Flexural Rigidity Research Articles

During the Paleolithic-Neolithic transition, modern human femoral diaphyses underwent significant structural changes, primarily driven by shifts in subsistence patterns including decreased mobility and increased sedentism. However, femoral remains from East Asia during this period are inadequately reported and studied. This study investigates the femoral diaphyseal structures across East Asia during this transition, exploring their variation, evolutionary processes, and links to subsistence patterns reflected in the archeological record. Human femora from Qihe Cave, Donghulin, and Taipinghu, representing South, North, and Northeast China during the transition, were analyzed. Midshaft cross-sectional shapes were compared with Early Upper Paleolithic (EUP), Late Upper Paleolithic (LUP), and recent sedentary agricultural (RSA) samples. Morphometric maps illustrating cortical bone thickness, external radius, and bending rigidity along the entire diaphysis were compared with Late Pleistocene early modern humans from South and North China and RSA specimens. Analysis of midshaft cross-sectional shapes revealed that DHL 4 and Qihe M2 align with the LUP group, whereas DHL M1 and TPH 45 show close affinities with the RSA group. Statistical analyses based on morphometric maps further reveal that DHL 4 and Qihe M2 share key features with Late Pleistocene early modern humans, whereas DHL M1 and TPH 45 fall within the RSA variation range. Two distinct femoral diaphyseal patterns are identified among East Asian modern humans during the transition, reflecting regional variations and intrapopulation divisions of labor, primarily associated with hunting and gathering strategies shaped by local environmental conditions and corresponding archeological cultures.

Composite sandwich panels are extensively used in aerospace, automotive, and construction applications due to their exceptional strength-to-weight ratio and structural efficiency. However, local surface deviations, such as waviness and dents, often develop during manufacturing and operation, potentially leading to adhesion failures and delamination between the composite skin and the core. This study aims to establish acceptable defect size limits that can be corrected through technological pressing, ensuring structural integrity of composite material while minimizing the negative impact on load-bearing capacity of sandwich panels. An analytical approach was adopted to assess the stress behavior of composite skins with waviness and elliptical dent defects. The analysis was based on beam and plate theory, incorporating the effects of flexural rigidity, material anisotropy, and applied technological pressure. The Hill strength criterion was applied to define permissible defect limits, considering variations in structural criticality levels. The study determined the maximum allowable sizes for waviness and dents in composite sandwich panels, factoring in the responsibility level of the panel, expressed as the maximum stress intensity coefficient. The results show that the acceptable defect size decreases with increasing structural criticality. It was also found that forced compression of dents induces pre-stress zones within the composite skin, potentially altering its stress distribution and reducing its long-term load-bearing capacity. The proposed methodology provides a quantitative framework for evaluating acceptable defect limits, supporting manufacturing quality control and repair optimization. The results offer practical insights for enhancing the reliability and durability of composite structures, ensuring that local surface deviations remain within permissible limits without compromising structural performance.

Fabric properties significantly influence the accuracy of pattern dimensions derived from 3D scanned garment samples. To enhance the generated pattern accuracy, a novel predictive model was proposed to estimate the pattern dimension change ratio by integrating fabric parameters using an artificial neural network (ANN). Thirty fabrics were tested for making flared skirts. The pattern generation involves 3D scanned garment samples, the Bowyer–Watson algorithm for surface reconstruction, and an energy model for surface development. After the pattern’s dimension change ratio was obtained, principal component analysis (PCA) was applied to reduce dimensionality before correlation analysis. Results indicated that thickness, bending rigidity, drapability, and shear performance were the primary fabric parameters influencing dimensional accuracy. Backpropagation (BP) neural networks were constructed to predict the pattern size change ratio using both full fabric parameters or a PCA-reduced set, including a 9-parameter input layer, four hidden layers, and a 12-parameter output layer. The BP ANN models outperformed the radial basis function (RBF) ANN models, achieving accuracies of 96.67% and 96.02% for the full-factor and dimension-reduced models, respectively. After parameter optimization, the dimension-reduced BP ANN model enhanced pattern accuracy by 5.11%, achieving a final 97.73% accuracy. Results validate utilizing fabric parameters and BP neural networks as a sophisticated pattern optimization method.

