Discrete Pitch-Angle Conditions for Helicoidal Stacking of Periodically Corrugated Rods

Résumé fourni par la source

Helical laminates, in which fibrous elements are stacked while rotating by a constant angle from one layer to the next, are common in natural and artificial materials, including Bouligand structures and fiber-reinforced composites. This study clarifies the geometric pitch-angle conditions that allow axially symmetric rod-like elements with periodic surface corrugations to form helical laminations. Using a rod model based on rods with axially symmetric periodic corrugations, we derive the stackability conditions under which the same stacking pattern can be repeated while maintaining concavity-to-concavity contact between adjacent layers. We show that the allowed intralayer phase shift is restricted to either zero or half the axial period and that the admissible pitch angles form discrete series determined by integer parameters. Mesh-based collision detection and rigid-body simulations confirm that these conditions predict stackable configurations for realistic rod shapes and that smaller pitch angles are mechanically more unstable.

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