Bending Energy Research Articles

Enhanced seismic performance: A novel cable brace with bending energy dissipation for semi-rigid steel frames

Ordinary braces upon experiencing compressive buckling, reach a fully plastic state, rendering them ineffective against further seismic action. Moreover, their post-earthquake repair and reinforcement pose significant challenges. Addressing these issues, this research introduces an innovative lateral force-resisting element: the bending energy dissipation-cable brace. This novel design utilizes steel cables in a unique tension-only arrangement, effectively dissipating seismic energy by inducing bending in a steel plate. A semi-rigid steel frame was constructed, incorporating two variations of the cable brace, differentiated by the thickness of their energy-dissipating frames. These were subjected to quasi-static cyclic loading tests to evaluate their hysteretic behavior, deformation pattern, load-bearing capacity decay, and energy dissipation capacity. The experimental results reveal the superior seismic performance of the bending energy dissipation-cable brace, evidenced by a 22 % enhancement in energy dissipation and a 38 % increase in stiffness when the thickness of the energy-dissipating frame is doubled. These results offer a promising solution to the current limitations in energy dissipation and difficulty of application of the combined brace of steel cable and bending yielding energy dissipation devices.

Calibration of binding energy and clarification of interfacial band bending for the Al2O3/diamond heterojunction

Due to the presence of an intrinsic C 1s peak in diamond, it is impossible to calibrate its binding energies using the adventitious C 1s peak (284.8 eV) during x-ray photoelectron spectroscopy measurement. The absence of accurate binding energy measurement makes it challenging to determine the interfacial band bending for the oxide/diamond heterojunction. To overcome this issue, a net-patterned gold (Au) mask is applied to the boron-doped diamond (B-diamond) to suppress the charge-up effect and calibrate the binding energy using the standard Au 4f peak (83.96 eV). The B-diamond epitaxial layer shows downward band bending toward the surface with a valence band maximum of 0.85 eV. Upon the formation of Al2O3 using an ozone precursor through the atomic layer deposition technique, the B-diamond continues to exhibit downward band bending toward the Al2O3/B-diamond interface. However, the bending energy has reduced, potentially attributed to the modification of the oxygen vacancies on the B-diamond surface by the ozone precursor during the Al2O3 deposition.

Modeling of textile composite using analytical network-averaging and gradient damage approach

In this contribution, we present a gradient damage model for anisotropic textile reinforcements including fiber inextensibility and fiber sliding. In contrast to previous works, the gradient damage formulation stems not from a numerical regularization basis but from the thermodynamics of internal variables. It results in a nonlocal term as the internal energy of fiber bending with measurable nonlocal parameter. Furthermore, to guarantee a priori that rotations and reflections determined by orthogonal tensors among the symmetry group do not affect the response function of the anisotropic constitutive law, a novel mesoscopic kinematic measure for the representative volume element of the fabric is defined on the basis of the analytical network-averaging concept. Such kinematic measure is of crucial importance for material modeling of damage-elastoplasticity in anisotropic textile reinforcements, and allows for analytical descriptions of inter- and intra-ply sliding of fibers. A mixed finite element formulation is then presented for textile reinforcements taking into account fiber inextensibility. The predictive capability of the computational model is demonstrated by comparing with multiple experimental datasets of dry textile fabrics.

Derivation of an effective plate theory for parallelogram origami from bar and hinge elasticity

Periodic origami patterns made with repeating unit cells of creases and panels bend and twist in complex ways. In principle, such soft modes of deformation admit a simplified asymptotic description in the limit of a large number of cells. Starting from a bar and hinge model for the elastic energy of a generic four parallelogram panel origami pattern, we derive a complete set of geometric compatibility conditions identifying the pattern’s soft modes in this limit. The compatibility equations form a system of partial differential equations constraining the actuation of the origami’s creases (a scalar angle field) and the relative rotations of its unit cells (a pair of skew tensor fields). We show that every solution of the compatibility equations is the limit of a sequence of soft modes — origami deformations with finite bending energy and negligible stretching. Using these sequences, we derive a plate-like theory for parallelogram origami patterns with an explicit coarse-grained quadratic energy depending on the gradient of the crease-actuation and the relative rotations of the cells. Finally, we illustrate our theory in the context of two well-known origami designs: the Miura and Eggbox patterns. Though these patterns are distinguished in their anticlastic and synclastic bending responses, they show a universal twisting response. General soft modes captured by our theory involve a rich nonlinear interplay between actuation, bending and twisting, determined by the underlying crease geometry.

