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.
Fabrication of a miniature Tigridia pavilion model.
Conventional heart stents are straight and typically chosen by the surgeon from a set of standard sizes. Recent research has shown the benefits of curved stents [Tomita et al. 2015]. Our method can be used to create freeform curved heart stents that can be adapted to the specific geometry of the patients’ blood vessels. Top row shows a zoom on the target vessel region and its 3D model reconstruction to approximate with our programmable auxetics. The stent is administered with a catheter to the correct position (bottom left) and inflated to its target geometry (bottom middle, right).
A hybrid shell structure integrates planar support arches in the interior into a deployable auxetic surface. The arches can be mounted after deploying the linkage.
Inflatable freeform domes for potential Mars habitats. Since the atmospheric pressure on Mars is 100 times lower than Earth’s, the interior must be pressurized. This motivates the use of inflatable structures that can be efficiently erected from flat configurations, offering the additional benefits of low weight and compact storage. Our deployable auxetics offer a rich design shape space, so we can optimize the shape of the freeform domes to match interior space objectives.
Inflatable freeform domes for potential Mars habitats. Since the atmospheric pressure on Mars is 100 times lower than Earth’s, the interior must be pressurized. This motivates the use of inflatable structures that can be efficiently erected from flat configurations, offering the additional benefits of low weight and compact storage. Our deployable auxetics offer a rich design shape space, so we can optimize the shape of the freeform domes to match interior space objectives.
Design study of deployable architecture. The freeform inflatable dome can be used as a semi-permanent, relocatable space.
Design study of a freeform chair realized using four layers of spatially graded auxetic material to fully cover the surface.
Interior decorative cladding. This hanging structure has been optimized to align with the boundary constraints imposed by the ambient space. The designer controls the shape by interactively modifying scale factors while allowing the triangles to slide along the boundary curves.
A shading pavilion deployed by gravity demonstrating how we can control the area covered with shadow by changing the shape of the linkage elements. Here we use hexagonal panels to create more shadow than with a single layer of triangular elements. Each hexagonal panel preserves the location of the three connection points as in the triangular case.
Multi-layer shading pavilion deployed by gravity.
A free-form facade constructed from uniform triangular elements connected with rotational joints. Thanks to the reconfigurable nature of the regular auxetic linkage, the facade can be used as a computer-controlled dynamic external shading system.
Our auxetic design tools can also be used to explore lighting design—here an “open” and “closed” configuration of the same linkage provide mechanical dimming.
A double-curved top fabricated from approximately inextensible leather. The zooms illustrate the global continuity of the pattern across the seams, which are fixed with pins.
The shoe model has been fabricated from a single piece of metallic material using our interactive rationalization method based on conformal geometry and global, non-linear optimization. Thanks to our global approach, the 2D layout of the material can be computed such that no discontinuities occur at the seam. The center zoom shows the region of the seam, where one row of triangles is doubled to allow for easy gluing along the boundaries. The base is 3D printed.
Fabrication of the Max Planck model. Top left: 3D printed reference model used for geometric guidance; Bottom left: flat, undeformed perforated copper sheet. The purple arrow indicates the singular vertex located at the tip of the nose; Middle, Right: two photographs of the final model.
Fabrication of a miniature Tigridia pavilion model. Conventional heart stents are straight and typically chosen by the surgeon from a set of standard sizes. Recent research has shown the benefits of curved stents [Tomita et al. 2015]. Our method can be used to create freeform curved heart stents that can be adapted to the specific geometry of the patients’ blood vessels. Top row shows a zoom on the target vessel region and its 3D model reconstruction to approximate with our programmable auxetics. The stent is administered with a catheter to the correct position (bottom left) and inflated to its target geometry (bottom middle, right).A hybrid shell structure integrates planar support arches in the interior into a deployable auxetic surface. The arches can be mounted after deploying the linkage.Inflatable freeform domes for potential Mars habitats. Since the atmospheric pressure on Mars is 100 times lower than Earth’s, the interior must be pressurized. This motivates the use of inflatable structures that can be efficiently erected from flat configurations, offering the additional benefits of low weight and compact storage. Our deployable auxetics offer a rich design shape space, so we can optimize the shape of the freeform domes to match interior space objectives.Inflatable freeform domes for potential Mars habitats. Since the atmospheric pressure on Mars is 100 times lower than Earth’s, the interior must be pressurized. This motivates the use of inflatable structures that can be efficiently erected from flat configurations, offering the additional benefits of low weight and compact storage. Our deployable auxetics offer a rich design shape space, so we can optimize the shape of the freeform domes to match interior space objectives.Design study of deployable architecture. The freeform inflatable dome can be used as a semi-permanent, relocatable space.Design study of a freeform chair realized using four layers of spatially graded auxetic material to fully cover the surface.Interior decorative cladding. This hanging structure has been optimized to align with the boundary constraints imposed by the ambient space. The designer controls the shape by interactively modifying scale factors while allowing the triangles to slide along the boundary curves.A shading pavilion deployed by gravity demonstrating how we can control the area covered with shadow by changing the shape of the linkage elements. Here we use hexagonal panels to create more shadow than with a single layer of triangular elements. Each hexagonal panel preserves the location of the three connection points as in the triangular case.Multi-layer shading pavilion deployed by gravity.A free-form facade constructed from uniform triangular elements connected with rotational joints. Thanks to the reconfigurable nature of the regular auxetic linkage, the facade can be used as a computer-controlled dynamic external shading system.Our auxetic design tools can also be used to explore lighting design—here an “open” and “closed” configuration of the same linkage provide mechanical dimming.A double-curved top fabricated from approximately inextensible leather. The zooms illustrate the global continuity of the pattern across the seams, which are fixed with pins.The shoe model has been fabricated from a single piece of metallic material using our interactive rationalization method based on conformal geometry and global, non-linear optimization. Thanks to our global approach, the 2D layout of the material can be computed such that no discontinuities occur at the seam. The center zoom shows the region of the seam, where one row of triangles is doubled to allow for easy gluing along the boundaries. The base is 3D printed.Fabrication of the Max Planck model. Top left: 3D printed reference model used for geometric guidance; Bottom left: flat, undeformed perforated copper sheet. The purple arrow indicates the singular vertex located at the tip of the nose; Middle, Right: two photographs of the final model.
