Crackling Noise during Slow Relaxations in Crumpled Sheets.

The statistics of noise emitted by ultrathin crumpled sheets is measured while they exhibit logarithmic relaxations under load. We find that the logarithmic relaxation advanced via a series of discrete, audible, micromechanical events that are log-Poisson distributed (i.e., the process becomes a Poisson process when time stamps are replaced by their logarithms). The analysis places constraints on the possible mechanisms underlying the glasslike slow relaxation and memory retention in these systems.

Geometric rules for the annihilation dynamics of step lines on fracture fronts.

The roughness of a fracture surface records a crack's complex path through a material and can affect the resultant frictional or fluid transport properties of the broken medium. For brittle fractures, some of the most prominent surface features are long, step-like discontinuities called step lines. In heterogeneous materials, the mean crack surface roughness created by these step lines is well captured by a simple, one-dimensional ballistic annihilation model, which assumes the creation of these steps is a random processes with a single probability that depends on the heterogeneity of the material, and that their destruction occurs via pairwise interactions. Here, through an exhaustive study of experimentally generated crack surfaces in brittle hydrogels, we examine step interactions and show that interaction outcomes depend on the geometry of the incoming steps. The rules that govern step interactions can be categorized into three unique classes and are fully described, providing a complete framework for predicting fracture roughness.

Hitting the mark: probing at the initiation site allows for accurate prediction of a thin shell's buckling load.

Geometric imperfections are understood to play an essential part in the buckling of a thin shell, but how multiple defects interact to control the onset of failure remains unclear. Here, we examine the failure of real cylindrical shells by experimentally poking soda cans with a large imparted dimple. By high-speed imaging of the can's surface, the initiation of buckling from axial loading is directly observed, revealing that larger dimples tend to set the initial buckling location. However, the influence of the shell's background geometric imperfections can still occasionally dominate, causing initiation to occur far from the dimple. In this situation, probing at the dimple leads to an over-prediction of the axial capacity. Using finite-element simulations, we understand our experimental results as a competition between the large dimple and the shell's inherent defect structure. In our simulations, we empirically observe a deformation-based criterion that connects the ideal poking location to the initiation site. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.

Measuring the energy landscape: an experimental approach to the study of buckling in thin shells.

Recent research into the buckling load of thin shells has focused on local poking of the shell. In this approach, the shell is poked under load to extract its stability landscape, and a ridge tracking method is performed to estimate the buckling load of the shell. It is the current understanding that the stability landscape measures the local stability of the shell and, as a result, that the accuracy of ridge tracking greatly relies on the location of poking. Currently, there is no method that can predict where poking should be performed on an experimental system. Here, we examine the global response of thin shells to poking through the energy landscape. We present an experimental method for measuring the energy landscape of thin shells and demonstrate its application on a thin plate strip. We show that by analysing the dynamics of the shell in the energy landscape we can experimentally measure the buckling mode of the system, which gives the correct point of poking for accurate ridge tracking, and identify two kinds of buckling points. Finally, we propose how this approach can be applied to more complex systems such as thin cylinders. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.

Beyond quality and quantity: Spatial distribution of contact encodes frictional strength.

Classically, the quantity of contact area A_{R} between two bodies is considered a proxy for the force of friction. However, bond density across the interface-quality of contact-is also relevant, and contemporary debate often centers around the relative importance of these two factors. In this work, we demonstrate that a third factor, often overlooked, plays a significant role in static frictional strength: The spatial distribution of contact. We perform static friction measurements, µ, on three pairs of solid blocks while imaging the contact plane. By using linear regression on hundreds of image-µ pairs, we are able to predict future friction measurements with three to seven times better accuracy than existing benchmarks, including total quantity of contact area. Our model has no access to quality of contact, and we therefore conclude that a large portion of the interfacial state is encoded in the spatial distribution of contact, rather than its quality or quantity.

How Material Heterogeneity Creates Rough Fractures.

