A ruled narrow elastic strip model with corrected energy
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912784976969728 |
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| author | Vitral, E. Hanna, J. A. Koens, L. |
| author_facet | Vitral, E. Hanna, J. A. Koens, L. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_19895 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A ruled narrow elastic strip model with corrected energy Vitral, E. Hanna, J. A. Koens, L. Soft Condensed Matter 74K99 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. |
| title | A ruled narrow elastic strip model with corrected energy |
| topic | Soft Condensed Matter 74K99 |
| url | https://arxiv.org/abs/2512.19895 |