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Mechanical Sciences An open-access journal for theoretical and applied mechanics

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Mech. Sci., 4, 79-96, 2013
https://doi.org/10.5194/ms-4-79-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
14 Feb 2013
Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping
J. Linn1, H. Lang2, and A. Tuganov1 1Fraunhofer Institute for Industrial Mathematics, Fraunhofer Platz 1, 67633 Kaiserslautern, Germany
2Chair of Applied Dynamics, Univ. Erlangen-Nürnberg, Konrad-Zuse-Str. 3–5, 91052 Erlangen, Germany
Abstract. We present the derivation of a simple viscous damping model of Kelvin–Voigt type for geometrically exact Cosserat rods from three-dimensional continuum theory. Assuming moderate curvature of the rod in its reference configuration, strains remaining small in its deformed configurations, strain rates that vary slowly compared to internal relaxation processes, and a homogeneous and isotropic material, we obtain explicit formulas for the damping parameters of the model in terms of the well known stiffness parameters of the rod and the retardation time constants defined as the ratios of bulk and shear viscosities to the respective elastic moduli. We briefly discuss the range of validity of the Kelvin–Voigt model and illustrate its behaviour for large bending deformations with a numerical example.

Citation: Linn, J., Lang, H., and Tuganov, A.: Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping, Mech. Sci., 4, 79-96, https://doi.org/10.5194/ms-4-79-2013, 2013.
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