Fiber Bending Stiffness Research Articles

The dynamics of fibres dispersed in viscoelastic turbulent flows

This study explores the dynamics of finite-size fibres suspended freely in a viscoelastic turbulent flow. For a fibre suspended in Newtonian flows, two different flapping regimes were identified by Rosti et al. (Phys. Rev. Lett., vol. 121, issue 4, 2018, 044501): one dominated by time scales from the flow, and another dominated by time scales associated with its natural frequency. We explore in this work how the fibre dynamics is modified by the elasticity of the carrier fluid. For this, we perform direct numerical simulations of a two-way coupled fibre–fluid system in a parametric space spanning different Deborah numbers, fibre bending stiffness (flexible to rigid) and linear density difference between the fibre and the flow (neutrally buoyant to denser-than-fluid fibres). We examine how these parameters influence various fibre characteristics such as the frequency of flapping, curvature, and alignment with the fluid strain and polymer stretching directions. Results reveal that the neutrally buoyant fibres, depending on their flexibility, oscillate with large and small time scales transpiring from the flow, but the smaller time scales are suppressed as the polymer elasticity increases. Polymer stretching is uncommunicative to denser-than-fluid fibres, which flap with large time scales from the flow when flexible, and with their natural frequency when rigid. Thus the characteristic elastic time scale has a subdominant effect when the fibres are neutrally buoyant, while its effect is absent when the fibres become more inertial. In addition, we also explore the fibre's bending curvature and its preferential alignment with the flow to identify the other roles of viscoelasticity in modifying the coupled fluid–structure dynamics. Inertial fibres have larger curvatures and are less responsive to the polymer presence, whereas the neutrally buoyant fibres show quantitative changes. The perceptible passivity of the denser fibres is again reflected in the way they align preferentially with the polymeric stretching directions: the neutrally buoyant fibres show a higher alignment with the polymer stretching directions compared to the denser ones. In a nutshell, the polymers exert a larger influence on neutrally buoyant fibres, which are more reflective of the polymeric influence in the flow. The study addresses comprehensively the interplay between polymer elasticity and the fibre structural properties in determining its response behaviour in an elasto-inertial turbulent flow.

Clots reveal anomalous elastic behavior of fiber networks.

The adaptive mechanical properties of soft and fibrous biological materials are relevant to their functionality. The emergence of the macroscopic response of these materials to external stress and intrinsic cell traction from local deformations of their structural components is not well understood. Here, we investigate the nonlinear elastic behavior of blood clots by combining microscopy, rheology, and an elastic network model that incorporates the stretching, bending, and buckling of constituent fibrin fibers. By inhibiting fibrin cross-linking in blood clots, we observe an anomalous softening regime in the macroscopic shear response as well as a reduction in platelet-induced clot contractility. Our model explains these observations from two independent macroscopic measurements in a unified manner, through a single mechanical parameter, the bending stiffness of individual fibers. Supported by experimental evidence, our mechanics-based model provides a framework for predicting and comprehending the nonlinear elastic behavior of blood clots and other active biopolymer networks in general.

Modeling the flexural rigidity of spunlace nonwoven fabrics

Nonwoven fabrics, especially spunlace varieties, find application across diverse fields. This study presents an analytical model that utilizes the energy method, factoring in bending and torsion strain energies. This model is integrated with the dynamic recursive splitting (DYRES) algorithm to predict the flexural rigidity by estimating fiber-to-fiber contacts within spunlace nonwoven fabrics. The input parameters for this proposed model encompass the number of bending couples, the bending stiffness of fibers, and the orientation characteristics of spunlace nonwoven fabrics. To validate the predictive capability of the model, six samples with varying fiber types, basis weights, and thicknesses were fabricated. A comparison between experimental and theoretical values reveals a consistent trend but with overestimated values in both the machine direction (MD) and cross-machine direction (CD). Through the utilization of two coefficients (0.7854 and 0.7823) to refine the presented model, an average relative error of 4.22% and 8.92% was achieved for the MD and CD directions, respectively. This research proposes a theory that utilizes fewer parameters compared to other studies in the field of nonwoven textiles. The proposed approach offers a more convenient and accessible method for obtaining these parameters, as well as determining the bending stiffness of the fabric. Moreover, advanced and more suitable techniques, including knot theory and image processing, have been employed to obtain accurate parameter measurements. This work is believed to lay the foundation for future investigations into the mechanical behavior of nonwoven fabrics.

