ArticleProceedings of the National Academy of Sciences of the United States of America2017
Growth patterns for shape-shifting elastic bilayers.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 35 papers.
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Who cites it
35 citing papers in PubMed.
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- Active twisting for adaptive droplet collection.Nature computational science · 2025Article
- Geometric modeling of knitted fabrics.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Programmable shape morphing of drying foods via symmetry breaking.Current research in food science · 2025Article
- Tuning the Properties of Multi-Stable Structures Post-Fabrication Via the Two-Way Shape Memory Polymer Effect.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2024Article
- TubULAR: tracking in toto deformations of dynamic tissues via constrained maps.Nature methods · 2023Article
- Growth anisotropy of the extracellular matrix shapes a developing organ.Nature communications · 2023Article
- Turing pattern-based design and fabrication of inflatable shape-morphing structures.Science advances · 2023Article
- Curvature-driven instabilities in thin active shells.Royal Society open science · 2022Article
- A Highly Multi-Stable Meta-Structure via Anisotropy for Large and Reversible Shape Transformation.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2022Article
- Controlling the shape and topology of two-component colloidal membranes.Proceedings of the National Academy of Sciences of the United States of America · 2022Article
- Programmed shape-morphing into complex target shapes using architected dielectric elastomer actuators.Science advances · 2022Article
- Interfacial metric mechanics: stitching patterns of shape change in active sheets.Proceedings. Mathematical, physical, and engineering sciences · 2022Article
- Article
- The Föppl-von Kármán equations of elastic plates with initial stress.Royal Society open science · 2022Article
- Active elastocapillarity in soft solids with negative surface tension.Science advances · 2022Article
- Totimorphic assemblies from neutrally stable units.Proceedings of the National Academy of Sciences of the United States of America · 2021Article
- Better tired than lost: Turtle ant trail networks favor coherence over short edges.PLoS computational biology · 2021Article
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3 authors.
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No grant is acknowledged in the PubMed record.
Abstract
Inspired by the differential-growth-driven morphogenesis of leaves, flowers, and other tissues, there is increasing interest in artificial analogs of these shape-shifting thin sheets made of active materials that respond to environmental stimuli such as heat, light, and humidity. But how can we determine the growth patterns to achieve a given shape from another shape? We solve this geometric inverse problem of determining the growth factors and directions (the metric tensors) for a given isotropic elastic bilayer to grow into a target shape by posing and solving an elastic energy minimization problem. A mathematical equivalence between bilayers and curved monolayers simplifies the inverse problem considerably by providing algebraic expressions for the growth metric tensors in terms of those of the final shape. This approach also allows us to prove that we can grow any target surface from any reference surface using orthotropically growing bilayers. We demonstrate this by numerically simulating the growth of a flat sheet into a face, a cylindrical sheet into a flower, and a flat sheet into a complex canyon-like structure.
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