Session U30: Programmable Matter

Mechanical Metamaterials You Can Count On

Most mechanical metamaterials perform a single-step function, such as shape-morphing under pressure. However, nonlinearities in mechanical building blocks - buckling, snapping, self-contacts - open a route towards multi-step metamaterials, crucial for storing and processing information. Here we present a class of structures whose state depends on a sequence of identical input cycli: these metamaterials count.   

Multifunctional Combinatorial Metamaterials

We introduce a novel class of combinatorial metamaterials that are multifunctional. We first define a combinatorial design space and find a rich phenomenology, ranging from disordered, to periodic and quasicrystalline tilings, who can host multiple yet a sub-extensive number of soft deformation modes. We then demonstrate the multifunctional nature of such metamaterials using both boundary textures and viscoelasticity. In particular, we realize a metamaterial that has a negative (positive) Poisson’s ratio for low (high) compression rate. Their ability our metamaterials to host multiple mechanical responses makes them an early example of multi-functional matter, thus paving the way for robust and adaptable devices.
  

A truly-programmable mechanical metamaterial using magnetic actuation

Mechanical metamaterials are engineered systems with a sub-structure that, when tiled, exhibits physical properties that may not exist in conventional bulk materials. While disrupting the definition of a ‘material’, the periodicity or the internal unit structure of a metamaterial is often optimized to target a specific (set of) function(s) or mechanical behavior. As such, upon fabrication, standard metamaterials are effectively “programmed”, once and for all, and their functionality cannot be altered a posteriori. Here, we show a truly-programmable metamaterial where both the periodicity and the internal structure are preserved during fabrication but each unit cell can be independently programmed and reprogrammed, reversely and on-demand. Programming of individual cells is achieved by switching between the equilibrium states of a multi-stable elastic shell using magnetic actuation. When tiled into sheets or columns, we are able to tune the effective mechanical properties of our system including its stiffness, strength, and localization strain. Through a combination of quasi-static compression of experimental fabricated prototypes and finite element simulations, we demonstrate both the programming and the range of the exhibited mechanical response of our designs.   

One Dimensional Mechanical Memory

Some bellows-like origami folded cylinders have bistable configurations, and the energy barriers between these bistable states are tunable with geometry. Stacked Kresling (twisted trianglular tesselations) patterns on a cylinder can be can be tuned to collapse or deploy incrementally. If these folded cells are allowed to interact, the interaction energy can shift transition barriers such that the bellows achieves geometrically suppressed configurations. We have developed laser-cut and folded cylinders where adjacent unit cells can either be elastically connected or completely decoupled. For cylinders where cells are non-interacting, these unit cells function as "bits" with perfect return-point memory. In experimental tests, we find that a cylinder-based memory unit of 4 bits can be predictably driven to any of its 16 allowable states with a prescribed sequence of compression and extension.   

Muscle-inspired flexible mechanical logic architecture for miniature robotics

Miniature robots (~10nm-100micron) that morph in response to external stimuli such as light or chemicals in their local environment have the potential to perform non-invasive treatments inside the body, clean up oil spills, or be embedded in textiles to intelligently tune fabric properties. Such robots can now be realized due to advancements in materials offering, e.g., stimuli-responsive polymers that actuate like artificial muscles. For maximum control using global triggers (stimuli), computation ability needs to be incorporated within these robots. The challenge is to design an architecture that is compact, material agnostic, stable under stochastic forces, and employs stimuli-responsive materials. Here we demonstrate such an architecture, which computes combinatorial logic via mechanical gates that use linear actuation (expansion and contraction). Additionally, the logic circuitry is physically flexible. We mathematically analyze gate geometry and discuss tuning it for the given signal requirements. We validate the design at colloidal scales using Brownian dynamics simulations. Finally, we simulate a complete robot that folds into Tetris shapes.   

Active stabilisation of patterned robotic swarms

Flocks of birds naturally order as a result of active forces which counteract destabilisation by random noise. Ordered patterns of drones or robotic agents are useful for many purposes such as surveying unknown territory, taking measurements of scientifically or economically important quantities over a large area, drone shows etc. Disruption of this pattern may occur due to many factors for e.g. atmospheric or ocean turbulence. Stabilising any given pattern in such a swarm is energy expensive and requires extensive computation and communication overheads. We propose an algorithm where one can achieve this is an energy efficient way. The strategy involves suppressing a class of fluctuations viz. non-affine displacements away from the given reference pattern while allowing affine deformations such as translations and rotations. The agents are not forced to sense, difficult to measure, environmental parameters such as local velocity of air or water in order to stabilise the swarm. Additionally, we show that by maintaining the structure/pattern of robotic swarms the statistics of the underlying flow field can be determined solely from "non-affine" forces. As the knowledge of these forces is a priori known, no extra measurement on the turbulent field is needed.   

Assembly by Solvent Evaporation: Equillibrium Clusters and Relaxation Times

We present a theoretical and computational description of equillibrium clusters of alkylthiolated gold nanocrystals assembled by solvent evaporation. We consider N nanocrystals in an octane or nonane liquid droplet. Equillibrium structures consist of Tetrahedron (N=4), Square pyramid (N=5), Octahedron (N=6), Pentagonal bipyrimad (N=7), Biaugmented triangular prism (N=8), Gyroelongated square pyramid (N=9), Sphenocorona (N=10), Icosahedron (N=13). We also characterize the relaxation times of the system and show that they increase linearly with N, thus deviating from the classical Maxwell theory of solvent evaporation. Implications for self-assembly of superlattices will also be discussed.   

