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  • Letter
  • Open Access

Origin of anticlastic curvature in a cellular metaplate

Taiki Toyonaga and Hirofumi Wada*

  • *Contact author: hwada@fc.ritsumei.ac.jp
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Phys. Rev. Research 6, L032051 – Published 3 September, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L032051

Abstract

Generating a three-dimensional curved surface from flat sheets using simple mechanical actuation is a crucial step in developing functional shape-shifting materials. Among the methodologies relying on emergent concepts, the traditional cellular solid-based plate, with its highly porous structures, provides a versatile tool for creating doubly curved surfaces through planar bending actuation. Leveraging a combination of digital fabrication, physical experiments, finite element simulation (FES), and linear elasticity theory, we demonstrate how such a cellular metaplate can exhibit doubly curved shapes. By extending Lamb's classical theory of the anticlastic effect in thin elastic plates to our cellular metaplate, we develop a scaling law for the crossover length below which the doubly curved surface appears as bc∼bLamb/ρ, where bLamb∼Rw, with R being the externally imposed radius of curvature, w being the plate thickness, and ρ being the relative density of a given cellular geometry. The prediction is validated by our experiment and FES. The proposed framework is versatile and emphasizes the fundamental physical principles governing the mechanics of shape-morphing surfaces.

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Phys. Rev. Research 6, L032051– Published 3 September, 2024
  • Received 9 January 2024
  • Accepted 17 July 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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