Geometric Aspects of Discrete Elastic Rods

Abstract

Elastic rods are curve-like elastic bodies that have one dimension (length) much larger than the others (cross-section). Their elastic energy breaks down into three contributions: stretching, bending, and twisting. Stretching and bending are captured by the deformation of a space curve called the centerline, while twisting is captured by the rotation of a material frame associated to each point on the centerline. Building on the notions of framed curves, parallel transport, and holonomy, we present a smooth and a corresponding discrete theory that establishes an efficient model for simulating thin flexible rods with arbitrary cross section and undeformed configuration.