Small Bending Stiffness Research Articles

Review of the Development of an Unbonded Flexible Riser: New Material, Types of Layers, and Cross-Sectional Mechanical Properties.

Unbonded flexible risers consist of several helical and cylindrical layers, which can undergo large bending deformation and can be installed in different configurations to adapt to harsh marine environments; thus, they can be applied to transport oil and gas resources from ultra-deep waters (UDW). Due to their special geometric characteristics, they can ensure sufficient axial tensile stiffness while having small bending stiffness, which can undergo large deflection bending deformation. In recent years, the development of unbonded flexible risers has been moving in an intelligent, integrated direction. This paper presents a review of unbonded flexible risers. Firstly, the form and properties of each interlayer of an unbonded flexible riser are introduced, as well as the corresponding performance and configuration characteristics. In recent years, the development of unbonded flexible risers has been evolving, and the development of machine learning on unbonded flexible risers is discussed. Finally, with emphasis on exploring the design characteristics and working principles, three new types of unbonded flexible risers, an integrated production bundle, an unbonded flexible riser with an anti-H2S layer, and an unbonded flexible riser with a composite armor layer, are presented. The research results show that: (1) the analytical methods of cross-sectional properties of unbonded flexible risers are solved based on ideal assumptions, and the computational accuracy needs to be improved. (2) Numerical methods have evolved from equivalent simplified models to models that account for detailed geometric properties. (3) Compared with ordinary steel risers, the unbonded flexible riser is more suitable for deep-sea resource development, and the structure of each layer can be designed according to the requirements of the actual environment.

Diffusion of nanochannel-confined knot along a tensioned polymer* *The National Natural Science Foundation of China under Grant Nos. 11864006, 11874309, 12164007, and 12204118.

The knots frequently occur in biopolymer and their diffusion plays an active role in the gene regulation. In this work, Langevin dynamics simulations were carried out to detect the diffusion behaviours of a knot along a tensioned polymer in different spatial constraints. The polymer accommodating a knot was tethered to two macrospheres to block the unravelling of the knot. As a result, the curves for the diffusion coefficients of the knot with different bending stiffness as a function of the tension in different spatial constraints were obtained. In the space without constraints or with weak constraints, the corresponding curves for the knot with relatively large bending stiffness exhibited two turnover behaviours. On the contrary, for the knot with relatively small bending stiffness, the diffusion coefficients were monotonically reduced with increasing tension. However, in a space with strong constraints, all the curves showed one turnover behaviour regardless of the bending stiffness. The turnover behaviours divided the curves into different regimes, and the dominant diffusion mechanisms in the regimes, namely, knot-region breathing, self-reptation, and internal friction, were clearly identified. The effective friction coefficients ξ of the knots with 31, 41, 51 and 52 types as a function of the knot size N at a fixed tension were well fitted by the relation ξ ∝ N. The effective friction coefficients of the knots at relatively large tension f > 3 sharply increased with the knot complexity, which is not dependent on the spatial constraints. By contrast, the values of these coefficients at relatively small tension f ≤ 3 were remarkably dependent on the spatial constraints. Our work not only provides valuable simulation results to assist the understanding of the diffusion of DNA knot, but also highlights the single-molecule design for the manipulation of DNA knots in future.

An Improved Analytical Model of a Thrust Stand with a Flexure Hinge Structure Considering Stiffness Drift and Rotation Center Offset

Micro-newton thrust stands are widely used in thruster ground calibration procedures for a variety of space missions. The conventional analytical model does not consider the gravity-induced extension effect and systematic error in displacement for thrust stands consisting of hanging pendulums based on flexure hinge structures. This paper proposes an improved analytical model of a hanging pendulum for thrust measurement, where an elliptical notched flexure hinge is the key component. A parametric model of the bending stiffness of the flexure hinge is developed. Equally, both the bending stiffness shift under the gravity-induced extension effect and the systematic error in displacement due to the assumed rotational center offset of the hinge are investigated. The presented stiffness equations for elliptical notched hinges can be degenerated into stiffness equations for circular notched as well as leaf-type hinges. The improved model aims to evaluate and highlight the influence of the two considered factors for use in thrust stand parameter design and thrust analysis. A finite element modeling solution is proposed to validate the proposed analytical model. The results show that the proposed model can quantify the hinge bending stiffness shift, which also demonstrates that even a small bending stiffness shift may introduce great uncertainty into the thrust analysis.

