Elizabeth R. Chen

3D Soft Metamaterials with Negative Poisson's Ratio

Buckling is exploited to design a new class of three-dimensional metamaterials with negative Poissons ratio. A library of auxetic building blocks is identified and procedures are defined to guide their selection and assembly. The auxetic properties of these materials are demonstrated both through experiments and finite element simulations and exhibit excellent qualitative and quantitative agreement.

Buckling-induced encapsulation of structured elastic shells under pressure

We introduce a class of continuum shell structures, the Buckliball, which undergoes a structural transformation induced by buckling under pressure loading. The geometry of the Buckliball comprises a spherical shell patterned with a regular array of circular voids. In order for the pattern transformation to be induced by buckling, the possible number and arrangement of these voids are found to be restricted to five specific configurations. Below a critical internal pressure, the narrow ligaments between the voids buckle, leading to a cooperative buckling cascade of the skeleton of the ball. This ligament buckling leads to closure of the voids and a reduction of the total volume of the shell by up to 54%, while remaining spherical, thereby opening the possibility of encapsulation. We use a combination of precision desktop-scale experiments, finite element simulations, and scaling analyses to explore the underlying mechanics of these foldable structures, finding excellent qualitative and quantitative agreement. Given that this folding mechanism is induced by a mechanical instability, our Buckliball opens the possibility for reversible encapsulation, over a wide range of length scales.

Harnessing instabilities for design of soft reconfigurable auxetic/chiral materials

Most materials have a unique form optimized for a specific property and function. However, the ability to reconfigure material structures depending on stimuli opens exciting opportunities. Although mechanical instabilities have been traditionally viewed as a failure mode, here we exploit them to design a class of 2D soft materials whose architecture can be dramatically changed in response to an external stimulus. By considering geometric constraints on the tessellations of the 2D Euclidean plane, we have identified four possible periodic distributions of uniform circular holes where mechanical instability can be exploited to reversibly switch between expanded (i.e. with circular holes) and compact (i.e. with elongated, almost closed elliptical holes) periodic configurations. Interestingly, in all these structures buckling is found to induce large negative values of incremental Poissons ratio and in two of them also the formation of chiral patterns. Using a combination of finite element simulations and experiments at the centimeter scale we demonstrate a proof-of-concept of the proposed materials. Since the proposed mechanism for reconfigurable materials is induced by elastic instability, it is reversible, repeatable and scale-independent.

Dense Crystalline Dimer Packings of Regular Tetrahedra

We present the densest known packing of regular tetrahedra with density

A Dense Packing of Regular Tetrahedra

\phi =\frac{4000}{4671}=0.856347\ldots\,

Complexity in surfaces of densest packings for families of polyhedra

. Like the recently discovered packings of Kallus et al. and Torquato–Jiao, our packing is crystalline with a unit cell of four tetrahedra forming two triangular dipyramids (dimer clusters). We show that our packing has maximal density within a three-parameter family of dimer packings. Numerical compressions starting from random configurations suggest that the packing may be optimal at least for small cells with up to 16 tetrahedra and periodic boundaries.

Reconfigurable origami-inspired acoustic waveguides

We construct a dense packing of regular tetrahedra, with packing density D>.7786157.

Random Sequential Adsorption of Discs on Surfaces of Constant Curvature: Plane, Sphere, Hyperboloid, and Projective Plane

Packings of hard polyhedra have been studied for centuries due to their mathematical aesthetic and more recently for their applications in fields such as nanoscience, granular and colloidal matter, and biology. In all these fields, particle shape is important for structure and properties, especially upon crowding. Here, we explore packing as a function of shape. By combining simulations and analytic calculations, we study three 2-parameter families of hard polyhedra and report an extensive and systematic analysis of the densest packings of more than 55,000 convex shapes. The three families have the symmetries of triangle groups (icosahedral, octahedral, tetrahedral) and interpolate between various symmetric solids (Platonic, Archimedean, Catalan). We find that optimal (maximum) packing density surfaces that reveal unexpected richness and complexity, containing as many as 130 different structures within a single family. Our results demonstrate the utility of thinking of shape not as a static property of an object in the context of packings, but rather as but one point in a higher dimensional shape space whose neighbors in that space may have identical or markedly different packings. Finally, we present and interpret our packing results in a consistent and generally applicable way by proposing a method to distinguish regions of packings and classify types of transitions between them.

Mandelbrot Set + Symmetry Groups ź Higher Dimensions = ?

Researchers use reconfigurable origami-inspired metamaterials to guide and redirect the propagation of sound. We combine numerical simulations and experiments to design a new class of reconfigurable waveguides based on three-dimensional origami-inspired metamaterials. Our strategy builds on the fact that the rigid plates and hinges forming these structures define networks of tubes that can be easily reconfigured. As such, they provide an ideal platform to actively control and redirect the propagation of sound. We design reconfigurable systems that, depending on the externally applied deformation, can act as networks of waveguides oriented along one, two, or three preferential directions. Moreover, we demonstrate that the capability of the structure to guide and radiate acoustic energy along predefined directions can be easily switched on and off, as the networks of tubes are reversibly formed and disrupted. The proposed designs expand the ability of existing acoustic metamaterials and exploit complex waveguiding to enhance control over propagation and radiation of acoustic energy, opening avenues for the design of a new class of tunable acoustic functional systems.

Harnessing Multiple Folding Mechanisms in Soft Periodic Structures for Tunable Control of Elastic Waves

We present an algorithm to simulate random sequential adsorption (random “parking”) of discs on constant curvature surfaces: the plane, sphere, hyperboloid, and projective plane, all embedded in three-dimensional space. We simulate complete parkings efficiently by explicitly calculating the boundary of the available area in which discs can park and concentrating new points in this area. We use our algorithm to study the number distribution and density of discs parked in each space, where for the plane and hyperboloid we consider two different periodic tilings each. We make several notable observations: (1) on the sphere, there is a critical disc radius such the number of discs parked is always exactly four: the random parking is deterministic. We prove this statement and also show that random parking on the surface of a d-dimensional sphere would have deterministic behaviour at the same critical radius. (2) The average number of parked discs does not always monotonically increase as the disc radius decreases: on the plane (square with periodic boundary conditions), there is an interval of decreasing radius over which the average decreases. We give a heuristic explanation for this counterintuitive finding. (3) As the disc radius shrinks to zero, the density (average fraction of area covered by parked discs) appears to converge to the same constant for all spaces, though it is always slightly larger for a sphere and slightly smaller for a hyperboloid. Therefore, for parkings on a general curved surface we would expect higher local densities in regions of positive curvature and lower local densities in regions of negative curvature.