Beyond developable: computational design and fabrication with auxetic materials

Konaković, Mina; Crane, Keenan; Deng, Bailin; Bouaziz, Sofien; Piker, Daniel; Pauly, Mark

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.

Citation

Konaković, M., Crane, K., Deng, B., Bouaziz, S., Piker, D., & Pauly, M. (2016). Beyond developable: computational design and fabrication with auxetic materials. ACM Transactions on Graphics, 35(4), 1-11. https://doi.org/10.1145/2897824.2925944

• Journal Article Type: Article
• Acceptance Date: Apr 1, 2016
• Publication Date: Jul 11, 2016
• Deposit Date: Apr 28, 2016
• Publicly Available Date: Jul 11, 2016
• Journal: ACM transactions on graphics
• Print ISSN: 0730-0301
• Electronic ISSN: 1557-7368
• Publisher: Association for Computing Machinery (ACM)
• Peer Reviewed: Peer Reviewed
• Volume: 35
• Issue: 4
• Article Number: 89
• Pages: 1-11
• DOI: https://doi.org/10.1145/2897824.2925944
• Keywords: Digital fabrication, Computational design, Global optimization, Differential geometry, Conformal mapping
• Public URL: https://hull-repository.worktribe.com/output/437316
• Publisher URL: http://lgg.epfl.ch/publications/2016/BeyondDevelopable/index.php
• Additional Information: © ACM, 2016. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM transactions on graphics, {VOL 35, ISS4, (2016)} http://doi.acm.org/10.1145/2897824.2925944
• Contract Date: Apr 28, 2016