Although broadly admired for its aesthetic qualities, the art of origami is now being recognized also as a framework for mechanical metamaterial design. Working with the Miura-ori tessellation, we find that each unit cell of this crease pattern is mechanically bistable, and by switching between states, the compressive modulus of the overall structure can be rationally and reversibly tuned. By virtue of their interactions, these mechanically stable lattice defects also lead to emergent crystallographic structures such as vacancies, dislocations, and grain boundaries. Each of these structures comes from an arrangement of reversible folds, highlighting a connection between mechanical metamaterials and programmable matter. Given origami's scale-free geometric character, this framework for metamaterial design can be directly transferred to milli-, micro-, and nanometer-size systems.

Origami is used beyond purely aesthetic pursuits to design responsive and customizable mechanical metamaterials. However, a generalized physical understanding of origami remains elusive, owing to the challenge of determining whether local kinematic constraints are globally compatible and to an incomplete understanding of how the folded sheet's material properties contribute to the overall mechanical response. Here, we show that the traditional square twist, whose crease pattern has zero degrees of freedom (DOF) and therefore should not be foldable, can nevertheless be folded by accessing bending deformations that are not explicit in the crease pattern. These hidden bending DOF are separated from the crease DOF by an energy gap that gives rise to a geometrically driven critical bifurcation between mono- and bistability. Noting its potential utility for fabricating mechanical switches, we use a temperature-responsive polymer-gel version of the square twist to demonstrate hysteretic folding dynamics at the sub-millimetre scale.

Human collective behavior can vary from calm to panicked depending on social context. Using videos publicly available online, we study the highly energized collective motion of attendees at heavy metal concerts. We find these extreme social gatherings generate similarly extreme behaviors: a disordered gas-like state called a mosh pit and an ordered vortex-like state called a circle pit. Both phenomena are reproduced in flocking simulations demonstrating that human collective behavior is consistent with the predictions of simplified models. . This variety and magnitude of stimuli are atypical of more moderate settings, and contribute to the collective behaviors studied here ( Fig. 1(A)).Videos filmed by attendees at heavy metal concerts [7] highlight a collective phenomenon consisting of 10 1 − 10 2 participants commonly referred to as a mosh pit. In mosh pits, the participants (moshers) move randomly, colliding with one another in an undirected fashion ( Fig. 1(B)). Qualitatively, this phenomenon resembles the kinetics of gaseous particles, even though moshers are self-propelled agents that experience dissipative collisions. To explore this analogy quantitatively, we obtained video footage, corrected for perspective distortions [8] as well as camera instability, and used PIV analysis [9] to measure the two-dimensional (2D) velocity field on an interpolated grid. From this data, we calculated the velocityvelocity correlation function c vv and noted an absence of the spatial oscillations typically found in liquid-like systems. Additionally, c vv was well fit by a pure exponential (R 2 = 0.97) with a decay length of 0.78 m. Taken together, these findings offer strong support for the analogy between mosh pits and gases. As a further check, we examined the 2D speed distribution; previous observations of human pedestrian traffic and escape panic led us to expect a broad distribution not well described by simple analytic expressions [2,10]. However, the measured speed distribution in mosh pits was well fit by the equilibrium speed distribution of classical 2D gasses (Fig. 1(C)), otherwise known as the Maxwell-Boltzmann distribution [11]. These observations present an interesting question: Why does an inherently non-equilibrium system exhibit equilibrium characteristics?Studies of collective motion in living and complex systems have found notable success within the framework of flocking simulations [12][13][14][15][16]. Thus, we use a Vicsek-like model [17] to simplify the complex behavioral dynamics of each human mosher to that of a simple soft-bodied particle we dub a Mobile Active Simulated Humanoid, or MASHer (SI). Our model includes two species of MASH-

Among mammalian soft tissues, articular cartilage is particularly interesting because it can endure a lifetime of daily mechanical loading despite having minimal regenerative capacity. This remarkable resilience may be due to the depth-dependent mechanical properties, which have been shown to localize strain and energy dissipation. This paradigm proposes that these properties arise from the depth-dependent collagen fiber orientation. Nevertheless, this structure-function relationship has not yet been quantified. Here, we use confocal elastography, quantitative polarized light microscopy, and Fourier-transform infrared imaging to make same-sample measurements of the depth-dependent shear modulus, collagen fiber organization, and extracellular matrix concentration in neonatal bovine articular cartilage. We find weak correlations between the shear modulus |G(∗)| and both the collagen fiber orientation and polarization. We find a much stronger correlation between |G(∗)| and the concentration of collagen fibers. Interestingly, very small changes in collagen volume fraction vc lead to orders-of-magnitude changes in the modulus with |G(∗)| scaling as (vc - v0)(ξ). Such dependencies are observed in the rheology of other biopolymer networks whose structure exhibits rigidity percolation phase transitions. Along these lines, we propose that the collagen network in articular cartilage is near a percolation threshold that gives rise to these large mechanical variations and localization of strain at the tissue's surface.