Membrane curvature sensing and symmetry breaking of the M2 proton channel from Influenza A.

The M2 proton channel aids in the exit of mature influenza viral particles from the host plasma membrane through its ability to stabilize regions of high negative Gaussian curvature (NGC) that occur at the neck of budding virions. The channels are homo-tetramers that contain a cytoplasm-facing amphipathic helix (AH) that is necessary and sufficient for NGC generation; however, constructs containing the transmembrane spanning helix, which facilitates tetramerization, exhibit enhanced curvature generation. Here, we used all-atom molecular dynamics (MD) simulations to explore the conformational dynamics of M2 channels in lipid bilayers revealing that the AH is dynamic, quickly breaking the fourfold symmetry observed in most structures. Next, we carried out MD simulations with the protein restrained in four- and twofold symmetric conformations to determine the impact on the membrane shape. While each pattern was distinct, all configurations induced pronounced curvature in the outer leaflet, while conversely, the inner leaflets showed minimal curvature and significant lipid tilt around the AHs. The MD-generated profiles at the protein-membrane interface were then extracted and used as boundary conditions in a continuum elastic membrane model to calculate the membrane-bending energy of each conformation embedded in different membrane surfaces characteristic of a budding virus. The calculations show that all three M2 conformations are stabilized in inward-budding, concave spherical caps and destabilized in outward-budding, convex spherical caps, the latter reminiscent of a budding virus. One of the C2-broken symmetry conformations is stabilized by 4 kT in NGC surfaces with the minimum energy conformation occurring at a curvature corresponding to 33 nm radii. In total, our work provides atomistic insight into the curvature sensing capabilities of M2 channels and how enrichment in the nascent viral particle depends on protein shape and membrane geometry.

Geometric frustration and pairing-order transition in confined bacterial vortices

Dense systems of active matter exhibit highly dynamic collective motion characterized by intermingled vortices, referred to as active turbulence. The interaction between these vortices is key to controlling turbulent dynamics, and a promising approach for revealing the rules governing their interaction is geometric confinement. In this study, we investigate the vortex-pairing patterns in confined bacterial suspensions as a model frustrated system in which a perfect antiferromagnetic state is prohibited. We find that three-body vortex interactions exhibit anomalous pairing-order transition from corotational vortex pairing to counterrotating patterns with frustration. Although an active matter system is in nonequilibrium, our theory based on bending energy accounts for significant features, including pattern transition and a shift of the transition point in frustrated systems. Moreover, the interplay between the chirality in collective motion and frustration in vortex pairing creates a collective rotational flow under the broad geometric conditions of a confined space. Our results show that frustrated vortex patterning promotes a geometric approach for arranging active turbulence in microfluidic systems. Published by the American Physical Society 2024

Mathematical analysis of a mesoscale model for multiphase membranes

AbstractIn this article, we introduce a mesoscale continuum model for membranes made of two different types of amphiphilic lipids. The model extends work by Peletier and the second author (Arch. Ration. Mech. Anal. 193, 2009) for the one‐phase case. We present a mathematical analysis of the asymptotic reduction to the macroscale when a key length parameter becomes arbitrarily small. We identify two main contributions in the energy: one that can be connected to bending of the overall structure and a second that describes the cost of the internal phase separations. We prove the ‐convergence towards a perimeter functional for the phase separation energy and construct, in two dimensions, recovery sequences for the convergence of the full energy towards a 2D reduction of the Jülicher–Lipowsky bending energy with a line tension contribution for phase separated hypersurfaces.

Conformational Transition of Semiflexible Ring Polyelectrolyte in Tetravalent Salt Solutions: A Simple Numerical Modeling without the Effect of Twisting.

In this work, the conformational behaviors of ring polyelectrolyte in tetravalent salt solutions are discussed in detail through molecular dynamics simulation. For simplification, here we have neglected the effect of the twisting interaction, although it has been well known that both bending and twisting interactions play a deterministic in the steric conformation of a semiflexible ring polymer. The salt concentration CS and the bending energy b take a decisive role in the conformation of the ring polyelectrolyte (PE). Throughout our calculations, the b varies from b = 0 (freely joint chain) to b = 120. The salt concentration CS changes in the range of 3.56 × 10-4 M ≤ CS ≤ 2.49 × 10-1 M. Upon the addition of salt, ring PE contracts at first, subsequently re-expands. More abundant conformations are observed for a semiflexible ring PE. For b = 10, the conformation of semiflexible ring PE shifts from the loop to two-racquet-head spindle, then it condenses into toroid, finally arranges into coil with the increase of CS. As b increases further, four phase transitions are observed. The latter two phase transitions are different. The semiflexible ring PE experiences transformation from toroid to two racquet head spindle, finally to loop in the latter two phase transitions. Its conformation is determined by the competition among the bending energy, cation-bridge, and entropy. Combined, our findings indicate that the conformations of semiflexible ring PE can be controlled by changing the salt concentration and chain stiffness.

