Controlled pathways and sequential information processing in serially coupled mechanical hysterons.

The complex sequential response of frustrated materials results from the interactions between material bits called hysterons. Hence, a central challenge is to understand and control these interactions, so that materials with targeted pathways and functionalities can be realized. Here, we show that hysterons in serial configurations experience geometrically controllable antiferromagnetic-like interactions.

Emergent nonlocal combinatorial design rules for multimodal metamaterials.

Combinatorial mechanical metamaterials feature spatially textured soft modes that yield exotic and useful mechanical properties. While a single soft mode often can be rationally designed by following a set of tiling rules for the building blocks of the metamaterial, it is an open question what design rules are required to realize multiple soft modes. Multimodal metamaterials would allow for advanced mechanical functionalities that can be selected on the fly.

Patterning Complex Line Motifs in Thin Films Using Immersion-Controlled Reaction-Diffusion.

The discovery of self-organization principles that enable scalable routes toward complex functional materials has proven to be a persistent challenge. Here, reaction-diffusion driven, immersion-controlled patterning (R-DIP) is introduced, a self-organization strategy using immersion-controlled reaction-diffusion for targeted line patterning in thin films. By modulating immersion speeds, the movement of a reaction-diffusion front over gel films is controlled, which induces precipitation of highly uniform lines at the reaction front.

Counting and Sequential Information Processing in Mechanical Metamaterials.

Materials with an irreversible response to cyclic driving exhibit an evolving internal state which, in principle, encodes information on the driving history. Here we realize irreversible metamaterials that count mechanical driving cycles and store the result into easily interpretable internal states. We extend these designs to aperiodic metamaterials that are sensitive to the order of different driving magnitudes, and realize "lock and key" metamaterials that only reach a specific state for a given target driving sequence.

Machine Learning of Implicit Combinatorial Rules in Mechanical Metamaterials.

Combinatorial problems arising in puzzles, origami, and (meta)material design have rare sets of solutions, which define complex and sharply delineated boundaries in configuration space. These boundaries are difficult to capture with conventional statistical and numerical methods. Here we show that convolutional neural networks can learn to recognize these boundaries for combinatorial mechanical metamaterials, down to finest detail, despite using heavily undersampled training sets, and can successfully generalize.

Rapid formation of uniformly layered materials by coupling reaction-diffusion processes with mechanical responsiveness.

Straightforward manufacturing pathways toward large-scale, uniformly layered composites may enable the next generation of materials with advanced optical, thermal, and mechanical properties. Reaction-diffusion systems are attractive candidates to this aim, but while layered composites theoretically could spontaneously arise from reaction-diffusion, in practice randomly oriented patches separated by defects form, yielding nonuniformly patterned materials. A propagating reaction front can prevent such nonuniform patterning, as is the case for Liesegang processes, in which diffusion drives a reaction front to produce layered precipitation patterns.

Sequential snapping and pathways in a mechanical metamaterial.

Materials that feature bistable elements, hysterons, exhibit memory effects. Often, these hysterons are difficult to observe or control directly. Here, we introduce a mechanical metamaterial in which slender elements, interacting with pushers, act as mechanical hysterons.

Contraction and Expansion of Nanocomposites during Ion Exchange Reactions.

The next generation of advanced functional materials can greatly benefit from methods for realizing the right chemical composition at the right place. Nanocomposites of amorphous silica and metal carbonate nanocrystals (BaCO/SiO) form an attractive starting point as they can straightforwardly be assembled in different controllable three-dimensional (3D) shapes, while the chemical composition of the nanocrystals can be completely converted via ion exchange. Nevertheless, it is still unknown-let alone predictable-how nanoscopic changes in the lattice volume of the nanocrystals translate to changes in the microscopic dimensions of 3D BaCO/SiO structures during ion exchange.

Conformal elasticity of mechanism-based metamaterials.

Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate symmetry due to the presence of a designer soft strain pathway. Here we show that low energy deformations of designer dilational metamaterials will be governed by a scalar field theory, conformal elasticity, in which the nonuniform, nonlinear deformations observed under generic loads correspond with the well-studied-conformal-maps.

Profusion of transition pathways for interacting hysterons.

The response, pathways, and memory effects of cyclically driven complex media can be captured by hysteretic elements called hysterons. Here we demonstrate the profound impact of hysteron interactions on pathways and memory. Specifically, while the Preisach model of independent hysterons features a restricted class of pathways which always satisfy return point memory, we show that three interacting hysterons generate more than 15 000 transition graphs, with most violating return point memory and having features completely distinct from the Preisach model.

Complex pathways and memory in compressed corrugated sheets.

The nonlinear response of driven complex materials-disordered magnets, amorphous media, and crumpled sheets-features intricate transition pathways where the system repeatedly hops between metastable states. Such pathways encode memory effects and may allow information processing, yet tools are lacking to experimentally observe and control these pathways, and their full breadth has not been explored. Here we introduce compression of corrugated elastic sheets to precisely observe and manipulate their full, multistep pathways, which are reproducible, robust, and controlled by geometry.

Design of Pseudo-Mechanisms and Multistable Units for Mechanical Metamaterials.

Mechanisms-collections of rigid elements coupled by perfect hinges which exhibit a zero-energy motion-motivate the design of a variety of mechanical metamaterials. We enlarge this design space by considering pseudo-mechanisms, collections of elastically coupled elements that exhibit motions with very low energy costs. We show that their geometric design generally is distinct from those of true mechanisms, thus opening up a large and virtually unexplored design space.

