Flexural Rigidity Research Articles

This study investigates the scattering of oblique waves by a submerged rigid block and a floating elastic plate. The plate is positioned at a defined distance from the rigid block and experiences localized forcing. Three edge conditions, free, simply supported, and built-in, are considered for the plate. The fluid domain is divided into sub-regions, and the Eigenfunction expansion matching method is employed to determine the velocity potential in each region. Numerical results are specifically presented for the built-in edge condition, examining the effects of wave, rigid block, plate, and fluid parameters. The results indicate that at smaller angles of incidence, a taller rigid block produces higher reflections. Reflection is also pronounced when there is no gap between the rigid block and the plate. Over time, a significant reduction in the amplitude of free surface deflection is observed. Additionally, the angle of incidence, flexural rigidity, and fluid depth play a crucial role in determining the amplitude of the deflection of the plate in the time domain.

Abstract This study presents the production of photothermal composite capsules using a newly developed method and their application to cotton fabric for the design of a fabric that exhibits both thermoregulation and UV protection properties. In this study, an environmentally friendly approach was adopted in the production of photothermal capsules and unlike the existing methods in the literature, the Pickering emulsion system was integrated into the complex coacervation method. The phase change material, a eutectic mixture of lauric acid and stearic acid, was encapsulated within a sodium alginate/copper (II) oxide (CuO) wall in three different ratios (1/0.5, 1/1 and 1/1.5). In microencapsulation, CuO nanoparticles were used as photothermal material both as Pickering stabilizers and wall structure polymer. Microcapsules with spherical morphology were found to store heat in the range of 99.1–118.7 J/g and have good thermal reliability. The photothermal performance of the capsules improved in direct proportion to the amount of CuO nanoparticles in the wall structure and the highest photothermal efficiency value with 96.97% efficiency was obtained in capsules with 1/1.5 S/CuO wall structure. Microcapsules with 1/1.5 S/CuO wall structure were fixed to cotton fabric at two different concentrations via the exhaustion method. The fabrics exhibited photothermal properties, reaching temperatures 5 °C higher than the untreated fabric during the same time period. The S/CuO walled microcapsules significantly improved the thermal conductivity of the fabrics. Besides, fabrics exhibited good UV protection with a 15 UPF value. In contrast, the bending rigidity and tear strength of the fabric were affected by the capsule application.

On the coupling between membrane bending and stretching in lipid vesicles.

ABSTRACTThe mechanical properties of Pickering layers are crucial for stabilizing Pickering emulsions by resisting coalescence and deformation under mechanical stress. Despite the importance of mechanical properties in determining emulsion stability and functionality, these properties remain poorly understood in general. This study examines the buckling behavior and mechanical stability of Pickering layers made from 5 µm polystyrene beads (PBs) and clay particles (CPs) at the air–water interface. Controlled mechanical stresses were applied using a Langmuir trough (LT) and a magnetic force setup (MFS) to analyze response under compression. PB monolayers showed buckling at a range from 40 to 70 mN/m. Partial elastic recovery upon release of compression force was observed only in the LT, presumably due to boundary conditions. CP layers resisted compression through particle overlap and exhibited no buckling or elastic recovery, showing permanent deformation measured from 55 to 350 mN/m. A key contribution of this work is a novel method for measuring bending rigidity (BR) in Pickering layers. The results obtained from both experimental setups are remarkably consistent, revealing BR values higher than previous theoretical predictions. Additionally, the experimental buckling wavelength is found to be smaller than the predicted theoretical value.Practical Applications: This research supports the development of advanced materials with tailored mechanical properties, enabling applications like stabilizing emulsions and creating robust, responsive interfacial films. It also opens new opportunities for designing smart coatings that adapt to mechanical stress. For example, depending on environmental conditions, Pickering layers could be used in sensors and protective surfaces that require stability or flexibility. The insights into the mechanical properties of clay‐based Pickering layers and the resistance to deformations extend to cosmetics, where clays like kaolin and bentonite are valued for their absorbent and soothing properties, improving the design of stable and effective formulations like face masks and creams. Additionally, these findings could benefit industries requiring high‐pressure stability, such as environmental remediation, by enhancing the development of robust and durable materials. The novel method for quantifying BR also has potential for material characterization, aiding in the development of new particle‐stabilized systems for pharmaceuticals, cosmetics, or food science, where precise control of interfacial properties is crucial.

