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geommaterials.pdf
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Embargo End Date:
2023-10-31
Type
ArticleKAUST Department
Computer, Electrical and Mathematical Science and Engineering (CEMSE) DivisionVisual Computing Center (VCC)
Applied Mathematics and Computational Science Program
Date
2021-11-12Online Publication Date
2021Print Publication Date
2022-02Embargo End Date
2023-10-31Permanent link to this record
http://hdl.handle.net/10754/672993
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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 computingCitation
Jiang, C., Rist, F., Wang, H., Wallner, J., & Pottmann, H. (2021). Shape-Morphing Mechanical Metamaterials. Computer-Aided Design, 103146. doi:10.1016/j.cad.2021.103146Sponsors
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
ElsevierJournal
Computer-Aided Designae974a485f413a2113503eed53cd6c53
10.1016/j.cad.2021.103146