Non-uniform Curvature Research Articles

An experimental and numerical study on the behavior of finite-length column vortex

This paper explores experimental and numerical investigation of the spatiotemporal dynamics of a finite-length vortex column in three dimensions using particle image velocimetry and large eddy simulation. The research examines the combined impact of bending, buckling, and core-splitting on a finite-length vortex column. More precisely, the work centers on the fundamental motions, evolutions in flow along the axis, how the shape of the vortex core changes over time, the instability caused by the long waves on the vortex column, and the division of the vortex core. A novel prototype is developed that utilizes piston-driven inflow and produces a vortex column through the principles of flow separation and Biot–Savart induction, which is studied for predicting an ex situ cyclonic line vortex. The present study discusses the complete three-dimensional overview of the same columnar vortex. The meridional swirl and the axial transport of vorticity deform the shape of the core cross sections in different lengths of the column. The jump in the axial velocity at the core boundary allows for the occurrence of bending instabilities with a left-handed helical structure. These instabilities have a long wavelength, similar to the length of the vortex column, and belong to the m = +1 mode. The vortex column experiences a non-uniform curvature and torsion caused by the intricate shape of the laboratory model and varying flow speeds at different heights of the vortex column. The results offer valuable insights into the role of inertia, Coriolis, and viscous forces on the dynamics of the vortex column.

Dynamics of Active Defects on the Anisotropic Surface of an Ellipsoidal Droplet

We investigate the steady state of an ellipsoidal active nematic shell using experiments and numerical simulations. We create the shells by coating microsized ellipsoidal droplets with a protein-based active cytoskeletal gel, thus obtaining ellipsoidal core-shell structures. This system provides the appropriate conditions of confinement and geometry to investigate the impact of nonuniform curvature on an orderly active nematic fluid that features the minimum number of defects required by topology. We identify new time-dependent states where topological defects periodically oscillate between translational and rotational regimes, resulting in the spontaneous emergence of chirality. Our simulations of active nematohydrodynamics demonstrate that, beyond topology and activity, the dynamics of the active material are profoundly influenced by the local curvature and viscous anisotropy of the underlying droplet, as well as by external hydrodynamic forces stemming from the self-sustained rotational motion of defects. These results illustrate how the incorporation of curvature gradients into active nematic shells orchestrates remarkable spatiotemporal patterns, offering new insights into biological processes and providing compelling prospects for designing bioinspired micromachines. Published by the American Physical Society 2024

Roller Position Design in the Roll Bending Process of a Non-Uniform Curvature Profile

Roller Position Design in the Roll Bending Process of a Non-Uniform Curvature Profile

When and Where Lithium Plating Occurs, Its Correlation with Microstructure Heterogeneity, and the Mechanisms That Initiate and Self-Regulate Electrochemical Heterogeneity

A microstructure scale electrochemical LIB model was used to investigate lithium plating onset, material non-uniform utilization, and in-plane heterogeneities for an NMC-graphite full cell [1]. Model predicts active material particle surface roughness and size distribution (respectively, non-uniform curvature within and between particles) initiate in-plane heterogeneity, and that particle size heterogeneity at the separator interface controls the lithium plating preferential deposition (“Where”). These in-plane heterogeneities are then exacerbated by through-plane heterogeneities induced at fast charge as electrolyte depletion occurs and concentrates intercalation reaction near the anode-separator interface. Also, overall magnitude and occurrence of lithium plating is controlled by effective, or macroscale, microstructure parameters (“When”).As local states of charge start to diverge between nearby active material regions, overpotential differences induced by OCP difference kick in and contribute to reduce these SOC local heterogeneities. However, for staged materials such as graphite, with OCP profile alternating between plateaus and varying regions, this balancing mechanism is, respectively, inactive and active. This leads to a dynamic, non-monotonic, in-plane heterogeneity time evolution for state of charge and Faraday current density, for which their respective in-plane heterogeneity magnitude alternates. Such behavior has been modeled both for the whole electrode at the microstructure scale and at the particle scale. In-plane heterogeneities are usually considered to be detrimental, as they result in material non-uniform utilization (i.e., under and over stressed regions) and earlier degradations. However, this work provides a more granular approach as it discriminates between a harmful in-plane heterogeneity (non-uniform curvature) that triggers SOC in-plane heterogeneity, and a beneficial in-plane heterogeneity (Faraday current density) that contributes to reduce SOC in-plane heterogeneity.This work comprehensively explains the mechanisms that initiate, exacerbate, and regulate heterogeneity at the microstructure scale, while providing some design suggestions to reduce both in-plane and through-plane heterogeneities, as summarized in the graphical abstract.[1] F. L. E. Usseglio-Viretta, A. M. Colclasure, J. Allen, D. P. Finegan, P. Graf, and K. Smith, Microstructure Scale Lithium-ion Battery Modeling, Part I: on lithium plating prediction and heterogeneity, in preparation. Figure 1

