Session T21: Mechanical Metamaterials I

Machine Learning Zero Modes in Combinatorial Metamaterials

All around us, simple building blocks combine into complex systems with emergent properties. A general problem is to classify these properties into distinct classes. Statistical measures often play an important role, yet for many cases, the misalignment or perturbation of a single building block can have a dramatic effect on the collective properties. Here we show that Convolutional Neural Networks (CNNs) are able to accurately classify the design space of a combinatorial metamaterial, despite its sensitivity to small perturbations and the sparsity of the data set. Moreover, we show that in spite of the combinatorial explosion of the design space, the trained networks' accuracy remains high over a range of increasing design sizes. Together, our results show that neural networks are an excellent tool for combinatorial classification problems with complex underlying rules.   

Metamaterials you can count on

Mechanical metamaterials gain their material properties form their structure. Most metamaterials considered so far have a unique response that does not depend on previous driving. Here we demonstrate how internal multi-stable mechanical bits can be used to memorize previous input and respond differently as a function of an internal computation. We show a mechanical structure consisting of coupled mechanical bits that, when cyclically compressed, records the number of driving cycles: the material counts. This work lays the foundation for the study of complex memory and computation in mechanical metamaterials.   

Non-Abelian Mechanical Metamaterials

An elastic material follows the principle of superposition and is impervious to the order of actuations, severely constraining the design of programmable metamaterials. Here, we introduce a non-Abelian metamaterial that is sensitive to sequential ordering of mechanical input signals. We demonstrate how to describe these materials as finite state machines, and show that the smallest non-Abelian metamaterial already encodes both logical gates and different flavours of one-bit memory. Our work establishes the groundwork for designer matter with memory.   

Sequential snapping of hysterons in a biholey metamaterial

We show that driven mechanical metamaterials exhibit complex pathways when they contain bistable switches. Here we embed a number of such switches - slender beams - in a biholey metamaterial, and observe and manipulate a range of mechanical pathways, each consisting of specific sequences of flipping of the switches. We show how we can globally manipulate the driving conditions to elicit multiple pathways from a single sample. Our work opens a new route to design complex pathways in metamaterials.   

Sequential deformation in metamaterials tuned by plastic buckling

Sequential deformations play an important role in the functionality of various natural and artificial systems. So far, such behaviors are mainly explored in elastic systems. Here, we demonstrate that the buckling modes in plastic systems come from the competition between geometry and plasticity where plasticity dominant mode can help achieve robust sequential deformations. we firstly design a basic two-layer structure where the two layers can buckle in sequence in plasticity dominant systems in contrast to the single buckling mode in geometry dominant systems. Then we exploit the higher number of buckling sequences in multi-layer metamaterials and 3D metamaterials. Our work establishes a general pathway to select the sequence of deformations in metamaterials with plastic buckling which can be useful in energy absorption and topological protection.   

Continuum field theory for the deformations of planar kirigami

Mechanical metamaterials exhibit exotic properties at the system level, that emerge from the interactions of many nearly rigid building blocks. Determining these emergent properties theoretically has remained an open challenge outside of a few select examples. Here, for a large class of periodic and planar kirigami, we provide a coarse-graining rule linking the design of the panels and slits to the kirigami's macroscale deformations. The procedure gives a system of nonlinear partial differential equations (PDE) expressing geometric compatibility of angle functions related to the motion of individual slits. Leveraging known solutions of the PDE, we present excellent agreement between simulations and experiments across kirigami designs. The results reveal a surprising nonlinear wave-type response persisting even at large boundary loads, the existence of which is determined completely by the Poisson's ratio of the unit cell.   

