Fluid-structure interactions of bristled wings: the trade-off between weight and drag.

The smallest flying insects often have bristled wings resembling feathers or combs. We combined experiments and three-dimensional numerical simulations to investigate the trade-off between wing weight and drag generation. In experiments of bristled strips, a reduced physical model of the bristled wing, we found that the elasto-viscous number indicates when reconfiguration occurs in the bristles. Analysis of existing biological data suggested that bristled wings of miniature insects lie below the reconfiguration threshold, thus avoiding drag reduction. Numerical simulations of bristled strips showed that there exist optimal numbers of bristles that maximize the weighted drag when the additional volume due to the bristles is taken into account. We found a scaling relationship between the rescaled optimal numbers and the dimensionless bristle length. This result agrees qualitatively with and provides an upper bound for the bristled wing morphological data analysed in this study.

The strength of surgical knots involves a critical interplay between friction and elastoplasticity.

Knots are the weakest link in surgical sutures, serving as mechanical ligatures between filaments. Exceeding their safe operational limits can cause fatal complications. The empirical nature of present guidelines calls for a predictive understanding of the mechanisms underlying knot strength. We identify the primary ingredients dictating the mechanics of surgical sliding knots, highlighting the previously overlooked but critical effect of plasticity and its interplay with friction. The characterization of surgeon-tied knots reveals the relevant ranges of tightness and geometric features. Using model experiments coupled with finite element simulations, we uncover a robust master curve for the target knot strength versus the tying pre-tension, number of throws, and frictional properties. These findings could find applications in the training of surgeons and robotic-assisted surgical devices.

Regulation of the swimming kinematics of lampreys Petromyzon marinus across changes in viscosity.

The bodies of most swimming fishes are very flexible and deform as result of both external fluid dynamic forces and internal musculoskeletal forces. If fluid forces change, the body motion will also change unless the fish senses the change and alters its muscle activity to compensate. Lampreys and other fishes have mechanosensory cells in their spinal cords that allow them to sense how their body is bending. We hypothesized that lampreys (Petromyzon marinus) actively regulate body curvature to maintain a fairly constant swimming waveform even as swimming speed and fluid dynamic forces change. To test this hypothesis, we measured the steady swimming kinematics of lampreys swimming in normal water, and water in which the viscosity was increased by 10 or 20 times by adding methylcellulose. Increasing the viscosity over this range increases the drag coefficient, potentially increasing fluid forces up to 40%. Previous computational results suggested that if lampreys did not compensate for these forces, the swimming speed would drop by about 52%, the amplitude would drop by 39%, and posterior body curvature would increase by about 31%, while tail beat frequency would remain the same. Five juvenile sea lampreys were filmed swimming through still water, and midlines were digitized using standard techniques. Although swimming speed dropped by 44% from 1× to 10× viscosity, amplitude only decreased by 4%, and curvature increased by 7%, a much smaller change than the amount we estimated if there was no compensation. To examine the waveform overall, we performed a complex orthogonal decomposition and found that the first mode of the swimming waveform (the primary swimming pattern) did not change substantially, even at 20× viscosity. Thus, it appears that lampreys are compensating, at least partially, for the changes in viscosity, which in turn suggests that sensory feedback is involved in regulating the body waveform.

Snap buckling of bistable beams under combined mechanical and magnetic loading.

We investigate the mechanics of bistable, hard-magnetic, elastic beams, combining experiments, finite-element modelling (FEM) and a reduced-order theory. The beam is made of a hard magneto-rheological elastomer, comprising two segments with antiparallel magnetization along the centreline, and is set into a bistable curved configuration by imposing an end-to-end shortening. Reversible snapping is possible between these two stable states. First, we experimentally characterize the critical field strength for the onset of snapping, at different levels of end-to-end shortening. Second, we perform three-dimensional FEM simulations using the Riks method to analyse high-order deformation modes during snapping. Third, we develop a reduced-order centreline-based beam theory to rationalize the observed magneto-elastic response. The theory and simulations are validated against experiments, with an excellent quantitative agreement. Finally, we consider the case of combined magnetic loading and poking force, examining how the applied field affects the bistability and quantifying the maximum load-bearing capacity. Our work provides a set of predictive tools for the rational design of one-dimensional, bistable, magneto-elastic structural elements. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.

