Fiber-fiber Interactions Research Articles

Non-linear analysis of anisotropic coated fabric utilizing Variational Asymptotic Method

The dimensional reduction of a hyperelastic coated fabric from 3D to 2D is accomplished asymptotically using the Variational Asymptotic Method (VAM). This method integrates constrained calculus of variations and asymptotics. The VAM bifurcates the analysis into two: a 1D through-the-thickness analysis and a 2D reference surface analysis. The 1D analysis leads to the derivation of an asymptotically correct 3D warping functions and a 2D non-linear constitutive law. The 2D non-linear reference surface analysis utilizes the derived 2D non-linear constitutive law to obtain 2D displacements and strains through the 2D non-linear FEA. The classification of 3D strain energy density into distinct orders is enabled by introducing two intrinsic small parameters: 1) a geometric small parameter denoted by the ratio of thickness to characteristic length (h/l≪1), and 2) a physical small parameter that ensures the largest component of 3D strain is restricted to 20 percent, which is less than 1. The model takes into account both geometric and material nonlinearities. The strain energy function, which describes the anisotropic characteristics of the coated fabric has contributions from the strain energies of fiber, matrix, and fiber-fiber interaction. The findings of the study include analytically derived 3D warping functions, a 2D nonlinear constitutive law, and the prediction of warp and weft stresses and strain for a biaxial loaded tensile specimen. These findings align with the experimental outcomes.

In situ experimental investigation of fiber orientation kinetics during uniaxial extensional flow of polymer composites

The demand for fiber-filled polymers has witnessed a significant upswing in recent years. A comprehensive understanding of the local fiber orientation is imperative to accurately predict the mechanical properties of fiber-filled products. In this study, we experimentally investigated the fiber orientation kinetics in uniaxial extensional flows. For this, we equipped a rheometer with a Sentmanat extensional measurement device and with an optical train that allows us to measure the fiber orientation in situ during uniaxial extension using small angle light scattering. We investigated an experimental system with glass fibers for the suspended phase (L/D=8−15), and for the matrix either low density polyethylene, which shows strain hardening in extension, or linear low density polyethylene, which shows no strain hardening. For these two polymer matrices, the fiber orientation kinetics were investigated as a function of fiber volume fraction (ϕ=1%, 5%, and 10%) and Weissenberg number (by varying the Hencky strain rate, ϵ˙H=0.01−1s−1). We found that all these parameters did not influence the fiber orientation kinetics in uniaxial extension and that these kinetics can be described by a multiparticle model, based on Jeffery’s equation for single particles. Our results show that, in uniaxial extension, fiber orientation is solely determined by the applied strain and that, up to the concentrated regime (ϕ≈D/L), fiber-fiber interactions do not influence the fiber orientation. The extensional stress growth coefficient of these composites, which is measured simultaneously with the orientation, shows high agreement with Batchelor’s equation for rodlike suspensions.

Simulation of fiber-induced melt pressure fluctuations within large scale polymer composite deposition beads

The process-structure-property relationship in Large Area Additive Manufacturing (LAAM) technology is an ongoing area of research as the inherent microstructural properties (chiefly fibers and voids) affect the performance of printed parts. Unfortunately, we currently lack adequate understanding of micro void nucleation and evolution during the LAAM and fused deposition modelling (FDM) processes. Modeling of the polymer melt flow during the extrusion process is important in understanding the underlying microstructural formation and associated properties of the print, that determines the part performance in service conditions. In this paper we compute fiber-induced local pressure fluctuations which may promote void formation in the bead’s microstructure. On a macro-scale, we determine flow fields of a purely viscous, Newtonian planar polymer deposition flow through a LAAM nozzle which are utilized on a micro-scale model where we simulate the evolution of a single ellipsoidal fiber along streamlines obtained from the macro-model. On the micro-scale, we determine instantaneous values of the translational and rotational velocities of the rigid ellipsoidal fiber that satisfies a balance of hydrodynamic forces and couples on the fiber’s surface based on a Newton Raphson algorithm and we track the fiber’s motion along the flow path via an explicit numerical iterative algorithm. Model verification is achieved by benchmarking results with solutions from well-known Jeffery’s equation of motion of a particle in homogeneous simple shear flow. We account for rotary diffusivity due to short-range fiber-fiber interaction in the FEA simulation by determining an effective fluid domain size representative of the interaction coefficient of the melt flow through a correlation analysis that yields an equivalent steady state orientation based on the Advani-Tucker equation. We also consider different possible motions of the fiber along individual LAAM flow paths from a given set of random initial fiber conditions to determine pressure bounds on the fiber surface along each streamline. For improved computational efficiency, calculations are carried out with respect to the fiber’s local coordinate axes to overcome the rigor of adaptive remeshing during the quasi-transient analysis. Results show low pressure extremes near the fiber’s surface which varies across the printed bead as well as through its thickness. Discussion is provided to gain insight into the effect of low-pressure extremes on micro void formation, particularly at the nozzle exit and during die swell/expansion.