Abstract Glass fiber‐reinforced polymer (GFRP) bars are increasingly used in construction due to their non‐corrosive nature. However, their inherent brittleness affects structural performance. This study examines the flexure–shear behavior of GFRP‐reinforced concrete (RC) beams with and without synthetic fibers. Also, their performance is compared with similar Thermo‐Mechanically Treated (TMT) RC beams. To ensure meaningful comparison, TMT beams are designed as under‐reinforced sections with reinforcement of 0.37%. GFRP beams are designed using two criteria: identical rebar ratio and equivalent flexural rigidity, the latter calculated as (EI) GFRP = (EI) TMT . The effect of discrete polypropylene fiber addition (0%, 0.5%, and 1.0%) is also evaluated. Nine RC beams are tested under flexure–shear loading. Performance is assessed based on load–displacement response, peak load, mid‐span deflection, and failure modes. Results indicate that fiber dosage significantly improves strength and post‐cracking stiffness. In TMT RC beams, even a nominal 0.5% fiber dosage alters the failure mode. However, GFRP‐RC beams show softening of failure with increasing fiber dosage but with no change in failure mode, even at a 1.0% fiber dosage. Interestingly, in GFRP beams with higher rebar ratios, fibers reduce brittleness. The findings highlight the potential of polypropylene fibers in enhancing the ductility of brittle GFRP‐RC beams failing in flexure–shear. The flexural and shear capacities of RC beams are predicted by suitably modifying the existing analytical model by RILEM (Réunion Internationale des Laboratoires et Experts des Matériaux, systèmes de construction et ouvrages) [International Union of Laboratories and Experts in Construction Materials, Systems and Structures].

Mixtures of the zwitterionic surfactant TDMAO and the anionic surfactant LiPFOS spontaneously self-assemble into well defined vesicles. The size of these vesicles is determined by the ratio of bending rigidity and line tension. By partially charging TDMAO, and thereby moving more to a catanionic system, the size of these vesicles can be controlled. Using stopped flow small angle neutron scattering we monitor the kinetics of vesicle formation and obtain their final size. Neutron spin echo spectroscopy allows for an independent measurement of the vesicle's bending rigidity. Combining this bending rigidity with the radius of newly formed vesicles, which is determined by the ratio of bending rigidity and line tension, we can determine the line tension. We find that it is the line tension that controls the trend in size of the vesicles. In summary, this means that here one has a surfactant mixture that delivers well-defined vesicles, whose size is controlled by the electrostatic interactions of the head groups.

The structural and dynamic properties of columnar cacti are key inputs for stability analyses; however, no previous studies have been able to resolve these properties from full-scale tests in situ. I present an approach using non-destructive ambient vibration data to measure the resonance properties (modal frequencies and mode shapes) of single-stem saguaro cacti and resolve key biomechanical properties. I tested the approach on 11 spears in the Tucson, Arizona region, United States. Saguaro fundamental frequencies ranged between 0.55 and 3.7 Hz with damping ratios of 1.5-2.1%. Additional higher-order modes were identified below 10 Hz. Fundamental frequencies scaled linearly with the ratio of stem diameter to height-squared, but deviated from analytical theory due to an observed increase in Young's modulus for taller plants. Calculated ratios between second- and first-order bending frequencies also deviated from beam theory, indicating that stiffness decreases vertically for a given stem, especially for taller spears. These deviations both likely arise from the morphology of internal wooden ribs, which provide the main flexural rigidity. Numerical modeling at one site confirmed the cantilever approximation and height-dependent stiffness, revealing an empirically derived Young's modulus that decreased exponentially from 107 Pa at the top of the stem to 108 Pa at its base. Twelve days of monitoring at another site showed that frequencies drift with diurnal cycles, suggesting softening of the outer tissue as temperatures warm during the day. This non-destructive approach for structural assessment provides valuable data for biomechanical characterization and stability and ecological analyses.

