- Project Summary
- Using insights from geometry and physical simulation, we can alter the behavior of materials to meet functional goals. For instance, we can cut slits into a solid, inextensible sheet of material to allow it to expand, and then by carefully designing these cuts, we can ensure the sheet pops into the curved surface of our choice when it is stretched. Or, we can design fine-scale microstructure geometry to create a 3D printed object that deforms in useful or surprising ways when forces are applied.
This approach to tailoring materials, known as metamaterial design, can enable exciting new fabrication methods and produce new classes of lightweight, robust designs. This project seeks to develop computational techniques and tools such as efficient PDE solvers and shape optimization algorithms to advance metamaterial research on several fronts.
We introduce a novel computational method for design and fabrication with auxetic materials. The term auxetic refers to solid materials with negative Poisson ratio — when the material is stretched in one direction, it also expands in all other directions. In particular, we study 2D auxetic materials in the form of a triangular linkage which exhibits auxetic behavior at the macro scale. This stretching, in turn, allows the flat material to approximate doubly- curved surfaces, making it attractive for fabrication. We physically realize auxetic materials by introducing a specific pattern of cuts into approximately inextensible material such as sheet metal, plastic, or leather. On a larger scale, we use individual rigid triangular elements and connect them with joints.
We study uniform auxetic materials in the form of a flat kinematic linkage, composed of identical equilateral triangles. When deformed into a curved shape, the linkage yields spatially-varying hexagonal openings. Using insights from conformal geometry, we develop a constraint-based optimization system to closely approximates a complex target 3D surface.
We are developing a computational method for design of novel deployable structures via programmable auxetics, i.e., spatially varying triangular linkage optimized to directly and uniquely encode the target 3D surface in the 2D pattern. The target surface is rapidly deployed from a flat initial state via inflation or gravitational loading.
We aim to provide a solution to the problem that auxetic deployables need external actuation to stay in the desired shape. Here, we combine the mechanics of planar bistable kirigami with the inverse design pipeline of the programmable auxetics.