A ruled narrow elastic strip model with corrected energy

E. Vitral; J. A. Hanna; L. Koens

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arXiv · 2512.19895

A ruled narrow elastic strip model with corrected energy

E. Vitral·J. A. Hanna·L. Koens

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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.

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E. Vitral, J. A. Hanna, L. Koens. 2025-12-22. A ruled narrow elastic strip model with corrected energy. https://arxiv.org/abs/2512.19895

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