Synergistic energy absorption mechanisms of a liquid crystal elastomer-based metamaterial

Architected materials (or metamaterials) have been designed to trap energy through elastic buckling instabilities, but it has a fixed energy absorption capability regardless of strain rates. Liquid crystal elastomers (LCEs) are highly dissipative materials compared to conventional elastomers. In this work, we applied LCEs to amplify the energy absorption capabilities of a mechanical metamaterial that experiences snap-through buckling under compressive loading. Compression tests showed that the energy absorption density of LCE unit cell increased with increasing strain rate, such that at a nominal strain rate of ~0.5/s, the energy absorption of the LCE structure was 4 times greater than the analogous PDMS (elastomeric) structure. Furthermore, the energy absorption density increased with stacking number of LCE unit cells. We measured an ~76% greater energy absorption density for a 4-layer stack of the LCE unit cells than a single unit cell. We also applied finite element simulations to calculate the energy dissipated by material viscoelasticity and the energy stored by snap buckling. In vertically stacked LCE structures, the unit cell structures did not buckle simultaneously. At lower strain rates, the buckling of some layers caused other layers to recover (i.e., straighten) then buckle again after the collapse of the preceding layers. This load-unloading cycle increased the viscoelastic dissipation without changing the stored energy. To further promote this dissipation mechanism, we varied the thickness of the beams in each layer to ensure sequential buckling of the different layers. In total, the simulations showed a synergistic interaction between the viscoelastic behavior of the material and the snap buckling of the metamaterial that greatly enhanced energy absorption.   

Complex Pathways in Serially Coupled Mechanical Hysterons

Interactions can significantly enlarge the space of pathways of hysterons. Here we show that serially coupled mechanical hysterons have antiferromagnetic interactions as a consequence of force balance. This allows for non-trivial pathways with avalanches. We realize all possible pathways of two coupled hysterons experimentally in metamaterials featuringsnapping elements. Systematic numerical simulations show that the pathways are robust and can be rationally designed. Our work introduces a simple yet general strategy for extending the space of achievable pathways in metamaterials.   

Particulated Granular Metamaterials

Granular materials have fascinating mechanical properties near the onset of jamming. For example, the elastic moduli depend strongly on the direction of the applied strain and they change abruptly when the grains rearrange, which occurs frequently in large systems near jamming onset. These features often make it difficult to control the mechanical properties of jammed granular materials. Here, we describe “particulated” granular materials---small numbers of grains confined within under-constrained trusses that are connected together into large frameworks---that allow us to design granular materials with specific mechanical properties. In this work, we focus on generating materials that can withstand large isotropic compression, but are extremely compliant under shear, i.e. they possess small values for the ratio of the shear modulus to the bulk modulus, G/B.  Our initial studies are in two dimensions using quadrilateral trusses with free angles at each joint. Using discrete element method simulations, we identify all possible grain configurations for N=6 and 7 monodisperse, frictionless and frictional particles over the full range of truss shapes. We then join the trusses together into a large ring and determine G/B for the ring structure in terms of the elastic moduli for the individual particle-filled trusses.  We show that we are able to design ring structures with extremely small G/B using specific grain arrangements in each truss. We validate the simulation results by comparing them to experiments on ring structures formed from 3D-printed truss elements and particles.     

On-demand spatial programmability of mechanical metamaterials

In recent decades, the concept of architected materials has received significant academic attention. Numerous seminal works have demonstrated novel materials whose characteristics do not exist in nature. In the design of mechanical metamaterials, researchers typically assume that these novel behaviors are determined, 1) by geometry and not by the constituent materials, 2) with a certain form of periodicity and 3) at the time of fabrication. Now, we have begun to challenge all three of these assumptions. In this work, I discuss a new paradigm of metamaterial design whereby each unit-cell is fabricated in an embryonic state. Consequently, the metamaterial has no preconceived notion or bias as to how it should behave. In this first stage, I demonstrate a multi-stable unit cell whose mechanical properties can be individually and independently controlled on-demand. By designing spatially varying programming pattern, the metamaterial can function in a dynamically controllable manner. I argue such spatial on-demand programmability has untapped potential in next generation metamaterials.   

Mechanical duality in Maxwell and non-Maxwell lattices

Duality is an important concept, which plays a crucial role in a wide range of physics problems. Recently, it is shown that in mechanical systems, duality can give rise to highly nontrivial phenomena, such as non-Abelian mechanics. In this talk, we study mechanical duality in Maxwell and non-Maxwell lattices as well as its connection to emergent higher symmetries, topological indices and topological edge states. Based on the graph connectivity of the underlaying lattice structure, we show that systems with mechanical duality can be classified in two classes. We identify universal elastic properties for each class and demonstrate this physics in various model systems. In addition, from these studies, we observed rich and unexpected phenomena, such as flat bands, self-dual lines and self-dual manifold.   