Analysis of planar arbitrarily curved microbeams with simplified strain gradient theory and Timoshenko–Ehrenfest beam model

As the first endeavor in the context of Mindlin’s strain gradient theory, this study contributes a systematic and rigorous derivation for governing equations and boundary conditions of planar arbitrarily curved microbeams. The Timoshenko–Ehrenfest beam model is incorporated into a simplified version of Mindlin’s strain gradient theory. Kinematic unknowns include displacement components of the beam axis in the local coordinate system and the rotation of cross-section. Since the derived governing equations and boundary conditions are extremely complex, analytical solutions are not achievable for microbeams having non-uniform curvature. To facilitate the numerical analysis, two isogeometric collocation formulations are proposed, that is, displacement-based and mixed formulations. Several tests are designed to evaluate the accuracy and reliability of the proposed isogeometric collocation formulations, especially with respect to the well-known locking pathology. It is found that the mixed formulation is more accurate and robust than the displacement-based one. Therefore, the mixed formulation is then used to numerically investigate the size-dependent behavior and stiffening effect. Furthermore, some informative tests are performed to delineate the significance of the curviness in the prediction of structural responses of planar arbitrarily curved microbeams, which appears to be still an unanswered issue.

Pneumatically tunable adherence of elastomeric soft hollow pillars with non-circular contacts

Dynamically tunable interfacial dry adhesion plays a significant role in numerous biological functions and industrial applications. Among various strategies, pneumatics-activated adhesive devices draw much attention due to their distinct advantages such as fast speed, reliable performance, large adhesion tunability and easily accessible materials. To understand and predict adhesion strength of pneumatics-activated adhesives, it is necessary to examine their interfacial mechanics that is nonlinearly coupled with the large deformation of the devices under pressure. However, previous studies have only focused on axisymmetric cases in which the outline of the contact area is circular, whereas the tunable adherence of non-circular contact controlled by pneumatics remains elusive. In this work, through a combination of experiments and simulations, we study the effect of non-circular contact geometry on tunable dry adhesion of pressure-activated soft hollow pillars. Specifically, elliptical, square, and rectangular contact shapes are considered and their effects on tunable adhesion of the soft hollow pillars are compared to that of circular contact geometry thoroughly. The results show that soft hollow pillars with elliptical, square, and rectangular contact surfaces demonstrate rich interfacial delamination behaviors that depend on the contact outline geometry and internal pressure. Among all contact geometries, elliptical contact has the highest adhesion tunability yet requires lowest activating pressure owing to the non-uniform curvature distribution of the contact outline. However, when the eccentricity increases, the elliptical contact has reduced tunability of adhesion caused by the contact of opposing sides of the sidewall upon buckling. For square and rectangular contacts, they have the lowest adhesion tunability and need higher activating pressure than those of circular and elliptical contact since the 90-degree edges of the sidewall prohibit buckling instability. Our findings greatly broaden the design space of pneumatics-activated adhesive devices by adding the contact geometry of the soft hollow pillars as a new design parameter, which can provide valuable guidance for tunable adhesive design for various applications in manufacturing and robotics.

