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International Journal of Differential Equations
Volume 2012 (2012), Article ID 718308, 15 pages
http://dx.doi.org/10.1155/2012/718308
Research Article

An Energy Conserving Numerical Scheme for the Dynamics of Hyperelastic Rods

1Fraunhofer Institut für Techno- und Wirtschaftsmathematk, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany
2Fachbereich Mathematik, Technische Universität Kaiserslautern, 67653 Kaiserslautern, Germany

Received 12 January 2012; Revised 21 June 2012; Accepted 5 July 2012

Academic Editor: Mapundi Banda

Copyright © 2012 Thorsten Fütterer et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A numerical method for special Cosserat rods based on Antman's description Antman, 2005 is developed for hyperelastic materials and potential forces. This method preserves the relevant properties of the underlying PDE system, namely, the orthonormality of the directors and the conservation of the energy.