Abstract Nanomechanical devices made from ultrathin materials are transforming diverse fields, including sensing, signal processing, and quantum technologies. However, as these materials become thinner, their low bending rigidity poses significant fabrication challenges, and achieving nanometer-thick flat cantilevers with consistent and predictable mechanical responses has remained elusive despite decades of research. Here we present nanometer-thick, ultraflat cantilever resonators fabricated using atomic layer deposition. By effectively mitigating the effects of uncontrollable built-in strain and geometric disorder, the ultraflat nanocantilevers exhibit resonance frequencies closely aligned with thin-plate theory predictions and display low sample-to-sample variability. These cantilevers maintain mechanical stability in both vacuum and air environments, even at large length-to-thickness ratios of up to 3000. The ultraflat nanocantilevers are approaching the thickness limit, beyond which thermal fluctuations at room temperature can spontaneously induce random ripples in otherwise flat films.

Organelles such as mitochondria have characteristic shapes that are critical to their function. Recent efforts have revealed that the curvature contributions of individual lipid species can be a factor in the generation of membrane shape in these organelles. Inspired by lipidomics data from yeast mitochondrial membranes, we used Martini coarse-grained molecular dynamics simulations to investigate how lipid composition facilitates membrane shaping. We found that increasing lipid saturation increases bending rigidity while reducing the monolayer spontaneous curvature. We also found that systems containing cardiolipin exhibited decreased bending rigidity and increased spontaneous curvature when compared to bilayers containing its precursor phosphatidylglycerol. This finding contradicts some prior experimental results that suggest that bilayers containing tetraoleoyl cardiolipin have greater rigidity than dioleoyl phosphatidylcholine bilayers. To investigate this discrepancy, we analyzed our simulations for correlations between lipid localization and local curvature. We found that there are transient correlations between curved lipids such as cardiolipin (CDL) and phosphatidylethanolamine (PE) and curvature; these interactions enrich specific bilayer undulatory modes and cause bilayer softening. Furthermore, we show that curvature-localization some lipids such as cardiolipin can influence lipids in the opposing leaflet. These observations add to the emerging evidence that lipid geometric features give rise to local interactions, which can cause membrane compositional heterogeneities. The cross-talk between composition-driven tuning of membrane properties and membrane shape has implications for membrane organization and its related functions.

We present the structural and dynamical behavior of an active polar filament that is pushing a load using overdamped Langevin dynamics simulations. By varying the bending rigidity and the connectivity between the filament and the load, we smoothly transition the boundary condition of the filament from pivoted to clamped. In the clamped state, the load remains strongly aligned with the filament, whereas in the pivoted state, the load is free to rotate at its attachment point. Under the pivoted boundary condition, the active polar filament buckles and exhibits various fascinating dynamical phases, including snake-like motion, rotational motion, and helical conformations. However, under the clamped boundary condition, the helical phase disappears, and the filament attains either an extended or a bent conformation. The transition from the extended state to the helical phase is characterized using a global helical order parameter in the parameter space of active force and a physical quantity associated with the boundary condition. We have obtained various power laws relating the curvature radius of the helical phase, effective diffusivity, and rotational motion of the monomers to the active force. Furthermore, we demonstrate that the filament’s effective diffusivity in the helical phase exhibits a non-monotonic dependence on the active force: it initially increases linearly but decreases sharply at high active force strengths.

The flow-induced oscillations of a clamped flexible ring in a uniform flow were explored using the penalty immersed boundary method. Both inverted and conventional ring configurations were examined, with systematic analysis focused on the effects of bending rigidity and eccentricity. Four distinct oscillation modes were identified across parameter variations: flapping (F), deflected oscillation (DO), transverse oscillation (TO) and equilibrium (E) modes. Each mode exhibited a 2S wake pattern. The inverted ring sustained the DO mode under low bending rigidity with a deflected shape, transitioning to the TO mode at higher bending rigidity. In the TO mode, a lock-in phenomenon emerged, enabling the inverted ring to achieve a high power coefficient due to a simultaneous rise in both oscillation amplitude and frequency. By contrast, the conventional ring exhibited the F mode at low bending rigidity and transitioned to the E mode as rigidity increased, although its power coefficient remained lower because of reduced critical bending rigidity. For the inverted ring, low eccentricity enhanced oscillation intensity but limited the operational range of the TO mode. In contrast, for the conventional ring, reducing eccentricity led to an increase in oscillation amplitude. Among the investigated configurations, the inverted-clamped ring achieved the highest energy-harvesting efficiency, surpassing those of the conventional clamped ring and a buckled filament.