Fractures are a critical process in how materials wear, weaken, and fail, whose unpredictable behavior can have dire consequences. While the behavior of smooth cracks in ideal materials is well understood, it is assumed that for real, heterogeneous systems, fracture propagation is complex, generating rough fracture surfaces that are highly sensitive to specific details of the medium. Here we show how fracture roughness and material heterogeneity are inextricably connected via a simple framework. Studying hydraulic fractures in brittle hydrogels that have been supplemented with microbeads or glycerol to create controlled material heterogeneity, we show that the morphology of the crack surface depends solely on one parameter: the probability to perturb the front above a critical size to produce a steplike instability. This probability scales linearly with the number density, and with heterogeneity size to the 5/2 power. The ensuing behavior is universal and is captured by the 1D ballistic propagation and annihilation of steps along the singular fracture front.

Observation of Remote Electroconvection and Inert-Cation Concentration Valley within Supporting Electrolytes in a Microfluidic-Based Electrochemical Device.

The electrochemical system is playing an increasingly important role in the advanced technology development for drinkable water and energy storage. While the binary electrolyte has been widely studied, such as the associated intriguing interfacial instabilities, multi-component electrolyte is by far less known. Here, based on the classic Cu|CuSO4 |Cu electrochemical system, the effect of supporting electrolyte is systematically investigated by highlighting the inert cations. In an annulus microfluidic device, the suppression of a previously known electro-osmotic instability and the emergence of an array of the remote electroconvection along the azimuthal direction is found. A distinctive inert-cation concentration valley propagates radially outward at a speed limited by the electromigration velocity. Remarkably, the simultaneous visualization of spatiotemporal evolution demonstrates the correlation of the concentration valley and electroconvection at a microscopic level. The underlying physical mechanism of their correlation is discussed, and the scaling analysis agrees with experiments. This work might inspire more future work on the multi-component electrolyte, such as for the suppression of interfacial hydrodynamic instability and mitigation of dendrite growth, with the technological implications for water treatment and energy storage in batteries.

A model for the fragmentation kinetics of crumpled thin sheets.

As a confined thin sheet crumples, it spontaneously segments into flat facets delimited by a network of ridges. Despite the apparent disorder of this process, statistical properties of crumpled sheets exhibit striking reproducibility. Experiments have shown that the total crease length accrues logarithmically when repeatedly compacting and unfolding a sheet of paper. Here, we offer insight to this unexpected result by exploring the correspondence between crumpling and fragmentation processes. We identify a physical model for the evolution of facet area and ridge length distributions of crumpled sheets, and propose a mechanism for re-fragmentation driven by geometric frustration. This mechanism establishes a feedback loop in which the facet size distribution informs the subsequent rate of fragmentation under repeated confinement, thereby producing a new size distribution. We then demonstrate the capacity of this model to reproduce the characteristic logarithmic scaling of total crease length, thereby supplying a missing physical basis for the observed phenomenon.

Nondestructive Prediction of the Buckling Load of Imperfect Shells.

From soda cans to space rockets, thin-walled cylindrical shells are abundant, offering exceptional load carrying capacity at relatively low weight. However, the actual load at which any shell buckles and collapses is very sensitive to imperceptible defects and cannot be predicted, which challenges the of such structures. Consequently, probabilistic descriptions in terms of empirical design rules are used and designing reliable structures requires the use of conservative strength estimates. We introduce a nonlinear description where finite-amplitude perturbations trigger buckling. Drawing from the analogy between imperfect shells which buckle and imperfect pipe flow which becomes turbulent, we experimentally show that lateral probing of cylindrical shells reveals their strength nondestructively. A new ridge-tracking method is applied to commercial cylinders with a hole showing that when the location where buckling nucleates is known we can accurately predict the buckling load of each individual shell, within ±5%. Our study provides a new promising framework to understand shell buckling, and more generally, imperfection-sensitive instabilities.

Turbulence generation through an iterative cascade of the elliptical instability.

The essence of turbulent flow is the conveyance of energy through the formation, interaction, and destruction of eddies over a wide range of spatial scales-from the largest scales where energy is injected down to the smallest scales where it is dissipated through viscosity. Currently, there is no mechanistic framework that captures how the interactions of vortices drive this cascade. We show that iterations of the elliptical instability, arising from the interactions between counter-rotating vortices, lead to the emergence of turbulence. We demonstrate how the nonlinear development of the elliptical instability generates an ordered array of antiparallel secondary filaments. The secondary filaments mutually interact, leading to the formation of even smaller tertiary filaments. In experiments and simulations, we observe two and three iterations of this cascade, respectively. Our observations indicate that the elliptical instability could be one of the fundamental mechanisms by which the turbulent cascade develops.