With growing environmental concerns and the need for ecofriendly materials, sustainable natural fibers have gained significant attention as viable alternatives to synthetic reinforcements in composite manufacturing. This study investigates the influence of fiber length - specifically sisal, kenaf, and banana fibers - on the mechanical, thermal, acoustic and physical properties of composite materials. Using compression moulding technique, nine composite samples were fabricated with fiber lengths of 1.5 cm, 6 cm, and 10 cm. These were systematically evaluated for tensile strength, flexural rigidity, shore hardness, thermal conductivity, Ultraviolet (UV) protection, acoustic properties, water absorption and dimensional stability. The findings indicate that increasing fiber length generally enhances mechanical strength and thermal insulation, while shorter fibers are more effective at reflecting sound, revealing a trade-off between structural reinforcement and acoustic behaviour. Among the tested fibers, 10 cm sisal fibers yielded the highest tensile strength (463.7 kgf) and shore hardness (75), whereas banana fibers outperformed others in UV shielding (UPF = 2148.8), thermal insulation, and sound waves reflection. These results underscore the importance of optimizing fiber type and fiber length to achieve a balanced integration of safety, comfort, and environmental sustainability in helmet design.

Bottle-brush polymers with aggrecan-like side chains represent a class of biomimetic macromolecules that replicate key structural and functional features of natural complexes of aggrecans with hyaluronic acid (HA) which are the major components of articular cartilage. In this study, we employ numerical self-consistent field (SCF) modeling combined with analytical theory to investigate the conformational properties of cylindrical molecular bottle-brushes composed of aggrecan-like double-comb side chains tethered to the main chain (the backbone of the bottle-brush). We demonstrate that the architecture of the brush-forming double-comb chains and, in particular, the distribution of polymer mass between the root and peripheral domains significantly influences the spatial distribution of primary side chain ends, leading to formation of a “dead” zone near the backbone of the bottle-brush and non-uniform density profiles. The axial stretching force imposed by grafted double-combs in the main chain, as well as normal force acting at the junction point between the bottle-brush backbone and the double-comb side chain are shown to depend strongly on the side-chain architecture. Furthermore, we analyze the induced bending rigidity and persistence length of the bottle-brush, revealing that while the overall scaling behavior follows established power laws, the internal structure can be finely tuned without altering the backbone stiffness. These theoretical findings provide valuable insights into relations between architecture and properties of bottle-brush-like supra-biomolecular structures, such as aggrecan-hyaluronan complexes.

Lipid membrane-bounded organelles often possess intricatemorphologieswith spatially varying curvatures and large membrane surface areasrelative to internal volume (small reduced volumes). These featuresare thought to be essential for protein sorting and vesicle trafficking,but challenging to reproduce in vitro. Here, we showthat weakly adhered giant unilamellar vesicles (GUVs) can be osmoticallydeflated to reduced volumes as low as 0.1, similar to what is foundin flattened, disc-shaped organelles such as Golgi cisternae and ERsheets. Using shape analysis with the Canham-Helfrich model, we determinemechanical parameters including adhesion strength, membrane tension,and pressure of individual vesicles. We find that the rate of shapeflattening during deflation is governed by a normalized adhesion strengththat combines vesicle size, adhesion energy, and bending rigidity.For highly flattened disc-like vesicles, we identify a geometric relationshipthat allows the adhesion strength to be estimated solely from thevesicle’s aspect ratio, size, and bending rigidity. These resultsprovide a quantitative experimental platform for bottom-up studiesof membrane shaping mechanisms and shape-dependent phenomena, suchas curvature-mediated protein sorting.