Electrohydrodynamic Printing of Microfibrous Architectures with Cell-Scale Spacing for Improved Cellular Migration and Neurite Outgrowth.

Electrohydrodynamic (EHD) printing provides unparalleled opportunities in fabricating microfibrous architectures to direct cellular orientation. However, it faces great challenges in depositing orderly microfibers with cell-scale spacing due to inherent fiber-fiber electrostatic interactions. Here a finite element method is established to analyze the electrostatic forces induced on the EHD-printed microfibers and the relationship between the fiber diameter and spacing for parallel deposition of EHD-printed microfibers is revealed theoretically and experimentally. It is found that uniform fiber arrangement can be achieved when the fiber spacing is five times larger than the fiber diameter. This finding enables the successful printing of parallel fibrous architectures with a fiber diameter of 4.9 ± 0.1µm and a cell-scale fiber spacing of 25.6 ± 1.9µm. The resultant microfibrous architectures exhibit unique capability to direct cellular alignment and enhance cellular density and migration as the fiber spacing decreases from 100 to 25µm. The EHD-printed parallel microfibers with cell-scale spacing are found to improve the outgrowth length of neurites and accelerate the migration of Schwann cells from Dorsal Root Ganglion spheres, which facilitate the formation of densely-arranged and highly-aligned cellular constructs. The presented method is promising to produce biomimetic microfibrous architectures for functional nerve regeneration.

Hybrid hierarchical homogenization theory for unidirectional CNTs-coated fuzzy fiber composites undergoing inelastic deformations

A new hybrid homogenization approach is proposed for simulating the homogenized and local response of unidirectional fuzzy fiber nanocomposites undergoing inelastic deformations. Fuzzy fiber composites are hierarchical reinforcing structures where the fibers coated with radially aligned carbon nanotubes (CNTs) are embedded in the matrix. In this spirit, the fuzzy fiber composites are modeled as a three-scale medium. At the microscale, the CNTs-reinforced matrix is homogenized as nanocomposite interphase (NCP) attached to the main fiber via the asymptotic expansion homogenization (AEH). At the mesoscale, an intermediate equivalent fiber that substitutes for the NCP and the main fiber is constructed using the composite cylinder assemblage (CCA) and the transformation field analysis (TFA) techniques. At the macroscale, homogenization of the equivalent fiber and the surrounding matrix is handled by AEH which yields the effective response of the whole fuzzy fiber composites. The new technique facilitates accurate and efficient studies of the inelastic deformation mechanisms of periodic fuzzy fiber arrays with single or multiple inclusions under biaxial and triaxial loading conditions, eliminating exhausting interphase mesh discretizations encountered in the classical full-field homogenization. An added advantage is that the proposed theory captures the fiber-fiber interaction neglected in the classical CCA-TFA, an issue that leads to the exceptionally stiff post-yielding stress-strain response common in the mean-field micromechanics approaches.