Shear Controls Frictional Aging by Erasing Memory.

We simultaneously measure the static friction and the real area of contact between two solid bodies. These quantities are traditionally considered equivalent, and under static conditions both increase logarithmically in time, a phenomenon coined aging. Here we show that the frictional aging rate is determined by the combination of the aging rate of the real area of contact and two memory-erasure effects that occur when shear is changed (e.g., to measure static friction.) The application of a static shear load accelerates frictional aging while the aging rate of the real area of contact is unaffected. Moreover, a negative static shear-pulling instead of pushing-slows frictional aging, but similarly does not affect the aging of contacts. The origin of this shear effect on aging is geometrical. When shear load is increased, minute relative tilts between the two blocks prematurely erase interfacial memory prior to sliding, negating the effect of aging. Modifying the loading point of the interface eliminates these tilts and as a result frictional aging rate becomes insensitive to shear. We also identify a secondary memory-erasure effect that remains even when all tilts are eliminated and show that this effect can be leveraged to accelerate aging by cycling between two static shear loads.

Geometric frustration induces the transition between rotation and counterrotation in swirled granular media.

Granular material in a swirled container exhibits a curious transition as the number of particles is increased: At low densities, the particle cluster rotates in the same direction as the swirling motion of the container, while at high densities it rotates in the opposite direction. We investigate this phenomenon experimentally and numerically using a corotating reference frame in which the system reaches a statistical steady state. In this steady state, the particles form a cluster whose translational degrees of freedom are stationary, while the individual particles constantly circulate around the cluster's center of mass, similar to a ball rolling along the wall within a rotating drum. We show that the transition to counterrotation is friction dependent. At high particle densities, frictional effects result in geometric frustration, which prevents particles from cooperatively rolling and spinning. Consequently, the particle cluster rolls like a rigid body with no-slip conditions on the container wall, which necessarily counterrotates around its own axis. Numerical simulations verify that both wall-disk friction and disk-disk friction are critical for inducing counterrotation.

A Sequence of Developmental Events Occurs Underneath Growing Bacillus subtilis Pellicles.

Biofilms are structured communities of bacteria that exhibit complex spatio-temporal dynamics. In liquid media, Bacillus subtilis produces an opaque floating biofilm, or a pellicle. Biofilms are generally associated with an interface, but the ability of Bacillus subtilis to swim means the bacteria are additionally able to reside within the liquid phase. However, due to imaging complications associated with the opacity of pellicles, the extent to which bacteria coexist within the liquid bulk as well as their behavior in the liquid is not well studied. We therefore develop a high-throughput imaging system to image underneath developing pellicles. Here we report a well-defined sequence of developmental events that occurs underneath a growing pellicle. Comparison with bacteria deficient in swimming and chemotaxis suggest that these properties enable collective bacterial swimming within the liquid phase which facilitate faster surface colonization. Furthermore, comparison to bacteria deficient in exopolymeric substances (EPS) suggest that the lack of a surface pellicle prevents further developmental steps from occurring within the liquid phase. Our results reveal a sequence of developmental events during pellicle growth, encompassing adhesion, conversion, growth, maturity, and detachment on the interface, which are synchronized with the bacteria in the liquid bulk increasing in density until the formation of a mature surface pellicle, after which the density of bacteria in the liquid drops.

Simple Law for Third-Body Friction.

A key difficulty to understanding friction is that many physical mechanisms contribute simultaneously. Here we investigate third-body frictional dynamics in a model experimental system that eliminates first-body interaction, wear, and fracture, and concentrates on the elastic interaction between sliding blocks and third bodies. We simultaneously visualize the particle motion and measure the global shear force. By systematically increasing the number of foreign particles, we find that the frictional dissipation depends only on the size ratio between surface asperities and the loose particles, irrespective of the particle's size or the surface's roughness. When the particles are comparable in size to the surface features, friction increases linearly with the number of particles. For particles smaller than the surface features, friction grows sublinearly with the number of particles. Our findings suggest that matching the size of surface features to the size of potential contaminants may be a good strategy for reliable lubrication.