Optimization of cable-stayed force for asymmetric single tower cable-stayed bridge formation based on improved particle swarm algorithm

PurposeThis paper aims to optimize cable-stayed force in asymmetric one-tower cable-stayed bridge formation using an improved particle swarm algorithm. It compares results with the traditional unconstrained minimum bending energy method.Design/methodology/approachThis paper proposes an improved particle swarm algorithm to optimize cable-stayed force in bridge formation. It formulates a quadratic programming mathematical model considering the sum of bending energies of the main girder and bridge tower as the objective function. Constraints include displacements, stresses, cable-stayed force, and uniformity. The algorithm is applied to optimize the formation of an asymmetrical single-tower cable-stayed bridge, combining it with the finite element method.FindingsThe study’s findings reveal significant improvements over the minimum bending energy method. Results show that the structural displacement and internal force are within constraints, the maximum bending moment of the main girder decreases, resulting in smoother linear shape and more even internal force distribution. Additionally, the tower top offset decreases, and the bending moment change at the tower-beam junction is reduced. Moreover, diagonal cable force and cable force increase uniformly with cable length growth.Originality/valueThe improved particle swarm algorithm offers simplicity, effectiveness, and practicality in optimizing bridge-forming cable-staying force. It eliminates the need for arbitrary manual cable adjustments seen in traditional methods and effectively addresses the optimization challenge in asymmetric cable-stayed bridges.

Bending performance and failure mechanism of CFRP/Al hat-shaped thin-walled hybrid beams

Hat-shaped beams played an important role in the body load-bearing structure, such as B-pillar. Fiber metal laminates possessed great advantages of excellent stiffness/strength, high damage tolerance and lightweight effect. In order to improve the catastrophic damage mode of carbon fiber, the hat-shape thin-walled hybrid beams consisting of carbon fiber reinforced thermoplastic (CFRP) prepreg and aluminum (Al) sheet were proposed and fabricated by hot-pressing molding. The effects of carbon fiber layer numbers, CFRP/Al stacking sequence, and the CFRP layup orientation on the three-point bending performance and failure mode of the hat-shaped hybrid beams were investigated. The results showed that the more CFRP layer, the better the bending performance of the hybrid hat-shaped beams. The CA-2 hat-shaped beams generated overall lateral deformation. The ACA (Al/CFRP/Al) hat-shaped beams achieved a higher CFE (ratio of average load to peak force) value and better energy absorption effect. The deformation processes of AC (Al/CFRP) and ACA stacking structures was similar, the horizontal web concave and the side walls on both sides convex. In terms of fiber lay-up orientation, ACA-OR (orthogonal) possessed superior bending performance and energy absorption to the ACA-UD (unidirectional) hybrid beams. Furthermore, the failure mechanism of the ACA hybrid beams was analyzed and the cross-sectional microstructure at different sections were observed by SEM. Matrix cracking, interfacial delamination, fiber fracture and metal plastic deformation were detected, which played a supporting effect and energy absorption role.

Comparative study on the impact behaviors of CFWST columns reinforced with steel spiral and tube

To obtain superior corrosion resistance and impact resistance, as well as good economic benefits, two new types of composite structure called as steel tube internally-reinforced concrete-filled weathering steel tube (STRCFWST) and steel spiral internally-reinforced concrete-filled weathering steel (SSRCFWST) columns are proposed and compared in terms of their impact resistance in this paper. Eleven impact tests were conducted and three parameters comprising steel spiral diameter, wall thicknesses of outer and inner steel tube were considered to evaluate their influences on the lateral impact behaviors. Results show the presence of inner steel tube and reinforcement cage significantly enhances the impact resistance while slightly decreases the energy absorption capacity. Increasing inner steel tube wall thickness helps to improve the impact resistance, however the contribution is not so good as that produced by increasing the outer steel tube wall thickness, whilst varying steel spiral diameter almost has no impact. Numerical models were developed by ABAQUS/Explicit and verified via the test, based on which the full-range behaviors of STRCFWST, SSRCFWST and unreinforced concrete-filled weathering steel tube (CFWST) columns under impact loading were compared and discussed. It is demonstrated that steel tube and reinforcement cage provide little confinement on concrete infill under impact. With the same internal steel ratio, inner steel tube makes a greater contribution to sectional bending moment resistance and energy absorption as compared to the reinforcement cage.

