Beyond Developable

Beyond Developable:
Computational Design and Fabrication with Auxetic Materials

Mina Konakovic, EPFL
Keenan Crane, CMU
Bailin Deng, University of Hull
Sofien Bouaziz, EPFL
Daniel Piker and Mark Pauly, EPFL

Authors 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.

Authors 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, they leverage conformal geometry to understand auxetic design.

In particular, authors compute a global conformal map with bounded scale factor to initialize an otherwise intractable non-linear optimization. They 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.

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