Bending Compliance Research Articles

Response of circular type sandwich panel using JUCO-glass fiber with PU foam under three-point bending loading

In this study, a circular type honeycomb sandwich panel using natural JUCO and synthetic woven glass fiber was fabricated, and the bending properties like bending strength, modulus of rupture (MOR), and modulus of elasticity (MOE) were evaluated. Polyurethane (PU) foam was injected into the core structure to improve the bending strength. The orientation of jute and cotton fiber was varied to investigate the best stiffness and strength. In addition, twill-type JUCO fiber mat and synthetic woven glass fiber were also used to fabricate the circular type honeycomb sandwich panel. Finite element modeling was undertaken to validate the experimental results. Prior to the finite element analysis, a tensile test was carried out to determine the boundary conditions. Injecting polyurethane foam into the honeycomb core does not show any significant impact on bending properties. However, the deformation rate increased considerably by adding PU foam in the core structure. According to the results, honeycomb sandwich panels made of woven glass fiber with PU foam exhibited more homogenous deflection and bending compliance compared with others.

New HCHO-scavenger for enhancing the HCHO-based adhesive in production environmentally friendly agro-based composites

Recently, green products are essential requirements. This work deals with synthesizing novel formaldehyde-scavenger based on black liquor to enhance the urea-formaldehyde (UF) adhesive for production of eco-friendly bio-composites. These HCHO-scavengers are synthesized from black liquor-based aerogel precursors. The assessment is carried out via estimating the HCHO adsorption capacities versus type of black liquor; as well as its beneficial effect on characterization of UF adhesive (Differential Scanning Calorimetry (DSC)-curing temperature; gel time and adhesive strength). The UF-scavenger system, which provides palm fiber-composite with properties (static bending, internal bond, and free-HCHO) compliance with the standard specifications is optimized. The data evidenced the effective role of black liquor (BL) from alkali pulping RS in presence of borohydride in resulting aerogel precursor of scavenger with higher HCHO-adsorption capacities (∼64 mg/g) than that produced from native aerogels (AG) in absence of BL. The kinetic adsorption is most applicable with the pseudo-second order equation. This observed behavior reflected on reducing the gel time and improved the bond strength of scavenger (Scv)-UF systems. It is interesting to note that all investigated BL-scavengers provide reduction in free HCHO of palm composites (from 30.7 mg/100g to 5–11 mg/g). These values are lower than that obtained from scavengers in absence of BLs (17.4 mg/100g). Based on the value of free-HCHO and mechanical properties, we recommend the scavenger resulted from black liquor of alkali pulping RS in presence of anthraquinone and borohydride (NaOH-AQ-BH) of screened RS as effective scavenger to provided eco-palm-wood composites with MOR, MOE, IB, free-HCHO and thickness swelling ∼ 27 MPa, 0.72 MPa, 7157 MPa, 7 % and 11 %, respectively. According to international standard specifications this type of palm-composite fulfills the grade H-3 and E1 according to environmental specification.

Modelling and performance analysis of a curvature-adjustable multiple-axis flexure hinge based on Bézier curve

In order to solve the uniqueness of the compliance equations and each notch profile, a curvature-adjustable multiple-axis flexure hinge with complex notch profiles is designed and investigated based on Bézier curve in this paper. The hinge can evolve into multiple-axis flexure hinges with single and hybrid, symmetric and asymmetric notch profiles composed of the ellipse, circle, hyperbola and parabola. In addition, analytical compliance equations in six degrees of freedom based on the Castigliano’s Second Theorem are proposed. Then, a simplified notch profile classification method based on a binary quadratic implicit equation is proposed. Moreover, analytical compliance equations are validated by finite element analysis. The maximum relative error between the finite element analysis and the analytical results is 6.07%. Finally, the compliance, precision of rotation and stress are investigated based on structural parameters. The results show that the change in the rotation centre does not significantly affect the axial and bending compliance for the flexure hinge with a specific single and flush Bézier curve notch profile. Moreover, the flexure hinge with a notch profile consisting of ellipse and hyperbola has the highest rotational precision. The proposed curvature-adjustable multiple-axis flexure hinge can provide more compliance options for the design of compliant mechanisms.