A water bridge refers to an experimental "flexible cable" made up of pure deionized water which can hang across two supports maintained with a sufficiently large voltage difference. The resulting electric fields within the deionized water flexible cable, maintain a tension which sustains the water against the downward force of gravity. A detailed calculation of the water bridge tension will be provided in terms of the Maxwell pressure tensor in a dielectric fluid medium. General properties of the dielectric liquid pressure tensor are discussed along with unusual features of dielectric fluid Bernoulli flows in an electric field. Analogies between dielectric fluid Bernoulli flows in strong electric fields and quantum Bernoulli flows in superfluids are explored.

We study the primary root growth of wild-type Medicago truncatula plants in heterogeneous environments using 3D time-lapse imaging. The growth medium is a transparent hydrogel consisting of a stiff lower layer and a compliant upper layer. We find that the roots deform into a helical shape just above the gel layer interface before penetrating into the lower layer. This geometry is interpreted as a combination of growth-induced mechanical buckling modulated by the growth medium and a simultaneous twisting near the root tip. We study the helical morphology as the modulus of the upper gel layer is varied and demonstrate that the size of the deformation varies with gel stiffness as expected by a mathematical model based on the theory of buckled rods. Moreover, we show that plant-to-plant variations can be accounted for by biomechanically plausible values of the model parameters.morphogenesis | plant biomechanics | biological chirality | root growth and remodeling

Osteoarthritis (OA) is a disease that involves the erosion and structural weakening of articular cartilage. OA is characterized by the degradation of collagen and proteoglycans in the extracellular matrix (ECM), particularly at the articular surface by proteinases including matrix metalloproteinases (MMPs) and a disintegrin and metalloproteinase with thrombospondin motifs (ADAMTSs).1 Degradation of collagen and proteoglycans is known to alter shear mechanical properties of cartilage, but study of this phenomenon has been focused on bulk tissue properties. The purpose of this study was to assess microscale cartilage damage induced by trypsin or collagenase using a technique to measure the local shear viscoelastic properties. Safranin-O histology revealed a decrease in proteoglycans near the articular surface after collagenase and trypsin digestions, with proteoglycan depletion increasing in time. Similarly, confocal reflectance micrographs showed increasing collagen degradation in collagenase treated samples, although the collagen network remained intact after trypsin treatment. Both treatments induced changes in shear modulus that were confined to a narrow range ($400mm) near tissue surface. In addition, collagenase altered the total energy dissipation distribution by up to a factor of 100, with longer digestion times corresponding to higher energy dissipation. The ability to detect local mechanical signatures in tissue composition and mechanics is an important tool for understanding the spatially non-uniform changes that occur in articular cartilage diseases such as OA. ß

Origami-based design holds promise for developing materials whose mechanical properties are tuned by crease patterns introduced to thin sheets. Although there has been heuristic developments in constructing patterns with desirable qualities, the bridge between origami and physics has yet to be fully developed. To truly consider origami structures as a class of materials, methods akin to solid mechanics need to be developed to understand their long-wavelength behavior. We introduce here a lattice theory for examining the mechanics of origami tessellations in terms of the topology of their crease pattern and the relationship between the folds at each vertex. This formulation provides a general method for associating mechanical properties with periodic folded structures, and allows for a concrete connection between more conventional materials and the mechanical metamaterials constructed using origami-based design.While for hundreds of years origami has existed as an artistic endeavor, recent decades have seen the application of folding thin materials to the fields of architecture, engineering, and material science [1][2][3][4][5][6][7]. Controlled actuation of thin materials via patterned folds has led to a variety of self-assembly strategies in polymer gels [8] and shape-memory materials [4], as well elastocapillary self-assembly [9], leading to the design of a new category of shape-transformable materials inspired by origami design. The origami repertoire itself, buoyed by advances in the mathematics of folding and the burgeoning field of computational geometry [10], is no longer limited to designs of animals and children's toys that dominate the art in popular consciousness, but now includes tessellations, corrugations, and other non-representational structures whose mechanical properties are of interest from a scientific perspective. These properties originate from the confluence of geometry and mechanical constraints that are an intrinsic part of origami, and ultimately allow for the construction of mechanical meta-materials using origami-based design [1-4, 6, 11-13]. In this paper we formulate a general theory for periodic lattices of folds in thin materials, and combine the language of traditional lattice solid mechanics with the geometric theory underlying origami.A distinct characteristic of all thin materials is that geometric constraints dominate the mechanical response of the structure. Because of this strong coupling between shape and mechanics, it is far more likely for a thin sheet to deform by bending without stretching. Strategically weakening a material with a crease or fold, and thus lowering the energetic cost of stretching, allows complex deformations and re-ordering of the material for negligible elastic energy cost. This vanishing energy cost, especially combined with increased control over micro-and nanoscopic material systems, indicates the great promise for structures whose characteristics depend primarily on geometry, rather than material composition.By patterning creases, hinges, or fold...