Abstract We develop a theoretical framework to quantify how active forces renormalize the effective bending rigidity, Gaussian modulus, and surface tension of thermally fluctuating membranes. Building on classical statistical mechanics, we extend the analysis to include nonequilibrium active forces—both direct forces and those coupled to membrane curvature—within a nonlinear continuum formulation. Our model also incorporates hydrodynamic interactions mediated by the surrounding viscous fluid, which significantly alter the fluctuation spectrum. We find that direct active forces enhance long-wavelength undulations, leading to a substantial reduction in both the effective bending rigidity and surface tension, with the extent of softening strongly modulated by fluid viscosity. In contrast, curvature-coupled active forces primarily influence intermediate and short-wavelength fluctuations and show minimal sensitivity to viscosity. Together, these findings provide key insights into the nonequilibrium mechanics of active membranes and yield testable predictions for interpreting fluctuation spectra in both biological contexts and engineered membrane systems.

Study Design. Randomized, placebo-controlled, double-blinded phase 2b study. Objective. To compare the effects of STA363 (90 or 180 mg intradiscally) and placebo on low-back pain (LBP) in patients with lumbar degenerative disc disease (DDD) Summary of Background Data. Results from preclinical studies and a small phase 1b study have indicated that STA363 transforms the nucleus pulposus (NP) into connective tissue and thereby increases flexural rigidity. Such effects may improve LBP in DDD patients. Methods. 109 patients were equally randomized into the three treatment groups. After screening, test formulation was injected intradiscally, and patients were followed-up for up to 12 months. Primary endpoint was improvement in LBP as evaluated using the numerical rating scale. Results. The percentage of patients reporting ≥1 adverse event was 50, 55 and 63% in the placebo, STA363 90 mg and STA363 180 mg groups, respectively. The patients of all groups showed a marked reduction in LBP after treatment but there was no difference between placebo and STA363 at any follow-up time. Water content as reflected by decrease in T2 time (ms) was reduced in a dose-dependent manner (6 mo: placebo 1.5±9.0; STA363 90 mg 2.3±7.3; STA363 180 mg 5.7±9.2 (P=0.06 vs. placebo). The corresponding values for 12 months were 1.5±6.4, 4.0±7.3 and 5.3±13.4 (P=0.11). Conclusion. While MRI results were consistent with fibrosis of the NP after treatment with STA363, these changes did not translate into any significant effects on LBP in DDD patients as compared with patients injected with placebo.

Deformable boundaries are omnipresent in the habitats of swimming microorganisms, leading to intricate hydroelastic couplings. Employing a perturbation theory, valid for small deformations, we study the swimming dynamics of pushers and pullers near instantaneously deforming boundaries, endowed with a bending rigidity and surface tension. Our results reveal that pushers can either reorient away from the boundary, leading to overall hydroelastic scattering, or become trapped by the boundary, akin to the enhanced trapping found for pullers. These findings demonstrate that the complex hydroelastic interactions can generate behaviors that are in striking contrast to swimming near planar walls.

The surface roughness of a thin film at a liquid interface exhibits contributions of thermally excited fluctuations. This thermal roughness depends on temperature (T), surface tension (γ), and elastic material properties, specifically the bending modulus (κ) of the film. A nonzero κ suppresses the thermal roughness at small length scales compared to an interface with zero κ, as expressed by the power spectral density of the thermal roughness. The description of the x-ray scattering of the standard capillary wave model (CWM), which is valid for zero κ, is extended to include the effect of κ. The extended CWM (eCWM) provides a single analytical form for both the specular x-ray reflectivity (XRR) and the diffuse scattering around the specular reflection, and recovers the expression of the CWM at its zero κ limit. This theoretical approach enables the use of single-shot grazing incidence x-ray off-specular scattering (GIXOS) measurements for characterizing the structure of thin films on a liquid surface. The eCWM analysis approach decouples the thermal roughness factor from the surface scattering signal, providing direct access to the intrinsic surface-normal structure of the film and its bending modulus. Moreover, the eCWM facilitates the calculation of reflectivity at any desired resolution (pseudo-XRR approach). The transformation into pseudo-XRR provides the benefit of using widely available XRR software to perform GIXOS analysis. The extended range of the vertical scattering vector (Qz) available with the GIXOS pseudo-XRR approach allows for a higher spatial resolution than with conventional XRR. Experimental results are presented for various lipid systems, showing strong agreement between conventional specular XRR and pseudo-XRR methods. This agreement validates the proposed approach and highlights its utility for analyzing soft, thin films.