Shape-Preserving Chemical Conversion of Architected Nanocomposites.

Forging customizable compounds into arbitrary shapes and structures has the potential to revolutionize functional materials, where independent control over shape and composition is essential. Current self-assembly strategies allow impressive levels of control over either shape or composition, but not both, as self-assembly inherently entangles shape and composition. Herein, independent control over shape and composition is achieved by chemical conversion reactions on nanocrystals, which are first self-assembled in nanocomposites with programmable microscopic shapes.

Non-Euclidean origami.

Traditional origami starts from flat surfaces, leading to crease patterns consisting of Euclidean vertices. However, Euclidean vertices are limited in their folding motions, are degenerate, and suffer from misfolding. Here we show how non-Euclidean 4-vertices overcome these limitations by lifting this degeneracy, and that when the elasticity of the hinges is taken into account, non-Euclidean 4-vertices permit higher order multistability.

Excess floppy modes and multibranched mechanisms in metamaterials with symmetries.

Floppy modes-deformations that cost zero energy-are central to the mechanics of a wide class of systems. For disordered systems, such as random networks and particle packings, it is well-understood how the number of floppy modes is controlled by the topology of the connections. Here we uncover that symmetric geometries, present in, e.

Multi-step self-guided pathways for shape-changing metamaterials.

Multi-step pathways-which consist of a sequence of reconfigurations of a structure-are central to the functionality of various natural and artificial systems. Such pathways execute autonomously in self-guided processes such as protein folding and self-assembly, but have previously required external control to execute in macroscale mechanical systems, provided by, for example, actuators in robotics or manual folding in origami. Here we demonstrate shape-changing, macroscale mechanical metamaterials that undergo self-guided, multi-step reconfiguration in response to global uniform compression.

From Bouncing to Floating: The Leidenfrost Effect with Hydrogel Spheres.

The Leidenfrost effect occurs when a liquid or stiff sublimable solid near a hot surface creates enough vapor beneath it to lift itself up and float. In contrast, vaporizable soft solids, e.g.

Softening and yielding of soft glassy materials.

Solids deform and fluids flow, but soft glassy materials, such as emulsions, foams, suspensions, and pastes, exhibit an intricate mix of solid- and liquid-like behavior. While much progress has been made to understand their elastic (small strain) and flow (infinite strain) properties, such understanding is lacking for the softening and yielding phenomena that connect these asymptotic regimes. Here we present a comprehensive framework for softening and yielding of soft glassy materials, based on extensive numerical simulations of oscillatory rheological tests, and show that two distinct scenarios unfold depending on the material's packing density.

Contact changes of sheared systems: Scaling, correlations, and mechanisms.

We probe the onset and effect of contact changes in two-dimensional soft harmonic particle packings which are sheared quasistatically under controlled strain. First, we show that, in the majority of cases, the first contact changes correspond to the creation or breaking of contacts on a single particle, with contact breaking overwhelmingly likely for low pressures and/or small systems, and contact making and breaking equally likely for large pressures and in the thermodynamic limit. The statistics of the corresponding strains are near-Poissonian, in particular for large-enough systems.

Criticality in Vibrated Frictional Flows at a Finite Strain Rate.

We evidence critical fluctuations in the strain rate of granular flows that are weakly vibrated. Strikingly, the critical point arises at finite values of the mean strain rate and vibration strength, far from the yielding critical point at a zero flow rate. We show that the global rheology, as well as the amplitude and correlation time of the fluctuations, are consistent with a mean-field, Landau-like description, where the strain rate and the stress act as conjugated variables.

Programmable mechanical metamaterials: the role of geometry.

We experimentally and numerically study the role of geometry for the mechanics of biholar metamaterials, which are quasi-2D slabs of rubber patterned by circular holes of two alternating sizes. We recently showed how the response to uniaxial compression of these metamaterials can be programmed by lateral confinement. In particular, there is a range of confining strains ε for which the resistance to compression becomes non-trivial-non-monotonic or hysteretic-in a range of compressive strains ε.

Origami building blocks: Generic and special four-vertices.

Four rigid panels connected by hinges that meet at a point form a four-vertex, the fundamental building block of origami metamaterials. Most materials designed so far are based on the same four-vertex geometry, and little is known regarding how different geometries affect folding behavior. Here we systematically categorize and analyze the geometries and resulting folding motions of Euclidean four-vertices.

Anisotropy of weakly vibrated granular flows.

We experimentally probe the anisotropy of weakly vibrated flowing granular media. Depending on the driving parameters-flow rate and vibration strength-this anisotropy varies significantly. We show how the anisotropy collapses when plotted as a function of the driving stresses, uncovering a direct link between stresses and anisotropy.

Discontinuous Buckling of Wide Beams and Metabeams.

We uncover how nonlinearities dramatically alter the buckling of elastic beams. First, we show experimentally that sufficiently wide ordinary elastic beams and specifically designed metabeams-beams made from a mechanical metamaterial-exhibit discontinuous buckling, an unstable form of buckling where the postbuckling stiffness is negative. Then we use simulations to uncover the crucial role of nonlinearities, and show that beams made from increasingly nonlinear materials exhibit an increasingly negative postbuckling slope.