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Beyond developable: Computational design and fabrication with auxetic materials

Konaković, Mina, Crane, Keenan, Deng, Bailin, Bouaziz, Sofien, Piker, Daniel and Pauly, Mark 2016. Beyond developable: Computational design and fabrication with auxetic materials. ACM Transactions on Graphics 35 (4) , 89. 10.1145/2897824.2925944

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Abstract

We present a computational method for interactive 3D design and rationalization of surfaces via auxetic materials, i.e., flat flexible material that can stretch uniformly up to a certain extent. A key motivation for studying such material is that one can approximate doubly-curved surfaces (such as the sphere) using only flat pieces, making it attractive for fabrication. We physically realize surfaces by introducing cuts into approximately inextensible material such as sheet metal, plastic, or leather. The cutting pattern is modeled as a regular triangular linkage that yields hexagonal openings of spatially-varying radius when stretched. In the same way that isometry is fundamental to modeling developable surfaces, we leverage conformal geometry to understand auxetic design. In particular, we compute a global conformal map with bounded scale factor to initialize an otherwise intractable non-linear optimization. We demonstrate that this global approach can handle non-trivial topology and non-local dependencies inherent in auxetic material. Design studies and physical prototypes are used to illustrate a wide range of possible applications.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Computer Science & Informatics
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Uncontrolled Keywords: digital fabrication, computational design, global optimization, differential geometry, conformal mapping
Publisher: Association for Computing Machinery (ACM)
ISSN: 0730-0301
Date of First Compliant Deposit: 2 May 2017
Last Modified: 10 Mar 2020 17:32
URI: http://orca.cf.ac.uk/id/eprint/98566

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