Study on the Bending Behaviors of a Novel Flexible Re-Entrant Honeycomb

Abstract In order to further improve the bending performance of the traditional re-entrant (RE) honeycomb, a novel auxetic honeycomb architecture, called RE-L honeycomb, was proposed by adding an additional link-wall structure to the RE cell. The bending behaviors of the novel RE-L honeycomb, including the properties under linear elastic deformation and the bending behaviors under large deformation, were comprehensively investigated by the analytical, numerical, and experimental models. Results show that the proposed RE-L honeycomb significantly improves the bending compliance in the x-direction due to the highly flexible performance of the additional structure, where the bending rigidity and the maximum bending force are only 23% and 29.4% of those of the RE honeycomb, respectively. Besides, the additional structure obviously improves the designability and orthotropic properties of the original auxetic honeycomb. In conclusion, the proposed RE-L shows improved bending performance, which deserves more attention in future research and related applications.

A Class of One Dimensional Periodic Microstructures Exhibiting Effective Timoshenko Beam Behavior

We study, from a variational viewpoint, the asymptotic behavior of a planar beam with a periodic wavy shape when the amplitude and the wavelength of the shape tend to zero. We assume that the beam behaves, at the microscopic level, as a compressible Euler–Bernoulli beam and that the material properties have the same period as the geometry. We allow for distributed or concentrated bending compliance and for a non-quadratic extensional energy. The macroscopic Γ-limit that we obtain corresponds to a non-linear model of Timoshenko type.

Functional compliance and protective stiffness: cross-veins in the hind wing of locust Locusta migratoria.

Locusts (Locusta migratoria) have outstanding flying abilities, and most of their lift is provided by their hind wings. Insect aerodynamic performance is strongly affected by wing deformation during stroke, which is closely related to its functional morphology (particularly its mechanical properties). The cross-vein is one of the main morphologies in the hind wing of locusts. However, few studies on the mechanical properties of cross-veins have been conducted. This study evaluated the cross-veins of the locust hind wing using uniaxial tensile tester, scanning electron microscope, and finite element methods. Four cross-vein types were identified at different locations on the hind wing, including periodical semi- and full-ellipsoidal humps and periodical semi- and full-conical humps. The four cross-veins showed similar tensile stiffness but differed in bending compliance. We suggest that the mechanical properties of the four cross-veins can be attributed to their physiological functions. This study elucidates cross-veins of locust hind wing and contributes our understanding of the flapping flight mechanism in locusts.

Unveiling the Mechanism Behind the Asymmetric Bending Compliance of Thin-Walled U-Shaped Strips: A Study Inspired by Plant Leaves

Unveiling the Mechanism Behind the Asymmetric Bending Compliance of Thin-Walled U-Shaped Strips: A Study Inspired by Plant Leaves

Multi-Parameter Layup Optimization and the Effect of Layup Homogenization on the Bending Compliance Matrix of Coupled Composites

The behaviour of fibre-reinforced composites greatly depends on their layup structures. Through a full-field layup optimization study based on multiple parameters, this paper investigates how different properties change with the layup. The aim was to maximize the extension-twist coupling performance while ensuring adequate bending stiffness and low thermal warpage to make the laminate suitable for shape-adaptive helicopter rotor blade application. The Classical Laminate Theory-based calculations revealed that satisfying the bending compliance and thermal warpage criteria significantly limited the achievable extension-twist performance. The warpage limit affected the desired coupling behaviour more because both properties are driven by terms in the extensional-bending compliance matrix, unlike bending compliance. Symmetric laminates do not have an intrinsic extension-twist capability, but some asymmetric laminates demonstrated significant coupling performance while being practically warpage-free (based on the ISO2768 standard). The results prove that the advantages of asymmetric laminates can outweigh their sometimes negligible disadvantages. The paper also investigates if there is a universal tendency in how layup homogenization affects the terms of the bending compliance matrix of composites. Through analytical calculations, we showed that depending on the layup of the sub-laminate, homogenization can increase or reduce the value of any term in the bending compliance matrix; therefore, there is no universal tendency. Based on these results, layup homogenization cannot only be exploited for its most general purpose – warpage mitigation – but also for improving other characteristics of the laminate (e.g. reducing the bending compliance for increased bending stiffness or increasing the bend-twist compliance for improved coupling performance).

