Shape-morphing mechanical metamaterials

Caigui Jiang, Florian Rist, Hui Wang, Johannes Wallner, Helmut Pottmann

Research output: Contribution to journalArticlepeer-review


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
Original languageEnglish (US)
JournalComputer-Aided Design
StatePublished - 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-11-01
Acknowledgements: 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.


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