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In this paper, we present a viscoelastic rod model that is suitable for fast and accurate dynamic simulations. It is based on Cosserats geometrically exact theory of rods and is able to represent extension, shearing (stiff dof), bending and torsion (soft dof). For inner dissipation, a consistent damping potential proposed by Antman is chosen. We parametrise the rotational dof by unit quaternions and directly use the quaternionic evolution differential equation for the discretisation of the Cosserat rod curvature. The discrete version of our rod model is obtained via a finite difference discretisation on a staggered grid. After an index reduction from three to zero, the right-hand side function f and the Jacobian f/(q,v,t) of the dynamical system q=v,v=f(q,v,t) is free of higher algebraic (e.g. root) or transcendental (e.g. trigonometric or exponential) functions and, therefore, cheap to evaluate. A comparison with Abaqus finite element results demonstrates the correct m echanical behaviour of our discrete rod model. For the time integration of the system, we use well established stiff solvers like Radau5 or Daspk. As our model yields computational times within milliseconds, it is suitable for interactive applications in virtual reality as well as for multi-body dynamics simulation

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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.

Classical geometrically exact Kirchhoff and Cosserat models are used to study the nonlinear deformation of rods. Extension, bending and torsion of the rod may be represented by the Kirchhoff model. The Cosserat model additionally takes into account shearing effects. Second order finite differences on a staggered grid define discrete viscoelastic versions of these classical models. Since the rotations are parametrisecl by unit quaternions, the space discretisation results in differential-algebraic equations that are solved numerically by standard techniques like index reduction and projection methods. Using absolute coordinates, the mass and constraint matrices are sparse and this sparsity may be exploited to speed-up time integration. Further improvements are possible in the Cosserat model, because the constraints are just the normalisation conditions for unit quaternions such that the null space of the constraint matrix can be given analytically. The results of the theoretical investigations are illustrated by numerical tests

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AbstractThis paper describes the numerical investigation of the mechanical behaviour of a structural component of an aircraft wing flap support impacted by a wheel rim fragment. The support link made of composite materials was modelled in the commercial finite element code Abaqus/Explicit, incorporating intralaminar and interlaminar failure modes by adequate material models and cohesive interfaces. Validation studies were performed step by step using quasi-static tensile test data and low velocity impact test data. Finally, high velocity impact simulations with a metallic rim fragment were performed for several load cases involving different impact angles, impactor rotation and pre-stress. The numerical rim release analysis turned out to be an efficient approach in the development process of such composite structures and for the identification of structural damage and worst case impact loading scenarios.

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