Giant compliance and spontaneous buckling of beams containing mobile solute atoms

Recent experiments have shown that the elastic compliance of a porous metal can be substantially enhanced when mobile solute is alloyed into interstitial sites of the crystal lattice. The observations agree with predictions – due to Gorsky and to Larché and Cahn – for the elasticity of open systems in which the elastic responses is probed at constant chemical potential. The underlying mechanism involves an exchange of solute between tensile and compressive fibers in beam-like elements of the microstructure. Here, we analyze the elastic deformation of such elements in a continuum approach, accounting explicitly for the coupling between chemistry and mechanics. We consider a regular solution with linear elasticity in the limit of constant composition and with a linear composition-strain coupling. Materials parameters are matched to experiments on Pd-H, so as to realistically account for the balance between chemical and mechanical energies. At constant chemical potential, the elastic response can be strongly nonlinear. With decreasing temperature, the bending goes from a monotonic moment-curvature relation to one including a horizontal tangent and, hence, a state of giant bending compliance. Reducing the temperature further brings first a temperature interval with a simple bistability and finally one with degeneracy including – depending on the chemical potential or on the mean solute fraction – the possibility of finite curvature at zero moment. Quenching the uniform solution into a two-phase region of the alloy phase diagram can lead to spontaneous buckling at no load. Furthermore, degenerate moment-curvature relations allow for bending states in which the radius is not a constant along the beam axis. Intervals of lar ge strain at constant load are similar to superelasticity, but the underlying phase transformation is here not martensitic.

Harnessing fractal cuts to design robust lattice metamaterials for energy dissipation

Lattice metamaterials exhibit remarkable mechanical properties and novel functionalities, such as high specific stiffness, fracture toughness, tunable vibroacoustic properties, and energy absorption. This study explores a group of lattice metamaterials with fractal cuts that feature energy dissipation via structural sliding friction mechanisms and intrinsic material damping. Lattice metamaterials with three types of fractal cuts patterns were designed and fabricated using additive manufacturing. Three-point bending tests and numerical analysis have been combined to investigate their bending behavior. Experimental results show that the structural bending compliance of the metamaterials can be sharply enhanced by increasing the fractal orders, while at the same time keeping the shape recoverability during cyclic loading. Loss factors associated with the cyclic bending of these metamaterials are almost independent of the fractal order used, which is attributed to the synergistic effect between friction and viscoelasticity. It is further demonstrated via validated finite element models that the sliding friction plays a critical role by investigating the effects of the bending displacement and sample thickness on the flexural behavior. Results suggest that the magnitude of the maximum bending displacement has a negligible effect on the loss factors, and a power scaling law exists between bending stiffness and sample thickness. This study suggests that fractal lattice metamaterials have unique energy dissipation properties, with potential applications in many industrial sectors such as defense, energy, and transportation.

Evaluation of a Feline Bone Surrogate and In Vitro Mechanical Comparison of Small Interlocking Nail Systems in Mediolateral Bending.

The aim of this study was to (1) evaluate bending structural properties of a machined short fibre epoxy (SFE) feline bone surrogate (FBS), (2) compare the bending behaviour of small angle-stable interlocking nails (I-Loc; Targon) and locking compression plates (LCP) and (3) evaluate the effect of implant removal on FBS bending strength. Part 1: Feline cadaveric femurs (n = 10) and FBS (n = 4) underwent cyclic four-point bending and load to failure. Part 2: Fracture gap FBS constructs (n = 4/group) were stabilized in a bridging fashion with either I-Loc 3 and 4, Targon 2.5 and 3.0, LCP 2.0 and 2.4, then cyclically bent. Part 3: Intact FBS with pilot holes, simulating explantation, (n = 4/group) underwent destructive bending tests. Bending compliance, angular deformation and failure moment (FM) were statistically compared (p < 0.05). Native bone and FBS were similar for all outcome measures (p > 0.05). The smallest and largest bending compliance and angular deformation were seen in the I-Loc 4 and LCP 2.0 respectively (p < 0.05). While explanted Targon FBS had the lowest FM (p < 0.05), I-Loc and LCP constructs FM were not different (p > 0.05). The similar bending properties of short fibre epoxy made FBS and native feline femurs suggest that this model could be used for mechanical testing of implants designed for feline long bone osteosynthesis. The I-Loc constructs smaller angular deformation which also suggests that these implants represent a valid alternative to size-matched Targon and LCP for feline fracture osteosynthesis. The significantly lower FM of explanted Targon may increase the risk of secondary fracture following implant removal.

