Cosserat Rods with Projective Dynamics.

We present a novel method to simulate Cosserat rods with Projective Dynamics (PD). The proposed method is both numerically robust and accurate with respect to the underlying physics, making it suitable for a variety of applications in computer graphics and related disciplines. Cosserat theory assigns an orientation frame to each point and is thus able to realistically simulate stretching and shearing effects, in addition to bending and twisting. Within the PD framework, it is possible to obtain accurate simulations given the implicit integration over time and its decoupling of the local-global solve. In the proposed method, we start from the continuous formulation of the Cosserat theory and derive the constraints for the PD solver. We extend the standard definition of PD and add body orientations as system variables. Thus, we include the preservation of angular momentum, so that twisting and bending can be accurately simulated. Our formulation allows the simulation of different bending behaviors with respect to a user-defined Young's modulus, the radius of the rod's cross-section, and material density. We show how different material specifications in our simulations converge within a few iterations to a reference solution, generated with a high-precision finite element method. Furthermore, we demonstrate mesh independence of our formulation: Refining the simulation mesh still results in the same characteristic motion, which is in contrast to previous position based methods.