Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Discrete cosserat rod models based on the difference geometry of framed curves for interactive simulation of flexible cables
 Ghezzi, L. ; European Consortium for Mathematics in Industry ECMI: Math for the Digital Factory Cham: Springer International Publishing, 2017 (Mathematics in industry 27) ISBN: 9783319639550 (Print) ISBN: 9783319639574 pp.289319 

 English 
 Book Article 
 Fraunhofer ITWM () 
Abstract
For software tools currently used in industry for computer aided design (CAD), digital mockup and virtual assembly there is an increasing demand to handle not only rigid geometries, but to provide also capabilities for realistic simulations of large deformations of slender flexible structures in real time (i.e.: at interactive rates). The theory of Cosserat rods provides a framework to perform physically correct simulations of arbitrarily large spatial deformations of such structures by stretching, bending and twisting. The kinematics of Cosserat rods is described by the differential geometry of framed curves, with the differential invariants of rod configurations corresponding to the strain measures of the mechanical theory. We utilize ideas from the discrete differential geometry of framed curves in combination with the variational framework of Lagrangian mechanics to construct discrete Cosserat rod models that behave qualitatively correct for rather coarse discretizations, provide a fast computational performance at moderate accuracy, and thus are suitable for interactive simulations. This geometry based discretization approach for flexible 1D structures has industrial applications in design and digital validation. We illustrate this with some application examples from automotive industry.