A Non-Second-Gradient Model for Nonlinear Electroelastic Bodies with Fibre Stiffness

The study of the mechanical behaviour of fibre-reinforced electroactive polymers (EAPs) with bending stiffness is beneficial in engineering for mechanical design and problem solving. However, constitutive models of fibre-reinforced EAPs with fibre bending stiffness do not exist in the literature. Hence, to enhance the understanding of the mechanical behaviour of fibre-reinforced EAPs with fibre bending stiffness, the development of a relevant constitutive equation is paramount. In this paper, we develop a constitutive equation for a nonlinear nonpolar EAP, reinforced by embedded fibres, in which the elastic resistance of the fibres to bending is modelled via the classical branches of continuum mechanics without using the second gradient theory, which assumes the existence of contact torques. In view of this, the proposed model is simple and somewhat more realistic, in the sense that contact torques do not exist in nonpolar EAPs.

A non-second-gradient model for nonlinear elastic bodies with fibre stiffness

In the past, to model fibre stiffness of finite-radius fibres, previous finite-strain (nonlinear) models were mainly based on the theory of non-linear strain-gradient (second-gradient) theory or Kirchhoff rod theory. We note that these models characterize the mechanical behaviour of polar transversely isotropic solids with infinitely many purely flexible fibres with zero radius. To introduce the effect of fibre bending stiffness on purely flexible fibres with zero radius, these models assumed the existence of couple stresses (contact torques) and non-symmetric Cauchy stresses. However, these stresses are not present on deformations of actual non-polar elastic solids reinforced by finite-radius fibres. In addition to this, the implementation of boundary conditions for second gradient models is not straightforward and discussion on the effectiveness of strain gradient elasticity models to mechanically describe continuum solids is still ongoing. In this paper, we develop a constitutive equation for a non-linear non-polar elastic solid, reinforced by embedded fibers, in which elastic resistance of the fibers to bending is modelled via the classical branches of continuum mechanics, where the development of the theory of stresses is based on non-polar materials; that is, without using the second gradient theory, which is associated with couple stresses and non-symmetric Cauchy stresses. In view of this, the proposed model is simple and somewhat more realistic compared to previous second gradient models.

On the fully coupled dynamics of flexible fibres dispersed in modulated turbulence

The present work investigates the mechanical behaviour of finite-size, elastic and inertial fibres freely moving in a homogeneous and isotropic turbulent flow at moderate Reynolds number. Four-way coupled, direct numerical simulations, based on a finite difference discretisation and the immersed boundary method, are performed to mutually couple the dynamics of fibres and fluid turbulence, allowing us to account for the backreaction of the dispersed phase to the carrier flow. An extensive parametric study is carried out in zero-gravity condition over the characteristic properties of the suspension, i.e. fibre's linear density (from iso-dense to denser-than-the-fluid fibres), length (from short fibres comparable with the dissipative scale to long fibres comparable with the integral scale) and bending stiffness (from highly flexible to almost rigid fibres), as well as the concentration (from dilute to non-dilute suspensions). Results reveal the existence of a robust turbulence modulation mechanism that is primarily controlled by the mass fraction of the suspension (with only a minor influence of the fibre's bending stiffness), which is characterised in detail by means of a scale-by-scale analysis in Fourier space. Despite such alteration with respect to the single-phase case due to the non-negligible backreaction, fibres experience only two possible flapping states (previously identified in the very dilute condition) while being transported and deformed by the flow. In addition, we show that the maximum curvature obeys different scaling laws that can be derived from the fibre dynamical equation. Finally, we explore the clustering and preferential alignment of fibres within the flow, highlighting the peculiar role of inertia and elasticity.