Asymptotic fiber orientation states of the quadratically closed Folgar–Tucker equation and a subsequent closure improvement

Anisotropic fiber-reinforced composites are used in lightweight construction, which is of great industrial relevance. During mold filling of fiber suspensions, the microstructural evolution of the local fiber arrangement and orientation distribution is determined by the local velocity gradient. Based on the Folgar–Tucker equation, which describes the evolution of the second-order fiber orientation tensor in terms of the velocity gradient, the present study addresses selected states of deformation rates that can locally occur in complex flow fields. For such homogeneous flows, exact solutions for the asymptotic fiber orientation states are derived and discussed based on the quadratic closure. In contrast to the existing literature, the derived exact solutions take into account the fiber-fiber interaction. The analysis of the asymptotic solutions relying upon the common quadratic closure shows disadvantages with respect to the predicted material symmetry, namely, the anisotropy is overestimated for strong fiber-fiber interaction. This motivates us to suggest a novel normalized fully symmetric quadratic closure. Two versions of this new closure are derived regarding the prediction of anisotropic properties and the fiber orientation evolution. The fiber orientation states determined with the new closure approach show an improved prediction of anisotropy in both effective viscous and elastic composite behaviors. In addition, the symmetrized quadratic closure has a simple structure that reduces the effort in numerical implementation compared to more elaborated closure schemes.

Thermosetting supramolecular polymerization of compartmentalized DNA fibers with stereo sequence and length control

Thermosetting supramolecular polymerization of compartmentalized DNA fibers with stereo sequence and length control

Theoretical approximation of hydrodynamic and fiber-fiber interaction forces for macroscopic simulations of polymer flow process with fiber orientation tensors

Flow processes of discontinuous fiber reinforced polymers (FRPs) are the essence of several polymer-based manufacturing processes. FRPs show a transient chemo-thermomechanical matrix behavior and fiber-induced anisotropic physical properties. Therefore, they are one of the most complex materials used in volume production. The general flow behavior is influenced by fibers and their interactions with the matrix and other fibers. The consideration of individual fibers is numerically not capable for process simulation of FRP parts. Therefore, orientation tensors are used in macroscopic simulations, leading to a loss of information about the fiber network. Within this work, novel approximation schemes are presented to determine hydrodynamic and fiber-fiber contact forces with information provided by the second order fiber orientation tensor. Approximation of these forces can henceforth facilitate fiber breakage modeling in macroscopic process simulations. The results are verified by numerical simulations with individual fibers of different orientation states and lengths, showing good agreement with the verification results.

Diffusion, extensibility, flow, and orientation coupling in polymers filled with extensible and flexible fibers

When a fiber is subjected to flow and mass transport, it deforms and swells and thus its orientation and length change accordingly. As a starting point, a semi-kinetic equation is proposed to describe the time evolution of the length and orientation of extensible fibers. Then a mesoscopic model, explicitly incorporating the coupling arising among flow, mass transport, and fibers extensibility and orientation in a mixture composed of a solvent and a fiber-reinforced polymer (FRP), is formulated. The derived governing and constitutive equations possess the GENERIC structure and are parameterized by mobility coefficients and the Helmholtz free energy density. The latter takes into account the orientational ordering of the fibers, the fiber-fiber topological interactions, and the flexible nature of the fibers. The unidirectional flow-free mass transport is thoroughly discussed via scaling analysis, numerical solutions, and comparison with sorption data selected from literature. The dynamics of the boundaries is also examined.

Direct simulation of fiber suspensions under smalland large amplitude oscillatory shear flow

Experimentally, oscillatory shear flow is used to investigate polymeric viscoelastic properties. However, the knowledge of the microstructure’s orientation evolution (kinematics) with time is essential in order to predict those properties, and is difficult experimentally. Therefore it is often required to conduct numerical simulations to get insight on the kinematics evolution of fiber suspensions. The main aim of the current work is to use direct numerical simulations to investigate the time evolution of the orientation and kinematics of fiber suspensions under small and large amplitude oscillatory shear flow. Keywords: fiber suspensions; direct numerical simulation; oscillatory shear flow; fiber-fiber interactions;

Effects of Fiber Density and Strain Rate on the Mechanical Properties of Electrospun Polycaprolactone Nanofiber Mats.