An experimental study for identifying crack initiation forces in single-lap bonded joints

This paper highlights a method for determining crack initiation force in adhesives used for single-lap joints (SLJs). Crack onset behavior was investigated by combining multiple techniques of failure progressive analysis. The proposed relative displacement method (RD) incorporated digital image correlation (DIC), focusing on bending strain behavior responses to the RD of substrates. Deformation acceleration calculated from the strain distribution drastically increased with increasing crack initiation force and lied within 3% accuracy range, as compared with the behavior of bending compliance measured by a strain gage. The RD was confirmed practical for detecting crack initiation force in SLJs.

Analysis of the Phenomena Causing Weave and Wobble in Two-Wheelers

The present work follows in the tracks of previous studies investigating the stability of motorcycles. Two principal oscillation modes of motorcycles are the well-known wobble and weave modes. The research in this field started about fifty years ago and showed how different motorcycle parameters influence the stability of the mentioned modes. However, there is sometimes a minor lack in the physical analysis of why a certain parameter influences the stability. The derived knowledge can be complemented by some mechanical momentum correlations. This work aims to ascertain, in depth, the physical phenomena that stand behind the influence of fork bending compliance on the wobble mode and behind the velocity dependence of the weave damping behaviour. After a summary of the relevant work in this field, this paper presents different rigid body simulation models with increasing complexity and discusses the related eigenvalue analysis and time behaviour. With these models, the mentioned modes are explained and the physical phenomena only partly covered by the literature are shown. Finally, the influence of the rider model on weave and wobble is presented.

Physical understanding of axonal growth patterns on grooved substrates: groove ridge crossing versus longitudinal alignment

Surface topographies such as micrometric edges and grooves have been widely used to improve neuron outgrowth. However, finding the mechanism of neuron–surface interactions on grooved substrates remains a challenge. In this work, PC12 cells and chick forebrain neurons (CFNs) were cultured on grooved and smooth polyacrylonitrile substrates. It was found that CFNs showed a tendency of growing across groove ridges; while PC12 cells were only observed to grow in the longitudinal direction of grooves. To further investigate these observations, a 3D physical model of axonal outgrowth was developed. In this model, axon shafts are simulated as elastic 3D beams, accounting for the axon outgrowth as well as the focal contacts between axons and substrates. Moreover, the bending direction of axon tips during groove ridge crossing is governed by the energy minimization principle. Our physical model predicts that axonal groove ridge crossing is contributed by the bending compliance of axons, caused by lower Young’s modulus and smaller diameters. This work will aid the understanding of the mechanisms involved in axonal alignment and elongation of neurons guided by grooved substrates, and the obtained insights can be used to enhance the design of instructive scaffolds for nerve tissue engineering and regeneration applications.

Non-linear bending compliance of thin ply composite beams by local compression flange buckling

Passive spanwise bending shape-adaption has the potential to increase the efficiency and manoeuvrability of vehicles with wing-like structures. By utilisation of compression flange buckling, the in-plane stiffness can be tuned to design beams with contrasting pre-buckling and post-buckling bending stiffness. The investigated concept is experimentally validated using a thin-ply laminated composite four-point bending beam, which is designed to experience compression flange buckling in the span with constant moment. The bending stiffness was reduced by more than 41% after the onset of buckling which shows the effectiveness of compression flange buckling for non-linear bending compliance.

Slack and Excessive Loading Avoidance in n-Tendon Continuum Robots

In this work, two tendon tension loading distributions (fixed and moving) are designed to prevent undesired slack and excessive loading in tendons of continuum manipulators. For any given beam configuration, the algorithms utilize the proposed loading distributions to find a new beam configuration as well as base displacement to control the orientation or position of the $n$ -tendon continuum robot. The algorithms account for the bending and axial compliance of the manipulator as well as tendon compliance. Numerical results are provided to demonstrate the orientation and position control algorithms under fixed or moving loading distributions. A 6-tendon continuum robot system is employed to experimentally evaluate the effectiveness and accuracy of the proposed control algorithms. Multiple experiments are carried out and results are reported. The results verify the performance of the proposed control algorithms in avoiding slack and excessive loading in tendons and controlling the orientation and position of continuum structures.

An Analytical Tension Model for Continuum Robots with n Generally Positioned Tendons

The estimation of tension loads in multi-tendon continuum robots or catheters plays an important role not only in the design process but also in the control algorithm to avoid slack. An analytical tension loading model is developed that, for any given beam configuration within the workspace, calculates tendon tensions in [Formula: see text]-tendon continuum robots with general tendon positioning. The model accounts for the bending and axial compliance of the manipulator as well as tendon compliance. A 6-tendon continuum robot integrated with a stereo vision-based 3D reconstruction system is utilized to experimentally validate the proposed analytical model in open-loop control architecture. The proposed model demonstrates around 95% accuracy in estimating tendon tensions in a continuum robot with general tendon positioning and axial stretch in its tendons for all of the trials and experiments.

