Reinforcement Paths on a Torus Under Internal Pressure: Toroidal Helix, Principal Stress Trajectory, and Geodesic Line

This contribution investigates and compares different fiber reinforcement paths on a torus subjected to internal pressure. In particular, the following three characteristic trajectories are considered: the toroidal helix, the path of the resultant principal stress, and a geodesic. The objective is to understand the role of fiber orientation on the structural strength and deformation of a pressurized torus. The wrapping angles of these trajectories vary along the cross-section of the torus. The geometrical wrapping angle of the toroidal helix and the toroidal neutral wrapping angle, which represents the orientation of the resultant principal stress path, behave qualitatively similar but quantitatively different, while the geodesic line behaves reciprocally. To characterize the mechanical response, we propose a stress ratio parameter that reflects how fiber paths relate to stress distribution and deformation behavior.