This study evaluates the formability of warp-knitted fabrics using polyester yarns of varying counts by investigating the effect of fabric structure, fabric side, and applied tension using a dimensionless index based on surface strain. The results indicate that tricot structures with 150-denier yarn exhibit approximately a 20% improvement in formability, due to lower bending rigidity. In contrast, the four-needle satin structure with high-tenacity 500-denier yarn shows about a 33% improvement in formability. Although higher bending rigidity generally reduces formability, the increased fabric thickness and induced tension from high-tenacity yarns facilitate yarn movement during forming, reducing wrinkling, and enhancing conformability. Also, applying tension during the forming process significantly reduces fabric consumption and wrinkle formation, thereby enhancing formability quality. These findings emphasize the importance of selecting appropriate fabric structures, yarn properties, and forming conditions to optimize warp-knitted fabric formability performance for applications such as sportswear, medical textiles, composites, and advanced manufacturing.

Approximating the stiffness of biological materials can give important insights into how structures deform and when they may fail. Some samples may be too precious to test to destruction, or too fine to position accurately for conventional material testing, which makes it challenging to obtain approximations of material stiffness. Using two‐dimensional scans, non‐destructive bending tests, and finite element (FE) modeling, we show that we can approximate the modulus of elasticity of samples by fitting FE model data to that of experimental bend tests. We demonstrate our protocol on representative whiskers from three species of Carnivorans, including a terrestrial red fox, semi‐aquatic Eurasian otter, and aquatic phocid grey seal. Grey seal whiskers had the highest approximated modulus of elasticity (0.5–19 GPa), followed by Eurasian otter (0.5–13 GPa) and red fox (0.1–1.5 GPa). We suggest that, as in many other biological structures, adaptations in both the shape and material stiffness of the whisker contribute to how it bends when loaded. Specifically, a larger base radius and higher material stiffness both act to increase whisker flexural rigidity in the aquatic grey seal. This protocol has broad applications in comparative biology and provides a way to determine shape and material stiffness information for various flexible specimen types.

The main focus of the study is to produce the natural, environmentally friendly and biodegradable polymeric shell-structured thermochromic microcapsules for textile applications. Three-component thermochromic system (TCTS) which consists of crystal violet lactone dye, phenolphthalein and 1-tetradecanol was microencapsulated into gelatin/gum arabic (G/GA) by complex coacervation method. Sodium dodecyl sulfate (SDS) and cetyl trimethyl ammonium bromide (CTAB) were used as surfactants with different ionic character. In the study, the effect of core and wall material ratio, and ionic character of the surfactant on morphology and thermochromic properties of microcapsules was also investigated. The microcapsules with spherical morphology produced in the study had a melting enthalpy ranging from 57.4 to 129.2 J/g and good thermal stability. The CTAB allowed better capsule formation with a spherical morphology and excellent thermochromic performance compared to SDS surfactant. It was determined that decreasing amount of wall polymer made the color change more pronounced, but did not significantly affect morphology. Microcapsules with core/shell of 1/0.5 ratio that offered the most pronounced color change were applied to cotton fabrics by impregnation method. The color measurements based on CIELab system confirmed the reversible color change of the composite fabric from blue to colorless. The fabrics exhibited antibacterial activity (99.49% bacterial decrease) besides the thermochromic and thermoregulating properties. However, the water vapour permeability of the fabrics decreased despite the increased hydrophilicity. Microcapsule application significantly affected air permeability, the bending rigidity and warp tear strength of the fabric.

The huge variety of microorganisms motivates fundamental studies of their behaviour with the possibility to construct artificial mimics. A prominent example is the Escherichia coli bacterium, which employs several helical flagella to exhibit a motility pattern that alternates between run (directional swimming) and tumble (change in swimming direction) phases. We establish a detailed E. coli model, coupled to fluid flow described by the dissipative particle dynamics method, and investigate its run-and-tumble behaviour. Different E. coli characteristics, including body geometry, flagella bending rigidity, the number of flagella and their arrangement at the body, are considered. Experiments are also performed to directly compare with the model. Interestingly, in both simulations and experiments, the swimming velocity is nearly independent of the number of flagella. The rigidity of a hook (the short part of a flagellum that connects it directly to the motor), polymorphic transformation (spontaneous change in flagella helicity) of flagella and their arrangement at the body surface strongly influence the run-and-tumble behaviour. Mesoscale hydrodynamics simulations with the developed model help us better understand physical mechanisms that govern E. coli dynamics, yielding the run-and-tumble behaviour that compares well with experimental observations. This model can further be used to explore the behaviour of E. coli and other peritrichous bacteria in more complex realistic environments.