Bayesian forces identification in cable networks with small bending stiffness

The regular monitoring of cable forces is essential for ensuring the safety of cable structures both during construction and throughout their lifetime. This paper aims at developing a vibration-based identification procedure of the axial forces, bending stiffness, and, secondarily, the crossing point position of cable networks. A model constituted by two crossing stays having small bending stiffness and negligible sag effects is considered. The in-plane direct dynamic problem is solved both numerically and through a perturbation approach. The obtained results are compared to the outcomes of a finite element model for verification purposes. The theoretical studies are also supported by experimental tests performed on a real cable-stayed bridge (Haccourt bridge), which provide insights into the dynamics of the system showing that models of cables with small bending stiffness are more appropriate than taut string models. The inverse analysis based on non-linear Bayesian regression is developed and the closed-form asymptotic formulations are used to prove that the bending stiffness, the cable forces, and the crossing point position can be separately identified from a set of observed frequencies. The implemented procedure is then applied to the tested bridge as a proof of concept, showing that the proposed in-plane identification strategy provides satisfactory results.

The bubble effect on the thermal expansion coefficient of few-layer MoS2

The thermal expansion coefficient of van der Waals layered structures plays an important role in governing the thermal stability of high-performance electronic devices. Meanwhile, bubbles are frequently observed in the van der Waals layered structures due to the weak inter-layer interaction and the extremely small bending stiffness of the layered structure, but the effect of bubbles on the thermal expansion coefficient for layered structures remains unclear. We derive an analytic formula for the bubble effect on the length variation of the MoS2 layer. In the analytic derivation, the MoS2 layer is described by three mechanics models, including the elastic membrane theory, the nonlinear plate theory, and the linear plate theory. The gas inside the bubble is described by two types of state equations, including the ideal gas law and the generalized van der Waals equation. It is found that the nonlinear plate theory with the generalized van der Waals equation gives the most accurate description for the bubble effect, since MoS2 has a moderate bending stiffness. The analytic formula shows that the bubble can cause strong thermal contraction for few-layer MoS2 with increasing temperature. The analytic predictions are verified by comprehensive molecular dynamic simulations for few-layer MoS2 with different layer numbers and different gas molecule numbers. These results shall be valuable for understanding the thermal stability of functional devices based on the van der Waals layered structure.

Effect of external tension on the wetting of an elastic sheet

Recent studies of elastocapillary phenomena have triggered interest in a basic variant of the classical Young-Laplace-Dupré (YLD) problem: the capillary interaction between a liquid drop and a thin solid sheet of low bending stiffness. Here we consider a two-dimensional model where the sheet is subjected to an external tensile load and the drop is characterized by a well-defined Young's contact angle θ_{Y}. Using a combination of numerical, variational, and asymptotic techniques, we discuss wetting as a function of the applied tension. We find that, for wettable surfaces with 0<θ_{Y}<π/2, complete wetting is possible below a critical applied tension due to the deformation of the sheet in contrast with rigid substrates requiring θ_{Y}=0. Conversely, for very large applied tensions, the sheet becomes flat and the classical YLD situation of partial wetting is recovered. At intermediate tensions, a vesicle forms in the sheet, which encloses most of the fluid, and we provide an accurate asymptotic description of this wetting state in the limit of small bending stiffness. We show that bending stiffness, however small, affects the entire shape of the vesicle. Rich bifurcation diagrams involving partial wetting and "vesicle" solution are found. For moderately small bending stiffnesses, partial wetting can coexist with both the vesicle solution and complete wetting. Finally, we identify a tension-dependent bendocapillary length, λ_{BC}, and find that the shape of the drop is determined by the ratio A/λ_{BC}^{2}, where A is the area of the drop.