Non-centrosymmetric solid core photonic crystal fiber for suppressing parasitic twist in fiber sensing coil

During the fabrication of fiber sensing coils, the parasitic twist of fibers would lead to the undesired elliptical birefringence in the fiber, which is the main cause of magnetically induced bias error for fiber optic gyroscope(FOG). For the purpose of suppressing the parasitic twist in the fiber coil, a polarization-maintaining solid core photonic crystal fiber (PCF) with non-centrosymmetric distribution of bending stiffness is proposed and investigated. The proposed PCF would bend towards a particular direction under the external forces, resulting in the consistency of birefringent axes arrangement, thus suppressing the nonreciprocal errors induced by both radial and axial components of the magentic field simultaneously. Dependence study of the fiber bending stiffness distribution on several key parameters is provided. The optical properties are also explored and compared with the previously studied PCF. Fiber coils fabricated with the proposed PCF are promising in reducing the magnetical sensitivity of FOG, thus making it possible for FOG to get rid of the thick magnetic shield, which is significant for the miniaturization of FOG.

Finite deformations of fibre-reinforced elastic solids with fibre bending stiffness – Part II: determination of the spherical part of the couple-stress

The indeterminacy of the spherical part of couple-stress is a well-known drawback of any theoretical formulation stemming from the Cosserat couple-stress theory of elasticity. The relevant theory of finite elastic deformations of solids reinforced by a family of fibres that resist bending is not an exception. The present communication extends and completes that theory in a manner that enables it to measure the spherical part of the couple-stress tensor outside the conventional equilibrium considerations. To achieve this, the present study reconsiders an extra piece of information that has surprisingly emerged already but, so far, has been left unexplained and unexploited; namely, the fact that the energy stored in a fibrous composite elastic solid with fibre-bending stiffness involves a couple-stress generated term that does not influence the relevant couple-stress constitutive equation. The thus resulting new theoretical development complements the theory previously presented without dismissing any of the theoretical results detailed or the conclusions drawn there. Its validity embraces boundary value problems concerning both finite and infinitesimal elastic deformations of polar fibrous composites. In the latter case, its applicability is also tested and verified through the successful determination of the spherical couple-stress of a polar transversely isotropic elastic plate subjected to pure bending.

A mixed finite element formulation for energy‐momentum time integrations of composites with fiber bending stiffness

AbstractWe aim at dynamic simulations of 3D‐fiber‐reinforced materials in light‐weight structures, which are reinforced by fiber rovings comprised of thousands of filaments. Each roving possesses a separate bending stiffness, which has a large influence on the material behaviour on the macro scale. For the description of this material behavior, we extend a hyperelastic anisotropic Cauchy continuum formulation, which models only the macro‐scopic behaviour of a reinforcement by filaments, by a higher‐order gradient of the deformation mapping as an independent field. The new mixed finite element formulation is based on well‐known mixed finite elements for anisotropic polyconvex material formulations, but include new additional mixed fields concernd with the fiber bending stiffness. As we aim at dynamic long‐term simulations, we apply higher‐order accurate time integrators. Here, we include the new mixed finite element formulation in a variational‐based time finite element method. As numerical examples serve a simple cantilever beam. Here, we first analyze the influence of the fiber bending stiffness.

Modeling of fiber‐bending stiffness in fiber‐reinforced composites with a dynamic mixed finite element method based on the principle of virtual power

AbstractInvestigating the bending stiffness of fibers in fiber‐reinforced composites for rotor‐dynamical systems which are subjected to dynamical loads are essential in the development of system design. The proposed numerical modeling approach of fiber‐reinforced composites uses a multi‐field mixed finite element formulation based on a dynamic variational approach to perform long‐term dynamic simulations with CPU‐time efficient and increased accurate numerical solutions. To model the bending stiffness of fibers accurately, we extend a Cauchy continuum with higher‐order gradients of the deformation mapping as an independent field in the functional formulation. This extended continuum also takes into account the higher‐order energy contributions including the fiber curvature along with popular proven approaches that efficiently avoid the numerical locking effect of the fibers. The effect of the proposed approach is demonstrated through transient dynamic analysis on a cantilever beam with a hyperelastic, transversely isotropic, polyconvex material behavior. The beam is subjected to bending load with a strong dependence of the overall stiffness on the fiber orientation. The material and conservation properties are analyzed.