Probabilistic buckling of imperfect hemispherical shells containing a distribution of defects.

The buckling of spherical shells is plagued by a strong sensitivity to imperfections. Traditionally, imperfect shells tend to be characterized empirically by the knockdown factor, the ratio between the measured buckling strength and the corresponding classic prediction for a perfect shell. Recently, it has been demonstrated that the knockdown factor of a shell containing a single imperfection can be predicted when there is detailed a priori knowledge of the defect geometry. Still, addressing the analogous problem for a shell containing many defects remains an open question. Here, we use finite element simulations, which we validate against precision experiments, to investigate hemispherical shells containing a well-defined distribution of imperfections. Our goal is to characterize the resulting knockdown factor statistics. First, we study the buckling of shells containing only two defects, uncovering non-trivial regimes of interactions that echo existing findings for cylindrical shells. Then, we construct statistical ensembles of imperfect shells, whose defect amplitudes are sampled from a lognormal distribution. We find that a 3-parameter Weibull distribution is an excellent description for the measured statistics of knockdown factors, suggesting that shell buckling can be regarded as an extreme-value statistics phenomenon. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.

3D stretchable and self-encapsulated multimaterial triboelectric fibers.

A robust power device for wearable technologies and soft electronics must feature good encapsulation, high deformability, and reliable electrical outputs. Despite substantial progress in materials and architectures for two-dimensional (2D) planar power configurations, fiber-based systems remain limited to relatively simple configurations and low performance due to challenges in processing methods. Here, we extend complex 2D triboelectric nanogenerator configurations to 3D fiber formats based on scalable thermal processing of water-resistant thermoplastic elastomers and composites. We perform mechanical analysis using finite element modeling to understand the fiber's deformation and the level of control and engineering on its mechanical behavior and thus to guide its dimensional designs for enhanced electrical performance. With microtexture patterned functional surfaces, the resulting fibers can reliably produce state-of-the-art electrical outputs from various mechanical deformations, even under harsh conditions. These mechanical and electrical attributes allow their integration with large and stretchable surfaces for electricity generation of hundreds of microamperes.

Spontaneous formation of a self-healing carbon nanoskin at the liquid-liquid interface.

Biological membranes exhibit the ability to self-repair and dynamically change their shape while remaining impermeable. Yet, these defining features are difficult to reconcile with mechanical robustness. Here, we report on the spontaneous formation of a carbon nanoskin at the oil-water interface that uniquely combines self-healing attributes with high stiffness. Upon the diffusion-controlled self-assembly of a reactive molecular surfactant at the interface, a solid elastic membrane forms within seconds and evolves into a continuous carbon monolayer with a thickness of a few nanometers. This nanoskin has a stiffness typical for a 2D carbon material with an elastic modulus in bending of more than 40-100 GPa; while brittle, it shows the ability to self-heal upon rupture, can be reversibly reshaped, and sustains complex shapes. We anticipate such an unusual 2D carbon nanomaterial to inspire novel approaches towards the formation of synthetic cells with rigid shells, additive manufacturing of composites, and compartmentalization in industrial catalysis.

Smooth Triaxial Weaving with Naturally Curved Ribbons.

Triaxial weaving is a handicraft technique that has long been used to create curved structures using initially straight and flat ribbons. Weavers typically introduce discrete topological defects to produce nonzero Gaussian curvature, albeit with faceted surfaces. We demonstrate that, by tuning the in-plane curvature of the ribbons, the integrated Gaussian curvature of the weave can be varied continuously, which is not feasible using traditional techniques. Further, we reveal that the shape of the physical unit cells is dictated solely by the in-plane geometry of the ribbons, not elasticity. Finally, we leverage the geometry-driven nature of triaxial weaving to design a set of ribbon profiles to weave smooth spherical, ellipsoidal, and toroidal structures.