Euglena’s atypical respiratory chain adapts to the discoidal cristae and flexible metabolism

Euglena gracilis, a model organism of the eukaryotic supergroup Discoba harbouring also clinically important parasitic species, possesses diverse metabolic strategies and an atypical electron transport chain. While structures of the electron transport chain complexes and supercomplexes of most other eukaryotic clades have been reported, no similar structure is currently available for Discoba, limiting the understandings of its core metabolism and leaving a gap in the evolutionary tree of eukaryotic bioenergetics. Here, we report high-resolution cryo-EM structures of Euglena’s respirasome I + III2 + IV and supercomplex III2 + IV2. A previously unreported fatty acid synthesis domain locates on the tip of complex I’s peripheral arm, providing a clear picture of its atypical subunit composition identified previously. Individual complexes are re-arranged in the respirasome to adapt to the non-uniform membrane curvature of the discoidal cristae. Furthermore, Euglena’s conformationally rigid complex I is deactivated by restricting ubiquinone’s access to its substrate tunnel. Our findings provide structural insights for therapeutic developments against euglenozoan parasite infections.

Complex motion of steerable vesicular robots filled with active colloidal rods

While the collective motion of active particles has been studied extensively, effective strategies to navigate particle swarms without external guidance remain elusive. We introduce a method to control the trajectories of two-dimensional swarms of active rod-like particles by confining the particles to rigid bounding membranes (vesicles) with non-uniform curvature. We show that the propelling agents spontaneously form clusters at the membrane wall and collectively propel the vesicle, turning it into an active superstructure. To further guide the motion of the superstructure, we add discontinuous features to the rigid membrane boundary in the form of a kinked tip, which acts as a steering component to direct the motion of the vesicle. We report that the system’s geometrical and material properties, such as the aspect ratio and Péclet number of the active rods as well as the kink angle and flexibility of the membrane, determine the stacking of active particles close to the kinked confinement and induce a diverse set of dynamical behaviors of the superstructure, including linear and circular motion both in the direction of, and opposite to, the kink. From a systematic study of these various behaviors, we design vesicles with switchable and reversible locomotions by tuning the confinement parameters. The observed phenomena suggest a promising mechanism for particle transportation and could be used as a basic element to navigate active matter through complex and tortuous environments.

Theoretical analysis and a parametric study on forced vibration of large statically deformed curved beam with rigid links and moving support

Forced vibration characteristics around large statically deformed configuration of curved beam system with rigid links and moving support are analyzed. In addition, the paper also investigates various parametric effects of height to span ratio and roller radius to height ratio coupled with support connection mechanism and profile shape, on dynamic characteristics of the curved beam system. The subject problem includes two interrelated problems: determining deformed configuration under static load and dynamic response of the loaded beam under harmonic excitation. The static problem is analyzed incrementally through the variational principle-based energy method in body-embedded curvilinear frame considering geometric nonlinearities due to combined bending-stretching and non-uniform initial curvature. In each incremental step, the nonlinear governing equation is solved iteratively, and kinematic constraints due to interactive deformation of the flexible curved beam with rigid links are imposed to obtain the global solution. Concerning the statically deformed configuration, governing equation for forced vibration is derived through Hamilton’s principle in curvilinear frame. Nonlinear effects caused by combined bending-stretching modes of vibration, non-uniform curvature, and lumped mass of the dead static load are considered. The set of inhomogeneous governing equations is solved through Broyden’s method. A direct substitution technique through successive relaxation is also employed to obtain an initial guess solution. Besides the forced vibration, free vibration analysis at static deformed configuration is also carried out for the completeness of the study. The theoretical model is validated through comparisons of loaded natural frequency results with finite element package. After the validation study, the effects of the mentioned geometric parameters on the dynamic response of the curved beam system are investigated and presented suitably. The physically insightful framework along with the parametric study may facilitate simulation and design of several practical structures involving moving support and rigid links subjected to continuous excitation around large statically deformed configurations.

Cross-stream migration of a vesicle in vortical flows.