Mechanical property analysis and design parameter optimization of a novel nitinol nasal stent based on numerical simulation.

Background: A novel braided nasal stent is an effective alternative to nasal packing after septoplasty that can be used to manage the mucosal flap after septoplasty and expand the nasal cavity. This study aimed to investigate the influence of design parameters on the mechanical properties of the nasal stent for optimal performance. Methods: A braided nasal stent modeling method was proposed and 27 stent models with a range of different geometric parameters were built. The compression behavior and bending behavior of these stent models were numerically analyzed using a finite element method (FEM). The orthogonal test was used as an optimization method, and the optimized design variables of the stent with improved performance were obtained based on range analysis and weight grade method. Results: The reaction force and bending stiffness of the braided stent increased with the wire diameter, braiding density, and external stent diameter, while wire diameter resulted as the most important determining parameter. The external stent diameter had the greatest influence on the elongation deformation. The influence of design parameters on von-Mises stress distribution of bent stent models was visualized. The stent model with geometrical parameters of 25mm external diameter, 30° braiding angle, and 0.13mm wire diameter (A3B3C3) had a greater reaction force but a considerably smaller bending stiffness, which was the optimal combination of parameters. Conclusion: Firstly, among the three design parameters of braided stent models, wire diameter resulted as the most important parameter determining the reaction force and bending stiffness. Secondly, the external stent diameter significantly influenced the elongation deformation during the compression simulation. Finally, 25mm external diameter, 30° braiding angle, and 0.13mm wire diameter (A3B3C3) was the optimal combination of stent parameters according to the orthogonal test results.

Wrinkling and multiplicity in the dynamics of deformable sheets in uniaxial extensional flow

The processing of thin-structured materials in a fluidic environment, from nearly inextensible but flexible graphene sheets to highly extensible polymer films, arises in many applications. So far, little is known about the dynamics of such thin sheets freely suspended in fluid. In this work, we study the dynamics of freely suspended soft sheets in uniaxial extensional flow. Elastic sheets are modeled with a continuum model that accounts for in-plane deformation and out-of-plane bending, and the fluid motion is computed using the method of regularized Stokeslets. We explore two types of sheets: "stiff" sheets that strongly resist bending deformations and always stay flat, and "flexible" sheets with both in-plane and out-of plane deformability that can wrinkle. For stiff sheets, we observe a coil-stretch-like transition, similar to what has been observed for long-chain linear polymers under extension as well as elastic sheets under planar extension: in a certain range of capillary number (flow strength relative to in-plane deformability), the sheets exhibit either a compact or a highly stretched conformation, depending on deformation history. For flexible sheets, sheets with sufficiently small bending stiffness wrinkle to form various conformations. Here, the compact-stretched bistability still occurs, but is strongly modified by the wrinkling instability: a highly-stretched planar state can become unstable and wrinkle, after which it may dramatically shrink in length due to hydrodynamic screening associated with wrinkling. Therefore, wrinkling renders a shift in the bistability regime. In addition, we can predict and understand the nonlinear long-term dynamics for some parameter regimes with linear stability analysis of the flat steady states.

Multi-Objective Collaborative Flexibility Optimization Design of the Strengthening Layer of a Flexible Riser

Abstract Marine flexible risers are widely used in ocean oil and gas extraction, and need to withstand environment loads (wave and current) and the large offset of the floater. Therefore, the flexible riser is subjected to tension, bending, and torsion loads, which are mainly resisted by the key strengthening layer. Small bending stiffness of a cross section of the strengthening layer with larger tension and torsion stiffness are required to be compliant with the ocean environment. The traditional design of the key strengthening layer is partially rigid with larger cross-sectional stiffnesses. Therefore, the innovative configurations of the strengthening layer are imperative to make sure that the flexible riser is reliable and safe during the installation and operation. The strengthening layer of the flexible riser is treated as the cylindrical shell composed of periodic unit-cell beam structures, which is a hypothetical model. The optimization design is conducted through the novel implementation of the asymptotic homogenization (NIAH) method. The multi-objective collaborative flexibility optimization formulation of cylindrical shell structure is proposed, considering the ratio of cross-sectional tensile torsion stiffness to bending stiffness of the strengthening layer as the objectives. The optimal configuration results, the helically wound structures, are obtained, which are the alternative strengthening components of flexible risers. Finally, the optimal structures are compared with the commonly used marine flexible riser, which gives a great verification of the methodology feasibility and explains why the strengthening layer is designed as the type of helically wound structure.

