## Simulation of quasistatic deformations using discrete rod models

• Recently we developed a discrete model of elastic rods with symmetric cross section suitable for a fast simulation of quasistatic deformations [33]. The model is based on Kirchhoff’s geometrically exact theory of rods. Unlike simple models of “mass & spring” type typically used in VR applications, our model provides a proper coupling of bending and torsion. The computational approach comprises a variational formulation combined with a finite difference discretization of the continuum model. Approximate solutions of the equilibrium equations for sequentially varying boundary conditions are obtained by means of energy minimization using a nonlinear CG method. As the computational performance of our model yields solution times within the range of milliseconds, our approach proves to be sufficient to simulate an interactive manipulation of such flexible rods in virtual reality applications in real time.

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Author: J. Linn, T. Stephan urn:nbn:de:hbz:386-kluedo-15699 Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (144) Report English 2008 2008 Fraunhofer-Institut für Techno- und Wirtschaftsmathematik energy minimization; geometrically exact rod models ; quasistatic deformations ; variational formulation Fraunhofer (ITWM) 510 Mathematik

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