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dc.contributor.authorvan Rees, Wim
dc.contributor.authorVouga, Etienne
dc.contributor.authorMahadevan, Lakshminarayanan
dc.date.accessioned2019-10-24T00:36:12Z
dc.date.issued2017-10-16
dc.identifier.citationVan Rees, Wim M., Etienne Vouga, and L. Mahadevan. 2017. Growth Patterns for Shape-shifting Elastic Bilayers. Proceedings of the National Academy of Sciences of the United States of America 114, no. 44: 11597-11602.en_US
dc.identifier.issn0027-8424en_US
dc.identifier.issn1091-6490en_US
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:41626987*
dc.description.abstractInspired 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.en_US
dc.description.sponsorshipEngineering and Applied Sciencesen_US
dc.description.sponsorshipOrganismic and Evolutionary Biologyen_US
dc.description.sponsorshipPhysicsen_US
dc.language.isoen_USen_US
dc.publisherProceedings of the National Academy of Sciencesen_US
dash.licenseLAA
dc.titleGrowth Patterns for Shape-Shifting Elastic Bilayersen_US
dc.typeJournal Articleen_US
dc.description.versionVersion of Recorden_US
dc.relation.journalProceedings of the National Academy of Sciences of the United States of America (PNAS)en_US
dash.depositing.authorMahadevan, Lakshminarayanan
dc.date.available2019-10-24T00:36:12Z
dash.workflow.commentsFAR2017en_US
dash.funder.nameNational Science Foundationen_US
dash.funder.nameArmy Research Office (ARO)en_US
dash.funder.nameSwiss National Science Foundationen_US
dash.funder.awardDMS-1304211en_US
dash.funder.awardDMR 14-20570en_US
dash.funder.awardDMREF 15-33985en_US
dash.funder.awardW911NF-15-1-0166en_US
dc.identifier.doi10.1073/pnas.1709025114
dc.source.journalProc Natl Acad Sci USA
dash.source.volume114;44
dash.source.page11597-11602
dash.contributor.affiliatedMahadevan, Lakshminarayanan


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