Bending Response of a Book with Internal Friction.

We study the bending of a booklike system, comprising a stack of elastic plates coupled through friction. The behavior of this layered system is rich and nontrivial, with a nonadditive enhancement of the apparent stiffness and a significant hysteretic response. A dimension reduction procedure is employed to develop a centerline-based theory describing the stack as a nonlinear planar rod with internal shear. We consider the coupling between the nonlinear geometry and the elasticity of the stacked plates, treating the interlayer friction perturbatively. This model yields predictions for the stack's mechanical response in three-point bending that are in excellent agreement with our experiments. Remarkably, we find that the energy dissipated during deformation can be rationalized over 3 orders of magnitude, including the regimes of a thick stack with large deflection. This robust dissipative mechanism could be harnessed to design new classes of low-cost and efficient damping devices.

Magneto-active elastic shells with tunable buckling strength.

Shell buckling is central in many biological structures and advanced functional materials, even if, traditionally, this elastic instability has been regarded as a catastrophic phenomenon to be avoided for engineering structures. Either way, predicting critical buckling conditions remains a long-standing challenge. The subcritical nature of shell buckling imparts extreme sensitivity to material and geometric imperfections. Consequently, measured critical loads are inevitably lower than classic theoretical predictions. Here, we present a robust mechanism to dynamically tune the buckling strength of shells, exploiting the coupling between mechanics and magnetism. Our experiments on pressurized spherical shells made of a hard-magnetic elastomer demonstrate the tunability of their buckling pressure via magnetic actuation. We develop a theoretical model for thin magnetic elastic shells, which rationalizes the underlying mechanism, in excellent agreement with experiments. A dimensionless magneto-elastic buckling number is recognized as the key governing parameter, combining the geometric, mechanical, and magnetic properties of the system.

Mechanics of two filaments in tight orthogonal contact.

Networks of flexible filaments often involve regions of tight contact. Predictively understanding the equilibrium configurations of these systems is challenging due to intricate couplings between topology, geometry, large nonlinear deformations, and friction. Here, we perform an in-depth study of a simple, yet canonical, problem that captures the essence of contact between filaments. In the orthogonal clasp, two filaments are brought into contact, with each centerline lying in one of a pair of orthogonal planes. Our data from X-ray tomography (µCT) and mechanical testing experiments are in excellent agreement with finite element method (FEM) simulations. Despite the apparent simplicity of the physical system, the data exhibit strikingly unintuitive behavior, even when the contact is frictionless. Specifically, we observe a curvilinear diamond-shaped ridge in the contact-pressure field between the two filaments, sometimes with an inner gap. When a relative displacement is imposed between the filaments, friction is activated, and a highly asymmetric pressure field develops. These findings contrast to the classic capstan analysis of a single filament wrapped around a rigid body. Both the µCT and FEM data indicate that the cross-sections of the filaments can deform significantly. Nonetheless, an idealized geometrical theory assuming undeformable tube cross-sections and neglecting elasticity rationalizes our observations qualitatively and highlights the central role of the small, but nonzero, tube radius of the filaments. We believe that our orthogonal clasp analysis provides a building block for future modeling efforts in frictional contact mechanics of more complex filamentary structures.

A reprogrammable mechanical metamaterial with stable memory.