We use numerical simulations to systematically investigate the vesicle dynamics in two-dimensional (2D) Taylor-Green vortex flow in the absence of inertial forces. Vesicles are highly deformable membranes encapsulating an incompressible fluid and they serve as numerical and experimental proxies for biological cells such as red blood cells. Vesicle dynamics has been studied in free-space or bounded shear, Poiseuille, and Taylor-Couette flows in 2D and 3D. Taylor-Green vortex are characterized with even more complicated properties than those flows such as nonuniform flow line curvature, shear gradient. We study the effects of two parameters on the vesicle dynamics: the ratio of the interior fluid viscosity to that of the exterior one and the ratio of the shear forces on the vesicle to the membrane stiffness (characterized by the capillary number). Vesicle deformability nonlinearly depends on these parameters. Although the study is in 2D, our findings contribute to the wide spectrum of intriguing vesicle dynamics: Vesicles migrate inwards and eventually rotate at the vortex center if they are sufficiently deformable. If not, then they migrate away from the vortex center and travel across the periodic arrays of vortices. The outward migration of a vesicle is a new phenomenon in Taylor-Green vortex flow and has not been observed in any other flows so far. Such cross-streamline migration of deformable particles can be utilized in several applications such as microfluidics for cell separation.

On effects of concentrated loads on perforated sensitive shells of revolution

Sensitive shells are a class of constructions with specific and perhaps unintuitive responses to different loading scenarios. There are new emerging applications for capsules with open cavities, and as the designs are optimised to maximise the payload, sensitivity has to be taken into account. Concentrated loads induce singularities that propagate along the characteristics of the surfaces. Perforation patterns do not have a strong effect on internal layers. Under a symmetric concentrated loads for parabolic and hyperbolic shells there exists a critical thickness at which local features of solution begin to dominate, whereas for elliptic cases there is always a dominant global response. In non-uniform curvature cases the elliptic part will dictate the solution even if the load is not acting on it. The extensive set of simulations has been computed using high-order finite element solvers including adaptivity.

Examining the Long-Range Effect in Very Long Graphene Nanoribbons: A First-Principles Study.

The role of long-range effect on the modulation of the electronic structure of graphene nanoribbons has been little studied due to the limitations of existing theoretical and computational methods. By splitting a molecule top-down and calculating and jointing the Fock matrix of fragments, we developed a computational method suitable for large-size molecules with random doping and arbitrary geometry. Utilizing this method, we achieved the study of the effects of dopants and curvature on graphene nanoribbons (GNRs). It reveals that both dopants and curvature can change the charge distribution of GNRs, while the influence of dopants is more significant and can extend up to 1-3 nm. The electronic excitation properties of GNRs are also largely modified by the doping state or nonuniform curvature. Our findings provide not only a feasible approach for studying the electronic structure of large-size molecules but also the possibility to improve the properties of graphene-based materials by dopants and local curvature.

The bending of thin strips with a non-uniform transverse curvature

The non-linear flexural behaviour of a tape spring — whose cross section has a uniform curvature — is produced by the presence of an elastic instability. However, these are not the only structures that possess non-linear flexural behaviour. Panel-springs and bridged tape springs are examples of structures that can also produce this behaviour. Predicting the flexural behaviour of these structures is more challenging because their cross section is non-uniform. This work presents an analytical model that can predict the opposite-sense flexural behaviour of thin strips that have a non-uniform cross section. The novel attribute of this model is in the utilisation of a univariate polynomial series to describe the initial cross section of the strip. The model is applied to a range of bridged tape springs and panel-springs, with the results compared with solutions obtained from the Finite Element (FE) method. A consistent error of less than 5.5% is achieved between the analytical model and the FE model when the snap-through moment and propagation moment are compared. The analytical model is also compared with independent experimental data of the flexural behaviour of a traditional carpenter’s tape measure. An error of less than 1% and 7% of the snap-through moment and propagation moment, respectively, is achieved.

Toward FBG-Sensorized Needle Shape Prediction in Tissue Insertions.

Complex needle shape prediction remains an issue for planning of surgical interventions of flexible needles. In this paper, we validate a theoretical method for flexible needle shape prediction allowing for non-uniform curvatures, extending upon a previous sensor-based model which combines curvature measurements from fiber Bragg grating (FBG) sensors and the mechanics of an inextensible elastic rod to determine and predict the 3D needle shape during insertion. We evaluate the model's effectiveness in single-layer isotropic tissue for shape sensing and shape prediction capabilities. Experiments on a four-active area, FBG-sensorized needle were performed in varying single-layer isotropic tissues under stereo vision to provide 3D ground truth of the needle shape. The results validate a viable 3D needle shape prediction model accounting for non-uniform curvatures in flexible needles with mean needle shape sensing and prediction root-mean-square errors of 0.479 mm and 0.892 mm, respectively.