A micropolar approach to microbuckling problems in unidirectionally reinforced polymer composites

The present contribution considers the application of micropolar continuum theory to predict the microbuckling strength of microbuckling problems in long fiber reinforced composites and to extend simulations into the collapse regime. The approach considers a homogenized description at a coarse length scale where fiber and matrix phases are not individually resolved, but are represented indirectly via an effectively equivalent homogenized solid. The salient characteristic of this approach is its superior numerical efficiency over a fine-scale micromechanical representation where fibers and matrix would need to be discretized separately. A disadvantage of conventionally homogenized models, however, is the circumstance that fiber curvature is not accounted for. Hence, the local fiber bending stiffness cannot be preserved in the homogenization process and the strain localization stage of microbuckling problems is rendered ill-posed. Micropolar homogenization rectifies this deficiency by introducing additional rotational degrees of freedom to account for curvature strain. The present contribution distinguishes itself from earlier micropolar homogenization approaches by adapting a Total-Lagrangian finite strain plasticity theory for micropolar continua to the microbuckling problem under consideration here. From this theoretical basis, a constitutive model and a finite element formulation are derived, and the extra parameters introduced by the micropolar solid are identified.

A finite deformation isogeometric finite element approach to fibre-reinforced composites with fibre bending stiffness

It is a common technique in many fields of engineering to reinforce materials with certain types of fibres in order to enhance the mechanical properties of the overall material. Specific simulation methods help to predict the behaviour of these composites in advance. In this regard, a widely established approach is the incorporation of the fibre direction vector as an additional argument of the energy function in order to capture the specific material properties in the fibre direction. While this model represents the transverse isotropy of a material, it cannot capture effects that result from a bending of the fibres and does not include any length scale that might allow the simulation of size effects. In this contribution, an enhanced approach is considered which relies on the introduction of higher-gradient contributions of the deformation map in the stored energy density function and which eventually allows accounting for fibre bending stiffness in simulations. The respective gradient fields are approximated by NURBS basis functions within an isogeometric finite element framework by taking advantage of their characteristic continuity properties. The isogeometric finite element approach that is presented in this contribution for fibre-reinforced composites with fibre bending stiffness accounts for finite deformations. It is shown that the proposed method is in accordance with semi-analytical solutions for a representative boundary value problem. In an additional example it is observed that the initial fibre orientation and the particular bending stiffness of the fibres influence the deformation as well as the stress response of the material.

On three-dimensional dynamics of fibre-reinforced functionally graded plates when fibres resist bending

This communication aims to initiate an investigation towards understanding the influence that fibre bending stiffness has on the three-dimensional dynamic behaviour of fibrous composites with embedded functionally graded stiff fibres. In this context, it (i) formulates the general dynamical problem of a rectangular plate with embedded a single family of straight fibres that possess bending resistance and are distributed in a controlled, functionally graded manner through the plate thickness, and (ii) for simple support boundary conditions, it solves the free relevant vibration problem. The problem formulation is based on principles of polar linear elasticity and leads to a high-order set of Navier-type partial differential equations with variable coefficients. For simply supported edge boundaries, solution of these equations is achieved with the use of a computationally efficient semi-analytical (so-called fictitious layer) mathematical method. Two types of possible inhomogeneous distributions of straight fibres are considered for computational and numerical result presentation purposes. These are both regarded as possible, realistic types of inhomogeneous redistributions of stiff fibres that in previous studies have been assumed homogeneously distributed throughout the plate body. The presented numerical results examine to a considerable extent the manner that either of the employed types of inhomogeneous fibre redistribution, in conjunction with the fibre ability to resist bending, affects the dynamic behaviour of the fibrous composite plate of interest.