Metamaterials are designed to realize exotic physical properties through the geometric arrangement of their underlying structural layout1,2. Traditional mechanical metamaterials achieve functionalities such as a target Poisson's ratio3 or shape transformation4-6 through unit-cell optimization7-9, often with spatial heterogeneity10-12. These functionalities are programmed into the layout of the metamaterial in a way that cannot be altered. Although recent efforts have produced means of tuning such properties post-fabrication13-19, they have not demonstrated mechanical reprogrammability analogous to that of digital devices, such as hard disk drives, in which each unit can be written to or read from in real time as required. Here we overcome this challenge by using a design framework for a tileable mechanical metamaterial with stable memory at the unit-cell level. Our design comprises an array of physical binary elements (m-bits), analogous to digital bits, with clearly delineated writing and reading phases. Each m-bit can be independently and reversibly switched between two stable states (acting as memory) using magnetic actuation to move between the equilibria of a bistable shell20-25. Under deformation, each state is associated with a distinctly different mechanical response that is fully elastic and can be reversibly cycled until the system is reprogrammed. Encoding a set of binary instructions onto the tiled array yields markedly different mechanical properties; specifically, the stiffness and strength can be made to range over an order of magnitude. We expect that the stable memory and on-demand reprogrammability of mechanical properties in this design paradigm will facilitate the development of advanced forms of mechanical metamaterials.

Printing on liquid elastomers.

In recent years the research community has paid significant attention to geometrically engineered materials. These materials derive their unique properties from their structure rather than their chemistry alone. Despite their success in the laboratory, the assembly of such soft functional materials remains an outstanding challenge. Here, we propose a robust fluid-mediated route for the rapid fabrication of soft elastomers architected with liquid inclusions. Our approach consists of depositing water drops at the surface of an immiscible liquid elastomer bath. As the elastomer cures, the drops are encapsulated in the polymer and impart shape and function to the newly formed elastic matrix. Using the framework of fluid mechanics, we show how this type of composite material can be tailored.

First-Principles Calculations on the Adsorption Behavior of Amino Acids on a Titanium Carbide MXene.

Due to their vast range of promising biomedical and electronic applications, there is a growing interest in bioinorganic lamellar nanomaterials. MXenes are one such class of materials, which stand out by virtue of their demonstrated biocompatibility, pharmacological applicability, energy storage performance, and feasibility as single-molecule sensors. Here, we report on first-principles predictions, based on density functional theory, of the binding energies and ground-state configurations of six selected amino acids (AAs) adsorbed on O-terminated two-dimensional titanium carbide, Ti2CO2. We find that most AAs (aspartic acid, cysteine, glycine, and phenylalanine) prefer to adsorb via their nitrogen atom, which forms a weak bond with a surface Ti atom, with bond lengths of around 2.35 Å. In contrast, histidine and serine tend to adsorb parallel to the MXene surface, with their α carbon about 3 Å away from it. In both adsorption configurations, the adsorption energies are on the order of the tenths of an electronvolt. In addition, we find a positive, nearly linear correlation between the binding energy of each studied AA and its van der Waals volume, which suggests an adsorption dominated by van der Waals forces. This relationship allowed us to predict the adsorption energies for all of the proteinogenic AAs on the same Ti2CO2 MXene. Our analysis additionally shows that in the parallel adsorption mode there is a negligible transfer of charge density from the AA to the surface but noticeable in the N-bonded adsorption mode. In the latter, the isosurfaces of charge density differences show accumulation of shared electrons in the region between N and Ti, confirming the predicted N-Ti bond. The moderate adsorption energy values calculated, as well as the preservation of the integrity of both the AAs and the surface upon adsorption, reinforce the capability of Ti2CO2 as a promising reusable biosensor for amino acids.

Evolution of critical buckling conditions in imperfect bilayer shells through residual swelling.

We propose and investigate a minimal mechanism that makes use of differential swelling to modify the critical buckling conditions of elastic bilayer shells, as measured by the knockdown factor. Our shells contain an engineered defect at the north pole and are made of two layers of different crosslinked polymers that exchange free molecular chains. Depending on the size of the defect and the extent of swelling, we can observe either a decreasing or increasing knockdown factor. FEM simulations are performed using a reduced model for the swelling process to aid us in rationalizing the underlying mechanism, providing a qualitative agreement with experiments. We believe that the working principle of our mechanism can be extended to bimetallic shells undergoing variations in temperature and to shells made of pH-responsive gels, where the change in knockdown factor could be changed dynamically.