Fiber Rearrangement and Matrix Compression in Soft Tissues: Multiscale Hypoelasticity and Application to Tendon.

It is widely accepted that the nonlinear macroscopic mechanical behavior of soft tissue is governed by fiber straightening and re-orientation. Here, we provide a quantitative assessment of this phenomenon, by means of a continuum micromechanics approach. Given the negligibly small bending stiffness of crimped fibers, the latter are represented through a number of hypoelastic straight fiber phases with different orientations, being embedded into a hypoelastic matrix phase. The corresponding representative volume element (RVE) hosting these phases is subjected to “macroscopic” strain rates, which are downscaled to fiber and matrix strain rates on the one hand, and to fiber spins on the other hand. This gives quantitative access to the fiber decrimping (or straightening) phenomenon under non-affine conditions, i.e. in the case where the fiber orientations cannot be simply linked to the macroscopic strain state. In the case of tendinous tissue, such an RVE relates to the fascicle material with 50 μm characteristic length, made up of crimped collagen bundles and a gel-type matrix in-between. The fascicles themselves act as parallel fibers in a similar matrix at the scale of a tissue-related RVE with 500 μm characteristic length. As evidenced by a sensitivity analysis and confirmed by various mechanical tests, it is the initial crimping angle which drives both the degree of straightening and the shape of the macroscopic stress-strain curve, while the final linear portion of this curve depends almost exclusively on the collagen bundle elasticity. Our model also reveals the mechanical cooperation of the tissue’s key microstructural components: while the fibers carry tensile forces, the matrices undergo hydrostatic pressure.

AFM-based indentation method for measuring the relaxation property of living cells

Probing the mechanical properties of cells is critical for understanding their deformation behaviors and biological functions. Although some methods have been proposed to characterize the elastic properties of cells, it is still difficult to measure their time-dependent properties. This paper investigates the use of atomic force microscope (AFM) to determine the reduced relaxation modulus of cells. In principle, AFM is hard to perform an indentation relaxation test that requires a constant indenter displacement during load relaxation, whereas the real AFM indenter displacement usually varies with time during relaxation due to the relatively small bending stiffness of its cantilever. We investigate this issue through a combined theoretical, computational, and experimental effort. A protocol relying on the choice of appropriate cantilever bending stiffness is proposed to perform an AFM-based indentation relaxation test of cells, which enables the measurement of reduced relaxation modulus with high accuracy. This protocol is first validated by performing nanoindentation relaxation tests on a soft material and by comparing the results with those from independent measurements. Then indentation tests of cartilage cells are conducted to demonstrate this method in determining time-dependent properties of living cells. Finally, the change in the viscoelasticity of MCF-7 cells under hyperthermia is investigated.

Behavior of concrete beams reinforced with FRP during bending

Article describes methods and results of experimental research for strain behavior, crack formation and fracture of concrete beams reinforced with fiber reinforced polymer (FRP) bars during bending moment action. 18 beams (3+3 series) reinforced with glass FRP (GFRP) and basalt (BFRP) 6, 10 and 14 mm in diameter were tested. Deflection in the middle of the beam, concrete and bars strain and ultrasonic transmission time for 4 routes were measured during tests besides visual inspection. Main crack formation occurred at 8-20% of the ultimate load for all beams. Crack formation was transition border to linear (elastic) straining at low bending stiffness. More than 15 times decrease in bending stiffness was seen for beam reinforced with two types of bars 6 mm in diameter compared to initial values. Existence of main cracks and major deflections is not allowed during design of bending elements. However small bending stiffness at linear elastic straining is a positive factor in case of «hard» loading and impact (pulsed) loading. It is possible to prevent structures collapse and people deaths at impact loading and cyclic «hard» loading by permitting crack formation in load bearing structures.

