Simple deformation measures for Discrete elastic rods and ribbons

Abstract

The Discrete elastic rod method (Bergou et al., 2008) is a numerical method for simulating slender elastic bodies. It works by representing the center-line 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 of the strain gradients are handled naturally.

References in corpus (7)

• "Wunderlich, meet Kirchhoff": A general and unified description of elastic ribbons and thin rods
• A discrete geometric approach for simulating the dynamics of thin viscous threads
• Bifurcations of buckled, clamped anisotropic rods and thin bands under lateral end translations
• Twist-induced snapping in a bent elastic ribbon
• A numerical investigation of the fluid mechanical sewing machine
• Force and moment balance equations for geometric variational problems on curves
• A one-dimensional model for elasto-capillary necking

Cited by in corpus (2)

• Curling morphology of knitted fabrics: Structure and Mechanics
• Stability of boundary conditions for the Sadowsky functional