ABSTRACTDual-energy x-ray absorptiometry (DXA)-derived areal bone mineral density (BMD) remains the clinical standard for assessing osteoporosis risk, yet it fails to identify over 75% of individuals who sustain fragility fractures. Direct in vivo mechanical assessment of cortical bone strength may address this diagnostic gap by capturing structural and material properties that govern whole-bone strength but are not reflected by BMD. We conducted a multicenter case-control study with cross-sectional assessment to compare ulna flexural rigidity, a biomechanical property correlated with whole-bone strength (R² ≈ 0.99), estimated using Cortical Bone Mechanics Technology (CBMT), with DXA-derived BMD for discriminating prior fragility fractures in postmenopausal women. A total of 372 women aged 50–80 years (109 with low-trauma fractures, 263 matched controls) were enrolled across four U.S. sites. Ulna flexural rigidity was assessed by dynamic vibrational analysis; BMD was measured at the spine, hip, and 1/3 radius. Women with prior fractures had significantly lower flexural rigidity than controls (absolute: 20.0 vs. 24.8 N·m²; 21% lower; weight-normalized: 0.29 vs. 0.36 N·m²/kg; 22% lower; both P < .001). CBMT demonstrated strong discriminatory accuracy (AUC = 0.80 normalized; 0.76 absolute) versus poor DXA performance (AUC ≤ 0.63) for discriminating all fragility fractures. In multivariable models including CBMT, DXA-derived BMD, age, and BMI, CBMT remained independently associated with fracture status, whereas BMD did not. Subgroup analyses showed CBMT retained strong performance in treatment-naïve women (AUC = 0.85) and in those with non-osteoporotic BMD (AUC = 0.80). Exploratory fracture-site analyses demonstrated that ulna EI discriminated upper and lower extremity fractures, including hip, whereas DXA-derived BMD generally showed modest or nonsignificant discrimination. These findings demonstrate that in vivo mechanical assessment of cortical bone rigidity provides clinically relevant information beyond areal BMD, including women not classified high risk. Direct in vivo assessment of cortical bone rigidity may enhance fracture risk stratification and enhance osteoporosis screening.Lay SummaryMost people who break a bone from a simple fall do not meet the standard definition of osteoporosis based on a bone density scan (DXA). This means many at risk are not identified or treated. Our study tested a new, noninvasive technology that directly measures how strong a bone is by assessing how much it resists bending. We found that this measure, called flexural rigidity, more accurately identified women with past fractures than DXA did, even in women whose bone density was “normal”. It also showed strong performance across different types of fractures, including hip fractures. Directly testing bone strength may help doctors better identify who needs treatment to prevent fractures. Figure