This study was an investigation of the knittability of wool/nylon yarns subjected to stretching, bending, and friction during the warp knitting process and the anti-pilling performance of the resulting knitted fabrics. Wool/nylon compact spun yarn, core-spun yarn, and Sirofil spun yarn were prepared with the same wool/nylon ratio, of 70/30. The abrasion resistance and mechanical and bending properties were measured to evaluate the knittability of wool/nylon yarns, and the hairiness of the yarns and the pilling performance of the fabrics produced were also examined. In addition, the mechanical property, bending rigidity, and air and moisture permeability of the fabrics were measured. The Sirofil spun yarn demonstrated superior performance in terms of abrasion resistance (377×), breaking strength (202.10 cN), and hook-joint strength (178.45 cN), which were all significantly higher than for compact and core-spun yarns. Sirofil spun yarn had the best knittability of the three yarns; the pilling grade of the fabric produced by Sirofil spun yarn and after soft finishing was 3 for 7000 abrasion cycles, and the warp breaking strength of fabric produced by Sirofil spun yarn after the soft finishing was 593.53 N. The moisture permeability of the fabric produced by Sirofil spun yarn and after smooth finishing was 339.93 g/m 2 ·h. It was concluded that the Sirofil spun yarn was more suitable for warp knitting than compact spun yarn or core-spun yarn.

We present a theoretical model of the hydrodynamic behaviour of a floating flexible plate of variable flexural rigidity connected to the seabed by a spring/damper system. Decomposition of the response into natural modes allows us to investigate the hydroelastic behaviour of the plate subject to monochromatic incident free-surface waves. We show that spatially dependent plate stiffness affects the eigenfrequencies and modal shapes, with direct consequences on plate dynamics. We also examine how plate length and Power Take-Off distribution affect the response of the system and its consequent absorbed energy. This work highlights the need to improve existing models of flexible floating platforms, expecially given their importance in coastal and ocean engineering.

Skeletal muscle tissue represents an attractive powering component for biohybrid robots, as traditional actuators used in the soft robotic context often rely on complex mechanisms and lack scalability at small dimensions. This article proposes a monolithic biohybrid flexure mechanism actuated by a bioengineered skeletal muscle tissue. The design leverages the contractile properties of a bioengineered skeletal muscle to produce a bending motion in a monolithic, tubular mechanism made of a soft and biocompatible silicone blend. This structure integrates two cylindrical pillars that facilitate force transmission from the bioengineered muscle tissue. Performance assessments reveal excellent contractile and stable behavior upon electrical stimulation, compared to current biohybrid actuation systems, with enhanced performance as the mechanism's internal and external diameters decrease. Finite‐element simulations further reveal distinct force–displacement responses in mechanisms with different flexural rigidity. This innovative, scalable, and easy‐to‐fabricate design represents a significant step forward in the development of novel biohybrid machines.

Circulating tumor cells (CTCs) have crucial roles in the spread of tumors during metastasis. A decisive step is the extravasation of CTCs from the blood stream or lymph system, which depends on the ability of cells to attach to vessel walls. Recent work suggests that such adhesion is facilitated by microtubule (MT)-based membrane protrusions called microtentacles (McTNs). However, how McTNs facilitate such adhesion and how MTs can generate protrusions in CTCs remain unclear. By combining fluorescence recovery after photobleaching experiments and simulations we show that polymerization of MTs provides the main driving force for McTN formation, whereas the contribution of MTs sliding with respect to each other is minimal. Further, the forces exerted on the McTN tip result in curvature, as the MTs are anchored at the other end in the MT organizing center. When approaching vessel walls, McTN curvature is additionally influenced by the adhesion strength between the McTN and wall. Moreover, increasing McTN length, reducing its bending rigidity, or strengthening adhesion enhances the cell-wall contact area and, thus, promotes cell attachment to vessel walls. Our results demonstrate a link between the formation and function of McTNs, which may provide new insight into metastatic cancer diagnosis and therapy.