Mechanical Properties of Selective Laser Sintering (SLS) Additive Manufactured Chiral Auxetic Cylindrical Stent

The mechanical properties of the stent are of key importance to the mechanical integrity and performance reliability of stent-plaque-artery system, and an ideal stent should have good bending compliance, axial deformation stability, hoop strength and stiffness, larger radial expandable ability, etc. In this paper, innovative chiral stent designs with auxetic properties are proposed, and amplified stent sample is fabricated with SLS additive manufacturing technique. Firstly, through combining micro-CT tomography and image-based finite element analysis, the mechanical properties of as fabricated SLS stent are explored; Secondly, two series of stent samples are fabricated with SLS additive manufacturing techniques, and in-situ compression experiments are performed for studying the deformation mechanisms and auxetic mechanical behaviors of stents. Finally, effects of geometrical parameters on the tensile mechanical performance of these stents are studied with finite element analysis. The proposed chiral stent exhibits auxetic behaviors, and can be tailored through adjusting the unit cell design parameters, such as: struct numbers along circumferential directions, ligament lengths, and node radius.

The effect of flexible joint-like elements on the adhesive performance of nature-inspired bent mushroom-like fibers.

Many organisms rely on densely packed, tilted and curved fibers of various dimensions to attach to surfaces. While the high elastic modulus of these fibers enables an extremely large number of fibers per unit area, where each fiber stands freely without sticking to its neighbors, the tilt/curvature provides them with the compliance and the directional adhesion properties to attach strongly and efficiently to a surface. Recent studies have revealed that many of such organisms also feature materials with a graded elastic modulus that is tailored towards improving the contact area without sacrificing the fiber density. In particular, for male ladybird beetles, research has shown that the adhesive setae feature a material gradient such that the elastic modulus of the material at the junction between the stalk and the divergent distal end is close to minimum. This soft material acts like a flexible joint, improving the bending compliance of the tip. Here, we mimic this feature using tilted, mushroom-like, stiff fibers comprised of a stiff stalk of elastic modulus 126 MPa, a softer tip of elastic modulus 8.89 MPa, and a joint-like element of elastic modulus 0.45 MPa (very soft), 8.89 MPa (soft), or 126 MPa (stiff) in between. The results from load–drag–pull (LDP) experiments performed along (gripping) and against (releasing) the tilt direction indicate that the soft and the very soft joint fibers performed superior to the stiff joint fibers and maintained directionally dependent performance. The soft joint fibers achieved up to 22 kPa in shear and 110 kPa in pull-off stress in the gripping direction, which are twice and ten times higher than that in the releasing direction, respectively. A model to optimize the elastic modulus of the joint-like elements to enable sliding without peeling of the tips has been proposed.

An Analytical Loading Model for &lt;inline-formula&gt; &lt;tex-math notation="LaTeX"&gt;$n$&lt;/tex-math&gt; &lt;/inline-formula&gt;-Tendon Continuum Robots

One of the key design parameters in tendon-driven continuum robots is the number of tendons and the tendon loading distribution. A load model is also helpful for avoiding slack in tendons that causes control inefficiency and inaccuracy. A quasi-static model of $n$ -tendon continuum robots is derived using the Euler–Lagrange formulation. The model is employed to derive an analytical loading model for equidistant tendon tensions for any given beam configuration within the workspace. The model accounts for the bending and axial compliance of the manipulator as well as tendon compliance. Features of the proposed model are discussed and some of the potential applications are explained. Based on the proposed model, a slack avoidance algorithm with analytical formulation is developed to dynamically optimize the tendon loads while preventing slack in tendons for a given configuration. The proposed model is experimentally validated in a multitendon continuum robot system for four case studies of three- to six-tendon arrangements in open-loop control architecture. A stereo vision-based three-dimensional reconstruction system measures the beam configuration and properties for each of the three- to six-tendon continuum robots. The effect of number of tendons on the tension loads in $n$ -tendon continuum robots is studied. A quantitative dimensionless relationship between the number of tendons, the maximum tendon loads, and the bending angles is developed that may be used as a design tool for tradeoff among the complexity and required force and size.