Abstract Knitted fabrics composed of bio-poly(trimethylene terephthalate)/polyethylene terephthalate (bio-PTT/PET) bicomponent yarns are introduced as sustainable substrates for screen-printed stretchable electrodes. These yarns exhibit inherent stretchability owing to their latent crimps, which provide a structural deformation mechanism distinct from the elastomeric behavior of conventional polyurethane (PU)-based substrates. A systematic investigation of the number of printing passes revealed that three passes yielded optimal performance, enabling the formation of a continuous conductive layer, maintaining electrical stability under repeated strains, and minimizing mechanical degradation. Exceeding this threshold resulted in excessive ink accumulation, as indicated by a 62.4% increase in ink thickness at the fourth pass, which corresponded to significant reductions in tensile strength and flexural rigidity. The optimized electrodes demonstrated superior durability compared with the PU-based counterparts, maintaining a surface resistance of 11.5 Ω/m² after five washing cycles, whereas that of PU electrodes increased to 20.7 Ω/m². Electrical conductivity was preserved under repeated stretching and laundering, enabling reliable surface electromyography (sEMG) monitoring. Clear muscle-activity signals and stable resting baselines were obtained, with root mean square (RMS) values comparable to those of Ag/AgCl gel electrodes and a signal-to-noise ratio of 22.1 dB, confirming sufficient signal quality for practical biosignal interpretation. These findings reveal the potential of bio-PTT/PET bicomponent yarns as robust and sustainable substrates for knitted stretchable electrodes, supporting reliable applications in biosignal monitoring, wearable electronics, and adaptive smart textiles. Moreover, this study provides a foundation for extending this approach to other latent-crimp fiber substrates, broadening the range of viable materials for sustainable and durable smart textiles.

The influences of mass ratio and flexural rigidity in flow-induced vibrations of a circular cylinder with an attached flexible plate

Escherichia coli cell shape and size are governed by the mechanochemistry of the cellular components. Inhibiting either cell-wall synthesis proteins such as FtsI leads to cell elongation and bulging, while inhibiting MreB cytoskeletal polymerization results in a loss of rod-shape. Here, we quantify cell shape dynamics of E. coli combinatorially treated with the FtsI inhibitor cephalexin and MreB inhibitor A22 and fit a shell mechanics model to the length-width dynamics to infer the range of effective mechanical properties governing cell shape. The model based on the interplay of intracellular pressure and envelope mechanics, predicts E. coli cell width grows and saturates. Bulging observed in cells treated with both MreB and FtsI inhibitors, is predicted by the model to result from a lower effective bending rigidity and higher effective surface tension compared with untreated. We validate the specificity of the predicted internal pressure of ∼0.6 MPa driving bulging, when placing treated cells in a hyperosmotic environment of comparable pressure results in reversal of cell bulging. Simulations of cell width dynamics predicting threshold values of envelope bending rigidity and effective surface tension required to maintain cell shape compared with experiment validate the effective mechanical limits of cell shape maintenance.

Divergent responses of branched and straight-chain lipid membranes to butanol stress revealed by molecular dynamics simulation.

This study presents high-fidelity, two-way coupled fluid–structure interaction (FSI) simulations to investigate the dynamic behavior of tandem perforated elastic vortex generators (EVGs) across a wide range of bending rigidity, mass ratio, and porosity, at a fixed Reynolds number and interspacing. Comparative simulations with non-perforated EVGs are also performed. Three response modes—Lodging, Vortex-Induced Vibration (VIV), and Static Reconfiguration—are observed in both configurations, while a distinct Cavity Oscillation mode emerges exclusively in non-perforated tandem EVGs. This mode is entirely suppressed with porosity due to disruption of the low-pressure cavity and increased flow transmission through pores. Frequency analyses reveal that VIV is consistently locked onto the second natural frequency, whereas the Cavity Oscillation mode is locked onto the first natural frequency and closely aligns with the first Rossiter mode, underscoring its distinct physical origin. Perforation modifies the natural frequency of the EVGs, shifting the lock-in and mode transitions toward lower bending rigidity and higher mass ratio values, and reducing oscillation amplitudes due to motion damping. Drag analysis shows consistently higher upstream drag due to wake shielding, while porosity reduces upstream drag and increases downstream drag by restoring streamwise momentum. Flow visualizations demonstrate that vortex shedding originates at the EVG tips, with perforated configurations producing smaller, more dissipative vortical structures. These results establish that porosity fundamentally alters dynamic regimes, suppresses cavity-driven instabilities, and enables passive modulation of wake dynamics in tandem EVG systems.

Two-phase fluid deformable surfaces with constant enclosed volume and phase-dependent bending and Gaussian rigidity