Interactions #Geometry #Helix (gastropod) #Loop (graph theory) #Mathematics #Mechanics #Physics #Planar #Rod #Structural Analysis and Optimization #Thermodynamics #Twist #Writhe #math-ph #math.DS #math.MP
paper · pdf · doi:10.1016/j.ijnonlinmec.2007.10.004
published in International Journal of Non-Linear Mechanics 43(1), 65-73 (Elsevier BV) · 35 pages, 9 figures, submitted to Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
arxiv created 2007/01/06 · openalex publication_date 2007/10/12 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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). KEY WORDS Rod Dynamics, Self-contact, Intertwining, DNA Supercoiling, Cable Hockling