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Interfacial metric mechanics: stitching patterns of shape change in active sheets.

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cam.issuedOnline2022-06-29
dc.contributor.authorFeng, Fan
dc.contributor.authorDuffy, Daniel
dc.contributor.authorWarner, Mark
dc.contributor.authorBiggins, John
dc.contributor.orcidFeng, Fan [0000-0002-5456-670X]
dc.contributor.orcidDuffy, Daniel [0000-0002-0383-5527]
dc.contributor.orcidWarner, Mark [0000-0003-3172-0265]
dc.contributor.orcidBiggins, John [0000-0002-7452-2421]
dc.date.accessioned2022-06-29T19:50:24Z
dc.date.available2022-06-29T19:50:24Z
dc.date.issued2022-06
dc.date.submitted2022-04-01
dc.date.updated2022-06-29T19:50:23Z
dc.description.abstractA flat sheet programmed with a planar pattern of spontaneous shape change will morph into a curved surface. Such metric mechanics is seen in growing biological sheets, and may be engineered in actuating soft matter sheets such as phase-changing liquid crystal elastomers (LCEs), swelling gels and inflating baromorphs. Here, we show how to combine multiple patterns in a sheet by stitching regions of different shape changes together piecewise along interfaces. This approach allows simple patterns to be used as building blocks, and enables the design of multi-material or active/passive sheets. We give a general condition for an interface to be geometrically compatible, and explore its consequences for LCE/LCE, gel/gel and active/passive interfaces. In contraction/elongation systems such as LCEs, we find an infinite set of compatible interfaces between any pair of patterns along which the metric is discontinuous, and a finite number across which the metric is continuous. As an example, we find all possible interfaces between pairs of LCE logarithmic spiral patterns. By contrast, in isotropic systems such as swelling gels, only a finite number of continuous interfaces are available, greatly limiting the potential of stitching. In both continuous and discontinuous cases, we find the stitched interfaces generically carry singular Gaussian curvature, leading to intrinsically curved folds in the actuated surface. We give a general expression for the distribution of this curvature, and a more specialized form for interfaces in LCE patterns. The interfaces thus also have rich geometric and mechanical properties in their own right.
dc.identifier.doi10.17863/CAM.86018
dc.identifier.eissn1471-2946
dc.identifier.issn1364-5021
dc.identifier.otherrspa20220230
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/338605
dc.languageen
dc.publisherThe Royal Society
dc.subjectResearch articles
dc.subjectGaussian curvature
dc.subjectactive materials
dc.subjectmetric compatibility
dc.subjectinterface
dc.titleInterfacial metric mechanics: stitching patterns of shape change in active sheets.
dc.typeArticle
dcterms.dateAccepted2022-06-09
prism.issueIdentifier2262
prism.publicationNameProc Math Phys Eng Sci
prism.volume478
pubs.funder-project-idEngineering and Physical Sciences Research Council (EP/L015552/1)
pubs.funder-project-idEngineering and Physical Sciences Research Council (EP/P034616/1)
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
rioxxterms.versionVoR
rioxxterms.versionofrecord10.1098/rspa.2022.0230

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