Abstract Poly (butylene succinate‐co‐terephthalate) (PBST) foams, produced using supercritical carbon dioxide (scCO2) as a physical blowing agent, exhibit significant shrinkage, with a shrinkage rate as high as 80%, which severely limits their practical applications. Current research on improving the dimensional stability of PBST foams mainly focuses on chain extension or mixed‐gas foaming. However, these methods struggle to balance biodegradability with process controllability. Therefore, developing an efficient modification approach to enhance the dimensional stability of PBST foams is crucial. In this study, PBST is modified by blending with poly(3‐hydroxybutyrate‐co‐3‐hydroxyhexanoate) (PHBH). By optimizing the PBST/PHBH ratio, saturation temperature, and pressure, the dimensional stability is significantly improved. After introduction to 20% PHBH, the PBST blend microcellular foams have a stable expansion ratio of 35.8, and the shrinkage rate decreased dramatically from 85% to 11.6%. SEM analysis shows that PHBH dispersed uniformly as rigid particles within the foam cell walls, inducing an open‐cell structure that facilitates gas exchange and minimizes internal‐external pressure differences. Rheological and cyclic compression tests indicates that PHBH increases the elastic modulus and rigidity of the foam walls, enhancing dimensional stability and shrinkage resistance. This work offers an innovative and eco‐friendly solution for producing high‐expansion, low‐shrinkage PBST foams with excellent dimensional stability.

Open-cellular Ti6Al4V lattice structures have found application in porous scaffolds that can match the properties of human bone, which consists of a dense cortical shell and a less-dense cancellous core with an apparent density ranging from 1.3 to 2.1 g/cm3 and 0.1 to 1.3 g/cm3, respectively. The implantation of porous scaffolds is essential for treating large bone defects and must mimic natural bone’s geometric and mechanical behaviour. Functionally graded lattice structures offer spatial variation in mechanical properties, making them suitable for biomedical applications. While the mechanical behaviour of lattice structures is typically evaluated under compression, their flexural properties remain largely underexplored. The aim of this research is to assess the flexural rigidity of a novel lattice material, namely Triply Arranged Octagonal Rings (TAORs), with both uniform and functionally graded architectures, to reproduce the flexural properties of long bones. Titanium alloy scaffolds have been designed with a TAOR cell, whose relative densities range from 10% to 40% with full and hollow sections. Morphological considerations were carried out during the design process to obtain a scaffold geometry which complies with the optimal characteristics required to promote osteointegration. A non-linear finite element (FE) model was developed. Three- and four-point bending tests were simulated, and the results were compared with those of a bone surrogate for long bones. Scaffolds with 10% and 20% relative densities showed flexural rigidity close to that of the bone surrogate and proved to be potential candidates for application in biomedical devices for long bones.

In this study, the objective and subjective hand properties of cotton/cashmere elastane and cotton/soybean protein elastane including denim fabrics were compared each other and a reference 94% cotton 6% elastane sample with the same washings. The surface roughness, compressibility, drape, overall flexural rigidity, and shear rigidity of the fabrics were also evaluated. In addition, subjective roughness, fabric hand and hardness-softness perceptions were evaluated by a group of jury members according to reference sample. Soybean protein containing fabrics exhibited higher compressibility, drape, overall flexural rigidity, and shear rigidity than cashmere containing fabrics. The S-twill fabrics exhibited higher compressibility and shear rigidity than Z-twill fabrics. It was concluded that rinse washed fabrics showed the highest surface roughness and compressibility, while stone washed fabrics showed the highest shear rigidity in the + 45° direction, and enzyme washing samples had the highest shear rigidity value in the − 45° direction. Compared to the 94% cotton 6% elastane fabric, it was observed that the use of cashmere and soybean protein blended yarns in the weft direction caused a decrease in the weft surface roughness values, causing an increase in the compressibility, drape the overall flexural rigidity, and + 45° shear rigidity values.

Pipe-framed solar greenhouses are susceptible to structural failure under extreme snow loads due to their inherent structural asymmetry. This study investigated the failure mechanisms of a 10 m-span pipe-framed greenhouse and proposed three reinforcement methods (reinforced by one brace, lattice column, and temporary column) to enhance snow resistance. A novel concept of reinforcement efficiency was proposed to optimize retrofitting decisions. Finite element (FE) analysis reveals that structural failure originates from full-section yielding of the north column caused by excessive bending moments. Among reinforcement methods, installing a temporary column 4.5 m from the south roof end (near mid-span) achieves the highest reinforcement efficiency (365.3% and 437.1% under uniform and non-uniform snow loads, respectively), followed by replacing single-tube columns with lattice columns (59.9% and 63.1% under uniform and non-uniform snow loads, respectively). Bracing between the south roof and column enhances stability, whereas bracing connecting the south and north roofs accelerates failure and should be avoided. It is recommended to set up one temporary column only under extreme snow loads. The north column of pipe-framed solar greenhouses should be designed as a lattice column. Additionally, flat elliptical hollow sections exhibit superior flexural rigidity compared to rectangular or hat-shaped sections under equivalent steel consumption. This study can provide references for the snow resistance design of other similar pipe-framed greenhouses.