Prediction of concrete cracking behavior under different strain rates based on the boundary effects model

Predicting the cracking behavior of concrete under different strain rates through fracture parameters has been a longstanding topic of interest. In this study, the effect of concrete strength and strain rate on the fracture toughness and initial fracture energy for three-point bending notched beams is investigated by boundary effect model (BEM). With the help of BEM, only a series of basic parameters (such as tensile strength, maximum aggregate size and specimen size) are used in the process of calculating the fracture toughness and initial fracture energy. The cumbersome concrete fracture experiment is avoided in this model. The initial fracture toughness and unstable fracture toughness, predicted by BEM are agreed with the experimental results in the literature. The results demonstrate that BEM is valid for predicting the fracture toughness of different concrete strengths, even at increased strain rates. As the loading strain rate increases, the initial fracture toughness of different concrete strength shows a slight growth with increasing loading strain rate, which indicates that the concrete needs more energy to reach the cracking condition.

Generalized thermoelastic damping in micro/nano-ring resonators undergoing out-of-plane vibration

Micro/nano-ring or ring-based resonators are popular core components of sensors and actuators. Accurately predicting the quality factor (Q) based on thermoelastic damping (TED) is intensively crucial for designing high-performance micro/nano-ring resonators. In this work, adopting the modified-couple-stress (MCS) and nonlocal-dual-phase-lagging (NDPL) models, analytical TED expressions are developed for circular cross-section micro/nano-rings undergoing out-of-plane vibration for the first time. Multiple effects are considered in the modeling procedure, which are size-dependence effects in the mechanical and thermal fields, the non-Fourier effect of heat conduction, and three-dimensional temperature gradients in the circumferential, radial, and tangential directions. Therefore, the proposed TED models are more comprehensive compared to existing TED models. The coefficients (CC and CM) associated with the out-of-plane vibration mode are examined from an energy-ratio perspective. Moreover, the investigation is focused on the impacts of the MCS and NDPL non-Fourier effects on the fluctuation temperature and TED spectra. The results indicate as CC and CM approach one, the bending energy emerges as the predominant component of the stored energy. Notably, the NDPL non-Fourier effect significantly affects the fluctuation temperature within the ring operated in high-order modes. In special, the distributions of fluctuation temperature in the circumferential direction exhibit periodic patterns that are closely correlated with the modal order. Furthermore, TED can be suppressed by the MCS size-dependence effect. Meanwhile, the behavior of TED at high frequencies is simultaneously determined by the dimension of heat conduction, phase-lagging times, and nonlocal thermal-length parameter.

Evaluating gloved hand performance based on the mechanical properties of the applied material

The hands are the most complex organs of the body for performing various activities. Therefore, it is critical to protect them against dangers. Protective gloves can reduce or prevent injuries, but they can downgrade hand performance in various aspects, including tactile sensitivity, strength, grip force and hand dexterity. In this study, eight protective gloves with different designs and materials were made. The study investigated the influence of the number of layers and several characteristics, e.g., mass per square meter, thickness, bending stiffness and compressibility, on the gloved hand performance regarding protection ability, tactile sensitivity, strength capability and manual dexterity. The results indicated that despite the improving effects of increasing layer thickness, weight, bending energy and compressibility on protection ability, the gloves diminish tactile sensitivity, grip and pinch force, and manual dexterity. Therefore, it is necessary to select an optimum design to ensure a satisfactory trade-off between protection and performance.

Relationship Between Advanced Footwear Technology Longitudinal Bending Stiffness and Energy Cost of Running.

