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    Shape-morphing mechanical metamaterials

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    Name:
    geommaterials.pdf
    Size:
    3.915Mb
    Format:
    PDF
    Description:
    Accepted Manuscript
    Embargo End Date:
    2023-10-31
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    Type
    Article
    Authors
    Jiang, Caigui cc
    Rist, Florian
    Wang, Hui
    Wallner, Johannes
    Pottmann, Helmut cc
    KAUST Department
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Visual Computing Center (VCC)
    Applied Mathematics and Computational Science Program
    Date
    2021-11-12
    Online Publication Date
    2021
    Print Publication Date
    2022-02
    Embargo End Date
    2023-10-31
    Permanent link to this record
    http://hdl.handle.net/10754/672993
    
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    Abstract
    Small-scale cut and fold patterns imposed on sheet material enable its morphing into three-dimensional shapes. This manufacturing paradigm has been receiving much attention in recent years and poses challenges in both fabrication and computation. It is intimately connected with the interpretation of patterned sheets as mechanical metamaterials, typically of negative Poisson ratio. We here present an affirmative solution to a fundamental geometric question, namely the targeted programming of a shape morph. We use optimization to compute kirigami patterns that realize a morph between shapes, in particular between a flat sheet and a surface in space. The shapes involved can be arbitrary; in fact we are able to approximate any mapping between shapes whose principal distortions do not exceed certain bounds. This amounts to a solution of the so-called inverse problem for kirigami cut and fold patterns. The methods we employ include a differential-geometric interpretation of the morph, besides drawing on recent progress in geometric computing
    Citation
    Jiang, C., Rist, F., Wang, H., Wallner, J., & Pottmann, H. (2021). Shape-Morphing Mechanical Metamaterials. Computer-Aided Design, 103146. doi:10.1016/j.cad.2021.103146
    Sponsors
    This work was supported by the Austrian Science Fund via grants I2978 (SFB-Transregio programme Discretization in geometry and dynamics), F77 (SFB grant Advanced Computational Design); further by the Vienna Science and Technology Fund (WWTF) under grant ICT15-082. C. Jiang, F. Rist, and H. Wang were supported by KAUST baseline funding.
    Publisher
    Elsevier
    Journal
    Computer-Aided Design
    DOI
    10.1016/j.cad.2021.103146
    Additional Links
    https://www.dmg.tuwien.ac.at/geom/ig/publications/geommaterials/geommaterials.pdf
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.cad.2021.103146
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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