MS Mechanical Sciences MS Mech. Sci. 2191-916X Copernicus Publications Göttingen, Germany 10.5194/ms-4-79-2013 Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping Linn J. 1 Lang H. 2 Tuganov A. 1 Fraunhofer Institute for Industrial Mathematics, Fraunhofer Platz 1, 67633 Kaiserslautern, Germany Chair of Applied Dynamics, Univ. Erlangen-Nürnberg, Konrad-Zuse-Str. 3–5, 91052 Erlangen, Germany 14 02 2013 4 1 79 96 Copyright: © 2013 J. Linn et al. 2013 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://ms.copernicus.org/articles/4/79/2013/ms-4-79-2013.html The full text article is available as a PDF file from https://ms.copernicus.org/articles/4/79/2013/ms-4-79-2013.pdf

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.

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