On the identification of the axial force and bending stiffness of stay cables anchored to flexible supports

The generic model of a cable with small bending stiffness and anchored to flexible supports in rotation and translation is considered. An asymptotic analysis of the natural frequencies of this generic model is derived and shows that, for small bending stiffness, the first few natural frequencies can be expressed as a function of the cable axial force, the small bending stiffness and a single dimensionless group collecting the information of all other problem parameters. This formulation is used to develop an identification procedure of the cable axial force. Two formulations are proposed, one numerical and one semi-analytical based on a simple linear regression model. Both methods do not attempt at separately identifying the problem parameters since the observability analysis has revealed that only the cable axial force, the bending stiffness and the dimensionless group can be identified. In particular, the second method is very simple to implement and provides estimates of the cable axial force which account for the flexibility of the support. The proposed method can therefore be seen as an extension of usual identification techniques based on linear regressions of natural frequencies vs. mode number relations, by considering at the same time the bending stiffness and the deformability of supports. Being simple and robust as shown by means of an uncertainty quantification analysis, the proposed method can be conveniently embedded in the framework of a continuous monitoring strategy.

Flexible heteroatom‐doped porous carbon nanofiber cages for electrode scaffolds

AbstractPorous carbon nanofibers (PCNFs) with rich functionalities and high surface areas are important electrode scaffolds to load active materials, but increasing their pore volumes and strength simultaneously is a challenge. Here, we report a scalable method to fabricate B‐F‐N triply doped PCNF cages with high porosity of greater than 92.8% and small bending stiffness of 10 mN by electrospinning the mixed sol of poly(tetrafluoroethylene), poly(vinyl alcohol), boric acid, and carbon nanotubes (CNTs) followed by pyrolysis. The macro‐micro dual‐phase separation creates well‐controlled macropores (&gt;60 nm) and meso‐micropores with large pore volumes (0.55 cm3/g) on carbon nanofibers, while the interior CNTs can cushion the applied stress and render the PCNF films with superior flexibility. Fabricated symmetrical supercapacitors with the PCNF cages exhibit high gravimetric capacitance of 164 F/g at 20 mV/s and 92.5% capacity retention after 20 000 cycles at 2 A/g. The reported approach allows the green synthesis of a new PCNF scaffold material with properties appealing for applications.

Multiplicity of stable orbits for deformable prolate capsules in shear flow.

This work investigates the orbital dynamics of a fluid-filled deformable prolate capsule in unbounded simple shear flow at zero Reynolds number using direct simulations. The motion of the capsule is simulated using a model that incorporates shear elasticity, area dilatation, and bending resistance. Here the deformability of the capsule is characterized by the nondimensional capillary number Ca, which represents the ratio of viscous stresses to elastic restoring stresses on the capsule. For a capsule with small bending stiffness, at a given Ca, the orientation converges over time towards a unique stable orbit independent of the initial orientation. With increasing Ca, four dynamical modes are found for the stable orbit, namely, rolling, wobbling, oscillating-swinging, and swinging. On the other hand, for a capsule with large bending stiffness, multiplicity in the orbit dynamics is observed. When the viscosity ratio λ ≲ 1, the long-axis of the capsule always tends towards a stable orbit in the flow-gradient plane, either tumbling or swinging, depending on Ca. When λ ≳ 1, the stable orbit of the capsule is a tumbling motion at low Ca, irrespective of the initial orientation. Upon increasing Ca, there is a symmetry-breaking bifurcation away from the tumbling orbit, and the capsule is observed to adopt multiple stable orbital modes including nonsymmetric precessing and rolling, depending on the initial orientation. As Ca further increases, the nonsymmetric stable orbit loses existence at a saddle-node bifurcation, and rolling becomes the only attractor at high Ca, whereas the rolling state coexists with the nonsymmetric state at intermediate values of Ca. A symmetry-breaking bifurcation away from the rolling orbit is also found upon decreasing Ca. The regime with multiple attractors becomes broader as the aspect ratio of the capsule increases, while narrowing as viscosity ratio increases. We also report the particle contribution to the stress, which also displays multiplicity.

