Simple deformation measures for Discrete elastic rods and ribbons

K Korner (1) , Basile Audoly (2) , K Bhattacharya (1)

1 CALTECH - California Institute of Technology
2 LMS - Laboratoire de mécanique des solides

The Discrete elastic rod method (Bergou et al., 2008) is a numerical method for simulating slender elastic bodies. It works by representing the centerline as a polygonal chain, attaching two perpendicular directors to each segment, and defining discrete stretching, bending and twisting deformation measures and a discrete strain energy. Here, we investigate an alternative formulation of this model based on a simpler definition of the discrete deformation measures. Both formulations are equally consistent with the continuous rod model. Simple formulas for the first and second gradients of the discrete deformation measures are derived, making it easy to calculate the Hessian of the discrete strain energy. A few numerical illustrations are given. The approach is also extended to inextensible ribbons described by the Wunderlich model, and both the developability constraint and the dependence of the energy on the strain gradients are handled naturally.

Mots clés: mechanical engineering; mechanics thin elastic rods; simulations; discrete geometry; ribbons

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des structures [physics.class-ph]; Physique mathématique [math-ph]

K Korner, Basile Audoly, K Bhattacharya. Simple deformation measures for Discrete elastic rods and ribbons. Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, 2021, 4477 (2256), ⟨10.1098/rspa.2021.0561⟩. ⟨hal-03414320v2⟩