A ruled narrow elastic strip model with corrected energy
Abstract
We present a new one-dimensional model for elastic strips based on a nondevelopable ruled surface. An auxiliary field regularizes the Sadowsky narrow-strip model to allow nonzero twist with vanishing curvature. The energy exhibits the scalings derived by Freddi and co-workers, and for a certain choice of parameter, convexifies the Sadowsky energy without patching. We present the kinematics and energetics of the model, and employ a variational approach featuring a rotation tensor to derive equilibrium equations. We perform a regular perturbation expansion to study the model behavior close to inflection points. When the energy is convex, curvature and moment are continuous at inflection points, while the auxiliary function suffers a jump, leading to a discontinuity in the ruled embedding for any finite width.
Keywords
Cite
@article{arxiv.2512.19895,
title = {A ruled narrow elastic strip model with corrected energy},
author = {E. Vitral and J. A. Hanna and L. Koens},
journal= {arXiv preprint arXiv:2512.19895},
year = {2025}
}