An isogeometric finite element approach to fibre-reinforced composites with fibre bending stiffness

In the modelling of fibre-reinforced composites, it is well established to consider the fibre direction in the stored energy in order to account for the transverse isotropy of the overall material, induced by a single family of fibres. However, this approach does not include any length scale and therefore lacks in the prediction of size effects that may occur from the fibre diameter or spacing. By making use of a generalised continuum model including non-symmetric stresses and couple-stresses, the gradient of the fibre direction vector can be taken into account as an additional parameter of the stored energy density function. As a consequence, the enhanced model considers the bending stiffness of the fibres and includes information on the material length scale. Along with additional material parameters, increased continuity requirements on the basis functions follow in the finite element analysis. The isogeometric finite element method provides a framework which can fulfil these requirements of the corresponding weak formulation. In the present contribution, the method is applied to two representative numerical examples. At first, the bending deformation of a cantilever beam is studied in order to analyse the influence of the fibre properties. An increasingly stiff response is observed as the fibre bending stiffness increases and as the fibre orientation aligns with the beam’s axis. Secondly, a fibre-reinforced cylindrical tube under a pure azimuthal shear deformation is considered. The corresponding simulation results are compared against a semi-analytical solution. It is shown that the isogeometric analysis yields highly accurate results for the boundary value problem under consideration.

Numerical modelling of 2D composite solids accounting for local fibre bending stiffness

This contribution deals with the development of a four-node membrane composite finite element to analyse two-dimensional (2D) fibre-reinforced solids taking into account the local bending stiffness of fibres. This plane composite element is a combination of a four-node membrane element with rotational degrees of freedom (DOFs), modelling a unit of the matrix domain, and two-node Timoshenko beam elements that represent fibres crossing each matrix element. The so-called ’Projected Fibre Approach’ is then considered to express the beam elements variables in terms of their corresponding matrix elements. Accordingly, the obtained system of equations size is equivalent to that of a non-reinforced medium which considerably reduces the computing cost. To assess the accuracy of the proposed plane element, three examples are presented and the obtained results are found to agree well with the reference solutions.

Length scale dependent elasticity in random three-dimensional fiber networks

The mechanics of fibrous materials are complicated by complex deformation mechanisms that result from the discrete fibrous structure. Though it is known that fibrous materials deform primarily by rotating and bending of fibers, the implications of rotating and bending on the mechanics of the network are not fully clear. Previous studies have investigated some effects of the fiber rotation and bending, observing fibers to rotate into directions of maximum principal stress, resulting in strain stiffening, and fibers under compression to buckle, resulting in compression softening. Nonlinear constitutive models have recently been developed to account for these deformation mechanisms, but the classical constitutive models that account for only stress and strain cannot fully account for fiber rotations and bending. Here, we interpret the mechanics of fibrous materials through micropolar elasticity, also called Cosserat elasticity, which differs from classical elasticity in that it accounts for local moments caused by rotation of points within a material. The resulting equations can be written in terms of characteristic lengths that cause stress to depend on both strain and the length scale of the material. We simulated three-dimensional networks of fibers and observed a strong effect of length scale on the stiffness of networks in bending with a more mild effect in torsion. The length-scale dependence of stiffness is consistent with micropolar elasticity and can be described in terms of characteristic lengths of the material. Factors affecting the characteristic length were investigated by altering the fiber density, alignment, and bending stiffness. Although density was found to have no effect on characteristic length, increased fiber alignment led to a decrease in characteristic length, and increased fiber bending stiffness led to an increase in characteristic length. These findings suggest that the characteristic length is increased by factors that increase bending moments supported by the fibers. Although our parameter study manipulated the magnitude of characteristic length, no combination of parameters gave a characteristic length of zero, indicating that the mechanics of fibrous materials depend on length scale.

