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A second order semi-discrete Cosserat rod model suitable for dynamic simulations in real time

: Lang, H.; Linn, J.


Simos, T.E. ; European Society of Computational Methods in Sciences and Engineering -ESCMSE-:
Numerical analysis and applied mathematics. International Conference on Numerical Analysis and Applied Mathematics 2009. Vol.2 : Rethymno, Crete, Greece, 18 - 22 September 2009
New York, N.Y.: AIP Press, 2009 (AIP Conference Proceedings 1168)
ISBN: 978-0-7354-0708-4
ISBN: 978-0-7354-0709-1
ISSN: 0094-243X
International Conference on Numerical Analysis and Applied Mathematics (ICNAAM) <2009, Rethymno/Crete>
Conference Paper
Fraunhofer ITWM ()

We present an alternative approach for a semi-discrete viscoelastic Cosserat rod model that allows both fast dynamic computations within milliseconds and accurate results compared to detailed finite element solutions. The model is able to represent extension, shearing, bending and torsion. For inner dissipation, a consistent damping potential from Antman is chosen. The continuous equations of motion, which consist a system of nonlinear hyperbolic partial differential algebraic equations, are derived from a two dimensional variational principle. The semi-discrete balance equations are obtained by spatial finite difference schemes on a staggered grid and standard index reduction techniques. The right-hand side of the model and its Jacobian can be chosen free of higher algebraic (e.g. root) or transcendent (e.g. trigonometric or exponential) functions and is therefore extremely cheap to evaluate numerically. For the time integration of the system, we use well established stiff solvers. As our model yields computational times within milliseconds, it is suitable for interactive manipulation. It reflects structural mechanics solutions sufficiently correct, as comparison with detailed finite element results shows.