Shoe longitudinal bending stiffness (LBS) is often considered to influence running economy (RE) and thus, running performance. However, previous results are mixed and LBS levels have not been studied in advanced footwear technology (AFT). The purpose of this study was to evaluate the effects of increased LBS from curved carbon fiber plates embedded within an AFT midsole compared to a traditional running shoe on RE and spatiotemporal parameters. Twenty-one male trained runners completed three times 4 min at 13 km/h with two experimental shoe models with a curved carbon fiber plate embedded in an AFT midsole with different LBS values (Stiff: 35.5 N/mm and Stiffest: 43.1 N/mm), and a Control condition (no carbon fiber plate: 20.1 N/mm). We measured energy cost of running (W/kg) and spatiotemporal parameters in one visit. RE improved for the Stiff shoe condition (15.71 ± 0.95 W/kg; p < 0.001; n2 = 0.374) compared to the Control condition (16.13 ± 1.08 W/kg; 2.56%) and Stiffest condition (16.03 ± 1.19 W/kg; 1.98%). However, we found no significant differences between the Stiffest and Control conditions. Moreover, there were no spatiotemporal differences between shoe conditions. Changes in LBS in AFT influences RE suggesting that moderately stiff shoes have the most effective LBS to improve RE in AFT compared to very stiff shoes and traditional, flexible shoe conditions while running at 13 km/h.

Existence of Optimal Flat Ribbons

We apply the direct method of the calculus of variations to show that any nonplanar Frenet curve in R3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {R}}^{3}$$\\end{document} can be extended to an infinitely narrow flat ribbon having minimal bending energy. We also show that, in general, minimizers are not free of planar points, yet such points must be isolated under the mild condition that the torsion does not vanish.

Novel triply periodic minimal surfaces sandwich structures: Mechanical performance and failure analysis

AbstractSandwich structures are known for their exceptional mechanical properties and widespread applications. This study integrates additive manufacturing (AM) technology, experiments, theoretical equations, and numerical simulations to investigate a novel lightweight sandwich structure with a core based on Triply Periodic Minimal Surfaces (TPMS). The core incorporates Primitive, Neovius, and Diamond structures and is designed and manufactured using AM. Three‐point bending experiments are conducted to assess bending performance, failure modes, and energy absorption capability. A numerical model is established to analyze behavior under bending loads, validated through comparison with theoretical equations and numerical simulations, focusing on stress concentration areas. A parametric study investigates the effects of skin material, thickness, and TPMS core relative density on bending performance and energy absorption capacity. Furthermore, a functionally graded core layer with a gradient change in relative density is designed to study its influence on bending performance. The parameters of the core have a decisive impact on TPMS sandwich panel performance. This study demonstrates that sandwich structures with TPMS cores can be designed to possess desirable bending performance and energy absorption capacity, providing insights for future engineering applications.Highlights A novel TPMS sandwich structure is fabricated using 3D printing technology. The gradient relative density core is introduced. The bending performance and failure behavior of the structure are evaluated. A parametric study was conducted to investigate the effects on performance.

A beam that can only bend on the Cantor set

In this work, we address the following question: Is it possible for a one‐dimensional, linearly elastic beam to only bend on the Cantor set and, if so, what would the bending energy of such a beam look like? We answer this question by considering a sequence of beams, indexed by , each one only able to bend on the set associated with the ‐th step in the construction of the Cantor set and compute the ‐limit of the bending energies. The resulting energy in the limit has a structure similar to the traditional bending energy, a key difference being that the measure used for the integration is the Hausdorff measure of dimension , which is the dimension of the Cantor set.

Patterning of multicomponent elastic shells by gaussian curvature.

Recent findings suggest that shell protein distribution and the morphology of bacterial microcompartments regulate the chemical fluxes facilitating reactions which dictate their biological function. We explore how the morphology and component patterning are coupled through the competition of mean and gaussian bending energies in multicomponent elastic shells that form three-component irregular polyhedra. We observe two softer components with lower bending rigidities allocated on the edges and vertices while the harder component occupies the faces. When subjected to a nonzero interfacial line tension, the two softer components further separate and pattern into subdomains that are mediated by the gaussian curvature. We find that this degree of fractionation is maximized when there is a weaker line tension and when the ratio of bending rigidities between the two softer domains ≈2. Our results reveal a patterning mechanism in multicomponent shells that can capture the observed morphologies of bacterial microcompartments, and moreover, can be realized in synthetic vesicles.

Γ-convergence of a discrete Kirchhoff rod energy

This work is motivated by the classical discrete elastic rod model by Audoly et al. We derive a discrete version of the Kirchhoff elastic energy for rods undergoing bending and torsion and prove Γ-convergence to the continuous model. This discrete energy is given by the bending and torsion energy of an interpolating conforming polynomial curve and provides a simple formula for the bending energy depending in each discrete segment only on angle and adjacent edge lengths. For the liminf-inequality, we need to introduce penalty terms to ensure arc-length parametrization in the limit. For the recovery sequence a discretization with equal Euclidean distance between consecutive points is constructed. Particular care is taken to treat the interaction between bending and torsion by employing a discrete version of the Bishop frame.