The effective tensile and bending stiffness of nanotube fibers

We analyze the pure bending state, preliminarily considering the pure traction problem, for a fiber with circular cross-section composed by monodispersed Nano Tube (NT) segments, whose length is much lower than the length of the fiber, arranged in a cross-sectional square lattice, possibly inclined with respect to the bending plane. The proposed model accounts for the compliant shear coupling of the constituent NTs along their lateral contact surfaces, and considers that the position of each NT is offset with respect to the neighboring ones by a fixed distance. The shearing of the NTs permits their mobility in longitudinal direction, inducing an internal rearrangement, calculated through energy minimization, that affects the macroscopic response. With a micro-macro approach, the internal actions in the whole fiber are calculated. We find that uniform axial macroscopic strain is associated with constant tensile normal force in the fiber and null moment; correspondingly, constant macroscopic curvature provides a constant bending moment in the plane of bending and null axial force. It is then possible to consider the NT fiber as an equivalent homogeneous beam, whose effective tensile and bending stiffness can be calculated, finding a dependence upon the aspect ratio of the fiber, the aspect ratio of the individual NTs and, more important, the offset of the NTs. The model permits to interpret recent experimental results.

Random fiber networks with inclusions: The mechanism of reinforcement.

The mechanical behavior of athermal random fiber networks embedding particulate inclusions is studied in this work. Composites in which the filler size is comparable with the mean segment length of the network are considered. Inclusions are randomly distributed in the network at various volume fractions, and cases in which fibers are rigidly bonded to fillers and in which no such bonding is imposed are studied separately. In the presence of inclusions, the small strain modulus increases, while the ability of the network to strain stiffen decreases relative to the unfilled network case. The reinforcement induced by fillers is most pronounced in sparse networks of floppier filaments that deform in the bending-dominated mode in the unfilled state. As the unfilled network density or the bending stiffness of fibers increases, the effect of filling diminishes rapidly. Fillers lead to a transition from the soft, bending-dominated, to the stiffer, stretching-dominated, deformation mode of the network, a transition which is primarily responsible for the observed overall reinforcement. The confinement, i.e., the restriction on network kinematics imposed by fillers, causes this transition. These results provide a justification for the observed difference in reinforcement obtained in sparsely versus densely cross-linked networks at a given filling fraction and provide guidance for the further development of network-based materials.

Preparation and testing of fibre reinforced <i>Zea mays</i> and <i>Calotropis gigantea</i> concrete material under various testing conditions

This paper provides an implementation of improved modelling of fibre reinforced composites with natural fibres namely: Zea mays and Calotropis gigantea. The main aim of inducing such natural fibres to form composites is to improve its structural and water resistant properties. These natural fibres are used for improving the fibre bending stiffness that enhances the strength of the concrete composites. The proposed method uses hand layup method to prepare the solid composite under varying temperature and period. The use of randomly oriented discontinuous fibre reinforced composite is used for preparing the mould. Further, three different samples are prepared using the mould for tensile testing, impact testing and water absorption testing. This improves the structural properties, composite strength with increased fibre length, fineness without grains, uniformity and stiffness. The test results show that the proposed pattern for improving the fibre reinforced concrete composite improves well its structural and other related properties of the concrete with higher tensile and impact factors.

Numerical simulation of the fiber trajectories in vortex spinning under different process parameters based on the finite element model

This paper studied the fiber movement in vortex spinning based on the flexible fiber finite element model, according to the theoretical mechanical analysis of the vortex spun yarn forming process. The finite element simulation and analysis of the different trajectories of free-end fiber in vortex spinning under different process parameters were carried out. The influence of the fiber count, fiber bending stiffness and nozzle pressure on the fiber transfer and distribution was analyzed and verified by experiments of tracer fiber and yarn slicing. The numerical simulation and the experiments’ results show a consistent correlation of different process parameters and fiber movement, such as the fiber diameter increasing, the fiber bending stiffness increasing, the nozzle pressure decreasing, and the fiber tending to get a smaller twist angle and becoming more easily distributed in the center of the yarn. This paper provides a theoretical basis for the structure design of vortex spun yarn and the production pr...