Abstract
AbstractWe apply the direct method of the calculus of variations to show that any nonplanar Frenet curve in $${\mathbb {R}}^{3}$$
R
3
can be extended to an infinitely narrow flat ribbon having minimal bending energy. We also show that, in general, minimizers are not free of planar points, yet such points must be isolated under the mild condition that the torsion does not vanish.
Publisher
Springer Science and Business Media LLC
Reference22 articles.
1. Audoly, B., Neukirch, S.: A one-dimensional model for elastic ribbons: a little stretching makes a big difference. J. Mech. Phys. Solids 153, Paper No. 104457, 31 pp (2021)
2. Bartels, S.: Numerical simulation of inextensible elastic ribbons. SIAM J. Numer. Anal. 58(6), 3332–3354 (2020)
3. Bevilacqua, G., Lussardi, L., Marzocchi, A.: Variational analysis of inextensible elastic curves. Proc. A. 478(2260), Paper No. 20210741, 16 pp (2022)
4. Chubelaschwili, D., Pinkall, U.: Elastic strips. Manuscr. Math. 133(3–4), 307–326 (2010)
5. Dal Maso, G.: An Introduction to $$\Gamma $$-Convergence, Progress in Nonlinear Differential Equations and Their Applications, vol. 8. Birkhäuser, Boston (1993)