%0 Journal Article
%T Geometrically exact Cosserat rods with Kelvin¨CVoigt type viscous damping
%A J. Linn
%A H. Lang
%A A. Tuganov
%J Mechanical Sciences (MS)
%D 2013
%I Copernicus Publications
%R 10.5194/ms-4-79-2013
%X We present the derivation of a simple viscous damping model of Kelvin¨CVoigt 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¨CVoigt model and illustrate its behaviour for large bending deformations with a numerical example.
%U http://www.mech-sci.net/4/79/2013/ms-4-79-2013.html