Full-scale experimental and numerical analyses of a flexible riser under combined tension-bending loading

The flexible riser top connection with floating production units presents additional tensile armour integrity assessment uncertainties associated to the bend stiffener contact interaction that leads to a non-uniform curvature and contact pressure distribution in a region of large dynamic forces and moments. In this paper, a full-scale 6″ flexible riser and bend stiffener bending-tension experimental campaign is carried out in a horizontal rig. The external tensile armour wires are instrumented with strain gauges for axial strain measurement in several riser cross-sections inside and outside the bend stiffener region. The rig assembly allows the riser rotation in order to measure strains at different circumferential angular positions. The bend stiffener polyurethane hyperelastic mechanical response is obtained by uniaxial tensile tests performed at room temperature. A nonlinear finite element model (FEM), including the riser/bend stiffener contact interaction and interlayer friction mechanisms, is employed to numerically investigate the mechanical behaviour of the flexible riser subjected to the experimental loading conditions. The FEM axial strains on the tensile armour wires are compared with the measured results for pure tension and tension-bending loads. Under axisymmetric loading a relevant experimental axial strain dispersion is observed when compared to the average values. Under tension-bending loading, the interlayer friction coefficient influences on the contact pressure and curvature distribution are initially assessed with the numerical model. The strain gauges located in the cross-sections with highest values of contact pressure and curvature are selected for a detailed numerical-experimental strains comparison. In addition, a parametric study is conducted to calibrate the friction coefficient that yields the minimum mean squared error for all measured data. Generally, good correlations are found between the experimental and numerical results.

Stabilizing a Double Gyroid Network Phase with 2 nm Feature Size by Blending of Lamellar and Cylindrical Forming Block Oligomers

Molecular dynamics simulations are used to study binary blends of an AB-type diblock and an AB2-type miktoarm triblock amphiphiles (also known as high-χ block oligomers) consisting of sugar-based (A) and hydrocarbon (B) blocks. In their pure form, the AB diblock and AB2 triblock amphiphiles self-assemble into ordered lamellar (LAM) and cylindrical (CYL) structures, respectively. At intermediate compositions, however, the AB2-rich blend (0.2 ≤ xAB ≤ 0.4) forms a double gyroid (DG) network, whereas perforated lamellae (PL) are observed in the AB-rich blend (0.5 ≤ xAB ≤ 0.8). All of the ordered mesophases present domain pitches under 3 nm, with 1 nm feature sizes for the polar domains. Structural analyses reveal that the nonuniform interfacial curvatures of DG and PL structures are supported by local composition variations of the LAM- and CYL-forming amphiphiles. Self-consistent mean field theory calculations for blends of related AB and AB2 block polymers also show the DG network at intermediate compositions, when A is the minority block, but PL is not stable. This work provides molecular-level insights into how blending of shape-filling molecular architectures enables network phase formation with extremely small feature sizes over a wide composition range.

Effects of circular and non-circular nozzle exit geometries on subsonic and supersonic jet propagations

The mixing enhancement and core length reduction of a jet without significant loss of thrust are essential for reducing infrared radiation, mitigating aeroacoustic noise, improving combustion characteristics, and thrust vectoring. The jet mixing can be improved by manipulating the flow behavior. In subsonic and sonic jets, the flow manipulation may be achieved by utilizing nozzles with non-circular geometries that shed vortices of varying size due to their non-uniform azimuth curvatures. Non-uniform vortices generate differential spreading along the nozzle’s perimeter, causing axis switching and improving entrainment characteristics. Therefore, the present study examines the effects of two non-circular nozzle exit shapes (elliptic and square) on the mixing augmenting efficacy at subsonic and sonic flow conditions. The circular nozzle is tested for comparison. Both quantitative and qualitative analyses evaluate the efficacy of nozzles with non-circular exit geometries. Among the configurations investigated, the elliptic nozzle is superior in shortening the potential core length and enhancing the jet spread. A maximum reduction of 18.75% in core length with rapid jet decay was accomplished with the elliptic nozzle. The measurement of pressure profiles at different streamwise locations reveals that the spread rate is greater for elliptic and square jets than their circular counterpart. The elliptic jet exhibits the highest spread along the minor-axis direction compared to the major-axis direction. The differential jet spread rate in the elliptical jet causes an early axis-switching––direct evidence of mixing augmentation. Shadowgraph images show the asymmetric pattern of shock cell structures and differential spreading in elliptic and square jets.