Experimental observation of gapped internal gravity waves in a periodic stratification

Stratified fluids such as the ocean or the atmosphere can carry internal gravity waves that can transport energy and momentum over large distances, and affect large-scale circulation patterns. When the density stratification is not uniform, internal waves can exhibit resonances, tunneling, and frequency-dependent transmissions. In the ocean, the interplay between heat diffusion and salt diffusion can lead to extended regions with spatially periodic density profiles called thermohaline staircases. In this talk, we report on the experimental observation of band gaps for internal gravity waves in a laboratory setting with similar periodic stratification. We also find the existence of surface states that are exponentially localized near interfaces and controlled by boundary conditions. Using analytical and numerical modeling, we show that these are formally equivalent to topological surface states found in one-dimensional topological insulators and photonic crystals. Our results suggest that energy transport by internal waves could be profoundly altered by the presence of periodic stratifications that occur in regions such as the Arctic Ocean.   

Design Princple of Hinge Structures with Duality-Induced Hidden Symmetry

Recently, a new type of duality was found in some deformable mechanical networks, which induces a hidden symmetry when the structures take a critical configuration at the self-dual point. However, such duality relies on meticulous structures which are usually found accidentally. In order to discover more self-dual structures with novel topological properties, a design principle of self-dual structures based on a deeper understanding of this duality is needed. In this work, we show that this duality originates from the partial center inversion (PCI) symmetry of the hinges in the structure, which gives each hinge an extra freedom degree without modifying the system dynamics. This property results in dynamic isomers for the hinge chain, i.e., dissimilar chain configurations with identical dynamic modes, which can be utilized to build a new type of flexible wave-guides. Based on this mechanism, we proposed simple rules to identify and design 1D and 2D periodic self-dual structures with arbitrary complexity. This design principle can guide the experimental realization of the mechanical duality. At last, by taking magnon in 2D hinge lattice as an example, we show that the duality and the associated hidden symmetry is a generic property of hinge structures, independent of specific dynamics of the systems.   

Shear driven propagation of solitons in metamaterials

Solitary waves steadily propagate in a system without changing their shape and are rarely observed in designed structures. We engineered a metamaterial using a network of nonuniform beams that can induce a localized kink under a pre-compression. By applying a shear deformation to the pre-compressed structure, the induced kink propagates, like a solitary wave, perpendicular to the direction of shear deformation. The shear-induced solitary wave is reversible since by changing the direction of shear, the kink travels in the inverse direction. The soliton in this structure appears because of multi-stable beams, where transitions between different states occur through an unstable intermediate state by shearing the system. Therefore, the kink propagates by the sequential snapping of beams that leads to oscillatory shear and normal force responses. We observe that the solitary waves for odd- and even-layer structures have an opposite phase. Localized kinks trigger surprising mechanical properties of the structure with negative shear and normal (Poynting) moduli. Our results provide an insight into harnessing mechanical instabilities for programming the shear and normal force responses of materials.   

Topologically Insulated Modes in Strongly Nonlinear Mechanical Chains

The adaption of topological band theory in classical mechanics is unlocking topologically protected waves in acoustic and elastic media. The theoretical underpinnings of insulator theory rely on the application of the Bloch theorem. However, this is not applicable in the strongly nonlinear regime. To address this, we consider a mechanical analog of the Su-Schrieffer-Heeger interface model with the addition of a strong cubic nonlinearity. Numerical continuation of the systems nonlinear normal modes (NNMs) reveals the frequency-energy evolution of the topological mode and bulk-spectra. Then, the nontrivial half-lattice is numerically simulated at the high-symmetry points of the Brillouin Zone to recover empirical estimates of the systems Zak Phase to define a critical energy level. The critical energy level is confirmed by numerically simulating the full system at various energy-frequency combinations to uncover at which energies the topological mode can be excited. Interestingly, this energy level is found to coincide nearly perfectly with the energy level at which the topological NNM intersects the linear bulk-spectrum.