Form finding in elastic gridshells.

Elastic gridshells comprise an initially planar network of elastic rods that are actuated into a shell-like structure by loading their extremities. The resulting actuated form derives from the elastic buckling of the rods subjected to inextensibility. We study elastic gridshells with a focus on the rational design of the final shapes. Our precision desktop experiments exhibit complex geometries, even from seemingly simple initial configurations and actuation processes. The numerical simulations capture this nonintuitive behavior with excellent quantitative agreement, allowing for an exploration of parameter space that reveals multistable states. We then turn to the theory of smooth Chebyshev nets to address the inverse design of hemispherical elastic gridshells. The results suggest that rod inextensibility, not elastic response, dictates the zeroth-order shape of an actuated elastic gridshell. As it turns out, this is the shape of a common household strainer. Therefore, the geometry of Chebyshev nets can be further used to understand elastic gridshells. In particular, we introduce a way to quantify the intrinsic shape of the empty, but enclosed regions, which we then use to rationalize the nonlocal deformation of elastic gridshells to point loading. This justifies the observed difficulty in form finding. Nevertheless, we close with an exploration of concatenating multiple elastic gridshell building blocks.

Buckling patterns in biaxially pre-stretched bilayer shells: wrinkles, creases, folds and fracture-like ridges.

We introduce a new experimental system to study the effects of pre-stretch on the buckling patterns that emerge from the biaxial compression of elastomeric bilayer shells. Upon fabrication of the samples, releasing the pre-stretch in the substrate through deflation places the outer film in a state of biaxial compression and yields a variety of buckling patterns. We systematically explore the parameter space by varying the pre-stretch of the substrate and the ratio between the stiffness of the substrate and film. The phase diagram of the system exhibits a variety of buckling patterns: from the classic periodic wrinkle to creases, folds, and high aspect ratio ridges. Our system is capable of readily transitioning between these buckling patterns, a first for biaxial systems. We focus on the wrinkle to ridge transition. In the latter, we find that pre-stretch plays an essential role and that the ridge geometry (width, height) remains nearly constant throughout their formation process. For the localized ridged patterns, we find that the propagation of the ridge tip depends strongly on both strain and stiffness ratio, in a way that is akin to hierarchical fracture.

Curvature-Controlled Defect Localization in Elastic Surface Crystals.

We investigate the influence of curvature and topology on crystalline dimpled patterns on the surface of generic elastic bilayers. Our numerical analysis predicts that the total number of defects created by adiabatic compression exhibits universal quadratic scaling for spherical, ellipsoidal, and toroidal surfaces over a wide range of system sizes. However, both the localization of individual defects and the orientation of defect chains depend strongly on the local Gaussian curvature and its gradients across a surface. Our results imply that curvature and topology can be utilized to pattern defects in elastic materials, thus promising improved control over hierarchical bending, buckling, or folding processes. Generally, this study suggests that bilayer systems provide an inexpensive yet valuable experimental test bed for exploring the effects of geometrically induced forces on assemblies of topological charges.

Deformation of a soft helical filament in an axial flow at low Reynolds number.

We perform a numerical investigation of the deformation of a rotating helical filament subjected to an axial flow, under low Reynolds number conditions, motivated by the propulsion of bacteria using helical flagella. Given its slenderness, the helical rod is intrinsically soft and deforms due to the interplay between elastic forces and hydrodynamic loading. We make use of a previously developed and experimentally validated computational tool framework that models the elasticity of the filament using the discrete elastic rod method and the fluid forces are treated using Lighthill's slender body theory. Under axial flow, and in the absence of rotation, the initially helical rod is extended. Above a critical flow speed its configuration comprises a straight portion connected to a localized helix near the free end. When the rod is also rotated about its helical axis, propulsion is only possible in a finite range of angular velocity, with an upper bound that is limited by buckling of the soft helix arising due to viscous stresses. A systematic exploration of the parameter space allows us to quantify regimes for successful propulsion for a number of specific bacteria.