TL;DR
This paper explores the deformation modes of periodic surfaces, demonstrating a fundamental orthogonality between membrane and bending modes and establishing a maximum combined mode count of three, with examples from origami tessellations.
Contribution
It introduces a theoretical framework showing the orthogonality of membrane and bending modes in periodic surfaces and limits their total number to three.
Findings
Membrane and bending modes are orthogonal in periodic surfaces.
Total number of effective modes (membrane + bending) cannot exceed three.
Examples from origami tessellations illustrate the theoretical results.
Abstract
A periodic surface is one that is invariant by a 2D lattice of translations. Deformation modes that stretch the lattice without stretching the surface are effective membrane modes. Deformation modes that bend the lattice without stretching the surface are effective bending modes. For periodic, piecewise smooth, simply connected surfaces, it is shown that the effective membrane modes are, in a sense, orthogonal to effective bending modes. This means that if a surface gains a membrane mode, it loses a bending mode, and conversely, in such a way that the total number of modes, membrane and bending combined, can never exceed 3. Various examples, inspired from curved-crease origami tessellations, illustrate the results.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Materials and Mechanics · Adhesion, Friction, and Surface Interactions · Surface Modification and Superhydrophobicity