Control Mechanism of Particle Flow in the Weak Liquid Metal Flow Field on Non-Uniform Curvature Surface Based on Lippmann Model

In order to realize the uniform distribution in the abrasive flow polishing of the titanium alloy workpiece with curved surface, a novel method based on the liquid metal-abrasive flow machining technology is proposed in this study. Based on the SST k-ω model, Preston model and fluid flow particle tracking model, the COMSOL software is employed to study the dynamic characteristics of liquid metal-abrasive flow under different AC electric field conditions, and the two-phase flow field is used to simulate the liquid state, the movement of liquid metal particles on the surface of the workpiece and the varitation of the Pv value in the near-wall region. It is found from numerical simulation results that the average Pv value in the strong flow field is 23,718.8 W/m2, and that in the weak flow field is 5,427.3 W/m2. By the assistance of the electric filed with the voltage of AC 36 V, the average Pv value of the liquid metal particles in the weak flow field is found to be 10,948.6 W/m2 with an increase of 101.7%. Therefore, to properly control the electric field strength, the movement of liquid metal in the flow field can be found to be controlled, and hence improving the uniformity of the turbulent kinetic energy on the workpiece surface and improving the processing quality.

A new method for high resolution curvature measurement applied to stress monitoring in thin films

By combining the well-known grid reflection method with a digital image correlation algorithm and a geometrical optics model, a new method is proposed for measuring the change of curvature of a smooth reflecting substrate, a common reporter of stress state of deposited layers. This tool, called Pattern Reflection for Mapping of Curvature (PReMC), can be easily implemented for the analysis of the residual stress during deposition processes and is sufficiently accurate to follow the compressive-tensile-compressive stress transition during the sputtering growth of a Ag film on a Si substrate. Unprecedented resolution below 10−5 m−1 can be reached when measuring a homogeneous curvature. A comparison with the conventional laser-based tool is also provided in terms of dynamical range and resolution. In addition, the method is capable of mapping local variations in the case of a non-uniform curvature as illustrated by the case of a Mo film of non-uniform film thickness under high compressive stress. PReMC offers interesting perspectives for in situ accurate stress monitoring in the field of thin film growth.

Stress concentration effect on deflection and stress fields of a master leaf spring through domain decomposition and geometry updation technique

Abstract Theoretical and experimental large deflection and stress analysis of a master leaf spring considering stress concentration effect of clamping is reported. The non-uniformly curved master leaf spring under three point bending subjected to moving boundaries is modeled. Geometrically nonlinear strain-displacement relations, as necessary for the theoretical analysis, are derived through visualization of physics behind the large deformation problem. An embedded curvilinear coordinate system is considered, to study the combined effects of non-uniform curvature, bending, stretching and shear deformation including cross-sectional warping. Governing equation of the non-uniformly curved beam system is derived in variational form using energy method, based on linear material constitutive relations and the derived nonlinear kinematic relations. An iterative solution scheme through successive geometry updation is developed and executed in MATLAB® software to solve the governing equation involving strong geometric nonlinearity together with complicating moving boundary effect. Experimental deflection profiles under static loading are obtained through manual image processing technique using AutoCAD® software. Whereas, strain measurements are performed using strain gauges with data acquisition system (HBM-MX840B). Comparison between the theoretical and experimental results lead towards observation on stress concentration effect due to presence of geometric discontinuity in form of a small hole in the physical system. A modified formulation is proposed using domain decomposition method incorporating effect of geometric discontinuity through an equivalent curved beam geometry of variable cross-section. The modified theoretical model is validated successfully with the experimental results, and observations on stress characteristics and effect of hole diameter to beam width ratio are made.