Discrete kinematics of Cosserat rods based on the difference geometry of framed curves

The theory of Cosserat rods provides versatile models for the simulation of large spatial deformations of slender flexible structures. As the strain measures of the mechanical theory are given in terms of the differential invariants of Cosserat curves, the kinematics of Cosserat rods are closely related to the differential geometry of framed curves. We utilize ideas from the difference geometry of framed curves in Euclidean space to construct the discrete kinematics of Cosserat rod models on a staggered grid, preserving the essential geometric properties independent of the coarseness of the discretization. On this basis, we also derive a vertex based model variant and discuss its relation to the discrete Cosserat rod kinematics obtained by a geodesic interpolation of the nodal variables in the Lie groups E 3 × SO(3) and SE(3).