Reprogrammable phononic metasurfaces

Mechanical metamaterials are materials with tailored, architected geometry, designed to retain properties that do not exist or rare in nature. Most of these mechanical properties are inscribed in the material’s frequency dispersion spectrum, ranging form its stiffness at zero frequency to its wave attenuation capacity at finite frequencies. These materials usually feature a structural pattern that repeats spatially (i.e., unit cell). A special class of these metamaterials can manipulate elastic waves (i.e., phonons). Most of the existing design frameworks for phononic metamaterials capitalize only one of there mechanisms; scattering, resonance or inertia amplification. In addition, once these designs are realized, their operational frequencies cannot be altered, limiting their potential for practical applications. Here, we present a reporgrammable metamterial platform for manipulating phonons utilizing all the aforementioned wave manipulation mechanisms [Foehr and Bilal et al.,PRL, 2018]. We program our nonlinear metamaterial to redirect stress waves, in real-time, in an element-wise fashion [Bilal et al., Adv. Mater. 2017]. Moreover, we use it to realize the first purely acoustic transistor (switching and cascading sound with sound) [Bilal et al., PNAS 2017].   

Synthetic Mechanoreceptors with Collocated Logic

We present a new class of synthetic mechanoreceptor exhibiting large changes in conductivity as a function of their shape. Concretely, such mechanoreceptors consist of a mechanical bistable structure showing shape-dependent electrical conductivity. The electromechanical response is designed such that on one state the unit shows large resistance, while on the second state the conductivity increases significantly. The bistable nature of such units and their ability to switch conductivity in response to external forcing allows our mechanoreceptors to serve as sensors with collocated input dependent memory. Specifically, the amplitude and frequency of the pressure/force inputs activating our mechanoreceptors change of shape (snap-through) result in distinct dynamical signatures, which are transduced by adding a voltage bias and reading current time histories. This allows to interpret specific external inputs into electrical output signatures that can be feed into an artificial neural network. We demonstrate this by subjecting a network of such mechanoreceptors to different force inputs resulting in recognizable electrical signatures which correlate to specific patterns of local states.   

Sending Signals Through Mechanical Wiring

Some progress has been made in the development of logic gates from mechanical systems, but in order to realize fully functioning devices, we need a reliable way to transmit a mechanical signal between logic gates. We consider a mechanical “wire”, a series of bistable units that interact with each other, as a way to connect the output of one logic gate to the input of another logic gate. Using both computer simulations and analytical calculation to analyze the propagation of a signal through the wire, we have determined how parameters such as the number of bistable units and the signal strength affect how far a signal can propagate through the wire. We determine whether and to what degree signals can propagate based on the shape of the bistable potential.   

Training for desired Folding Pathways in Self Folding Origami

Creased sheets can possess an exponential number of folding pathways accessible from the flat state. This property poses an engineering challenge in the design of specialized self-folding origami patterns with one or a few prescribed folding pathways. We seek an alternative means to eliminating undesired folding pathways via physical training. We fold creased sheets along desired folding pathways and allow the initially equal crease stiffnesses to dynamically evolve according to a local rule dependent on folding strain. We find that undesired folding pathways are eliminated in saddle-node bifurcations, leaving behind only one or two desired folded pathways. In this way, we find that physical folding, combined with a plasticity rule for crease stiffness, can naturally arrive at design parameters needed for non-linear behaviors that are hard to predict otherwise.   

Computational wrapping: A novel method for wrapping 3D-curved surfaces with brittle, nonstretchable materials for conformable devices

In this talk, we propose a novel method to make conformable devices on non-zero Gaussian surfaces, i.e. flexible devices that can be transformed into any complex 3-dimensional shape. We used computational polyhedral edge unfolding methods to obtain planar figures of arbitrary complex 3-dimensional shapes. It is well-known that 2-dimensional substrates cannot be attached on the non-zero surfaces without stretching, however, by computational approximation of 3-D surface and making it flat by algorithmic method, we could convert any 3-D shapes into a 2-D sheet. We can make devices having the programmed unfolded figures and return it to the original 3D shape. In this way, we could make electroluminescent lighting and primary battery which can conformably wrap diverse 3-D surfaces without failure. Shape programmable devices with computational wrapping design can cover anywhere on the 3-dimensional shapes including human skin and are able to be applied not only personalized wearable or skin attachable devices but also various industries, such as automotive design, clothing, and fashion accessories, medical services and so on.   

How to weave a perfect sphere with curved strips

Triaxial weaving, a craft technique that enables the generation of surfaces with tri-directional arrays of initially straight elastic strips, has long been loved by basket makers and artists seeking a combination of practical and aesthetically-pleasing structures. The design principles of traditional weaving are based on the observation that the non-hexagonal topology of unit cells imparts out-of-plane shapes. In the realm of differential geometry, the weaving tradition is rooted in the concept of Euler characteristics through the Gauss-Bonnet theorem, with discrete topological defects being used as building blocks. Taking an alternative point of departure, we introduce a novel approach for triaxial weaving that enables us to continuously span a variety of 3D shapes of the weave by tuning the natural in-plane curvature of the strips. We systematically explore the validity of the new strategy by quantifying the shape of experimental specimens with X-ray tomography in combination with continuum-based simulations. To demonstrate the potential of our design scheme, and as a canonical example, we present a fullerene-like weave that is perfectly spherical, which cannot be readily achieved using straight strips. Ellipsoidal and toroidal structures are also explored.