Coupled flow and deformation fields due to a line load on a poroelastic half space: effect of surface stress and surface bending.

In the past decade, many experiments have indicated that the surfaces of soft elastic solids can resist deformation by surface stresses. A common soft elastic solid is a hydrogel which consists of a polymer network swollen in water. Although experiments suggest that solvent flow in gels can be affected by surface stress, there is no theoretical analysis on this subject. Here we study the solvent flow near a line load acting on a linear poroelastic half space. The surface of this half space resists deformation by a constant, isotropic surface stress. It can also resist deformation by surface bending. The time-dependent displacement, stress and flow fields are determined using transform methods. Our solution indicates that the stress field underneath the line load is completely regularized by surface bending-it is bounded and continuous. For small surface bending stiffness, the line force is balanced by surface stresses; these forces form what is commonly known as 'Neumann's triangle'. We show that surface stress reduces local pore pressure and inhibits solvent flow. We use our line load solution to simulate the relaxation of the peak which is formed by applying and then removing a line force on the poroelastic half space.

Numerical analysis of the wrinkling behavior of thin membranes

Membranes are widely applied in the large-span buildings and spatial deployable structures. They are prone to wrinkle under compression due to their small bending stiffness. The wrinkling deformation may affect the surface precision of a membrane structure and its static and dynamic behaviors. Research on the wrinkling behavior of a membrane and its variation with the wrinkle-influencing factors would shed light on the evolution of wrinkles and contribute significantly to the effective control over the wrinkling deformation. In this paper, a rectangular membrane under shear is numerically studied based on the stability theory of plates and shells to explore the wrinkle-influencing factors, such as boundary conditions, pre-stress, thickness and material constants, and their effects on the characteristic parameters of wrinkles. Besides, some of the results are also compared with those derived from the membrane element previously proposed by the authors for a further exploration. Some new and interesting findings are obtained.

Unusually high flexibility of graphene-Cu nanolayered composites under bending.

The mechanical properties of graphene-Cu nanolayered (GCuNL) composites under bend loading are investigated via an energy-based analytical model and molecular dynamics (MD) simulations. For an anisotropic material, if it has a weak strength in a certain direction, improving the mechanical properties along this direction is normally difficult for its composites. Here, we find that the flexibility of GCuNL composites can be improved considerably by graphene interfaces, despite graphene's small bending stiffness. The graphene interfaces can delocalize slip bands in the inner Cu layers of GCuNL composites, and impede local nucleation of dislocations, thus greatly increasing the yield and failure bend angles. As the thickness decreases, the flexibility of GCuNL nanofilms increases. However, the GCuNL nanofilms are thermodynamically unstable due to interface instability when the repeat layer spacing is less than 2 nm. The energy-based analytical model for large deformation can accurately characterize the bending response of GCuNL nanofilms.

Oscillations of a visco‐elastic belt drive

AbstractWe investigate the loss of stability of the steady configuration of a planar visco‐elastic belt drive. The belt is considered as a linearly visco‐elastic slender beam with small bending stiffness, which is driven by a steadily rotating drum. For a belt clamped on both ends at different heights no Hopf bifurcation is found, but a perturbed pitchfork bifurcation is observed. For a belt on a drum different Hopf bifurcation points are detected, which depend strongly on the viscous damping.

On boundary damping to reduce the rain\u2013wind oscillations of an inclined cable with small bending stiffness

In this paper, a model will be derived to describe the rain–wind-induced oscillations of an inclined cable. Water rivulets running along the cable and aerodynamics forces acting on the cable are taken into account to describe these oscillations. A boundary damper is assumed to be present near the lower endpoint of the cable. For a linearly formulated initial-boundary value problem for a tensioned beam equation describing the in-plane transversal oscillations of the cable, the effectiveness of this damper is determined by using a two-timescales perturbation method. It is shown how mode interactions play an important role in the dynamic behaviour of the cable system. Some resonant and non-resonant cases have been studied in detail.