Machine learning in a data-limited regime: Augmenting experiments with synthetic data uncovers order in crumpled sheets.

Machine learning has gained widespread attention as a powerful tool to identify structure in complex, high-dimensional data. However, these techniques are ostensibly inapplicable for experimental systems where data are scarce or expensive to obtain. Here, we introduce a strategy to resolve this impasse by augmenting the experimental dataset with synthetically generated data of a much simpler sister system. Specifically, we study spontaneously emerging local order in crease networks of crumpled thin sheets, a paradigmatic example of spatial complexity, and show that machine learning techniques can be effective even in a data-limited regime. This is achieved by augmenting the scarce experimental dataset with inexhaustible amounts of simulated data of rigid flat-folded sheets, which are simple to simulate and share common statistical properties. This considerably improves the predictive power in a test problem of pattern completion and demonstrates the usefulness of machine learning in bench-top experiments where data are good but scarce.

Nonmonotonic Aging and Memory in a Frictional Interface.

We measure the static frictional resistance and the real area of contact between two solid blocks subjected to a normal load. We show that following a two-step change in the normal load the system exhibits nonmonotonic aging and memory effects, two hallmarks of glassy dynamics. These dynamics are strongly influenced by the discrete geometry of the frictional interface, characterized by the attachment and detachment of unique microcontacts. The results are in good agreement with a theoretical model we propose that incorporates this geometry into the framework recently used to describe Kovacs-like relaxation in glasses as well as thermal disordered systems. These results indicate that a frictional interface is a glassy system and strengthen the notion that nonmonotonic relaxation behavior is generic in such systems.

Matrix Production and Sporulation in Bacillus subtilis Biofilms Localize to Propagating Wave Fronts.

Bacterial biofilms are surface-attached microbial communities encased in self-produced extracellular polymeric substances. Here we demonstrate that during the development of Bacillus subtilis biofilms, matrix production is localized to an annular front propagating at the periphery and sporulation to a second front at a fixed distance at the interior. We show that within these fronts, cells switch off matrix production and transition to sporulation after a set time delay of ∼100 min. Correlation analyses of fluctuations in fluorescence reporter activity reveal that the fronts emerge from a pair of gene-expression waves of matrix production and sporulation. The localized expression waves travel across cells that are immobilized in the biofilm matrix in contrast to active cell migration or horizontal colony spreading. Our results suggest that front propagation arises via a local developmental program occurring at the level of individual bacterial cells, likely driven by nutrient depletion and metabolic by-product accumulation. A single-length scale and timescale couples the spatiotemporal propagation of both fronts throughout development. As a result, gene expression patterns within the advancing fronts collapse to self-similar expression profiles. Our findings highlight the key role of the localized cellular developmental program associated with the propagating front in describing biofilm growth.

Kirigami skins make a simple soft actuator crawl.

Bioinspired soft machines made of highly deformable materials are enabling a variety of innovative applications, yet their locomotion typically requires several actuators that are independently activated. We harnessed kirigami principles to significantly enhance the crawling capability of a soft actuator. We designed highly stretchable kirigami surfaces in which mechanical instabilities induce a transformation from flat sheets to 3D-textured surfaces akin to the scaled skin of snakes. First, we showed that this transformation was accompanied by a dramatic change in the frictional properties of the surfaces. Then, we demonstrated that, when wrapped around an extending soft actuator, the buckling-induced directional frictional properties of these surfaces enabled the system to efficiently crawl.

Stability Landscape of Shell Buckling.

We measure the response of cylindrical shells to poking and identify a stability landscape, which fully characterizes the stability of perfect shells and imperfect ones in the case where a single defect dominates. We show that the landscape of stability is independent of the loading protocol and the poker geometry. Our results suggest that the complex stability of shells reduces to a low dimensional description. Tracking ridges and valleys of this landscape defines a natural phase-space coordinates for describing the stability of shells.