This study examines the effects of electrospun polycaprolactone (PCL) fiber density and strain rate on nanofiber mat mechanical properties. An automated track collection system was employed to control fiber number per mat and promote uniform individual fiber properties regardless of the duration of collection. Fiber density is correlated to the mechanical properties of the nanofiber mats. Young's modulus was reduced as fiber density increased, from 14,901 MPa for samples electrospun for 30 s (717 fibers +/– 345) to 3,615 MPa for samples electrospun for 40 min (8,310 fibers +/– 1,904). Ultimate tensile strength (UTS) increased with increasing fiber density, where samples electrospun for 30 s resulted in a UTS of 594 MPa while samples electrospun for 40 min demonstrated a UTS of 1,250 MPa. An average toughness of 0.239 GJ/m3 was seen in the 30 s group, whereas a toughness of 0.515 GJ/m3 was observed at 40 min. The ultimate tensile strain for samples electrospun for 30 s was observed to be 0.39 and 0.48 for samples electrospun for 40 min. The relationships between UTS, Young's modulus, toughness, and ultimate tensile strain with increasing fiber density are the result of fiber-fiber interactions which leads to network mesh interactions.

Collagen fiber interweaving is central to sclera stiffness

The mechanical properties of the microstructural components of sclera are central to eye physiology and pathology. Because these parameters are extremely difficult to measure directly, they are often estimated using inverse-modeling matching deformations of macroscopic samples measured experimentally. Although studies of sclera microstructure show collagen fiber interweaving, current models do not account for this interweaving or the resulting fiber-fiber interactions, which might affect parameter estimates. Our goal was to test the hypothesis that constitutive parameters estimated using inverse modeling differ if models account for fiber interweaving and interactions. We developed models with non-interweaving or interweaving fibers over a wide range of volume fractions (36–91%). For each model, we estimated fiber stiffness using inverse modeling matching biaxial experimental data of human sclera. We found that interweaving increased the estimated fiber stiffness. When the collagen volume fraction was 64% or less, the stiffness of interweaving fibers was about 1.25 times that of non-interweaving fibers. For higher volume fractions, the ratio increased substantially, reaching 1.88 for a collagen volume fraction of 91%. Simulating a model (interweaving/non-interweaving) using the fiber stiffness estimated from the other model produced substantially different behavior, far from that observed experimentally. These results show that estimating microstructural component mechanical properties is highly sensitive to the assumed interwoven/non-interwoven architecture. Moreover, the results suggest that interweaving plays an important role in determining the structural stiffness of sclera, and potentially of other soft tissues in which the collagen fibers interweave. Statement of SignificanceThe collagen fibers of sclera are interwoven, but numerical models do not account for this interweaving or the resulting fiber-fiber interactions. To determine if interweaving matters, we examined the differences in the constitutive model parameters estimated using inverse modeling between models with interweaving and non-interweaving fibers. We found that the estimated stiffness of the interweaving fibers was up to 1.88 times that of non-interweaving fibers, and that the estimate increased with collagen volume fraction. Our results suggest that fiber interweaving is a fundamental characteristic of connective tissues, additional to anisotropy, density and orientation. Better characterization of interweaving, and of its mechanical effects is likely central to understanding microstructure and biomechanics of sclera and other soft tissues.

The shear and compressive yield stress of fibrillated acacia pulp fiber suspensions

Abstract The degree of interactions between fibers and the tendency of fibers to form flocs play an important role in effective unit operation in pulp and paper industry. Mechanical treatments may damage the structure of the fiber cell wall and geometrical properties, and ultimately change the fiber-fiber interactions. In this study, the gel crowding number, compressive and shear yield stress of fibrillated acacia pulps were investigated, and the results showed that the gel crowding number of the refined pulp samples ranged from 8.7 to 10.7, which were much lower than that of un-refined pulps. As the concentration increased, both the compressive yield stress P y {P_{y}} and shear yield stress τ y {\tau _{y}} of all suspensions increased accordingly, and the yield stress was found to depend on a power law of the crowding number. Moreover, the values of τ y / P y {\tau _{y}}/{P_{y}} were also examined and the variation of τ y / P y {\tau _{y}}/{P_{y}} became largely dependent on the fiber morphology and mass concentration.

The morphological effect of carbon fibers on the thermal conductive composites

The locally-exact homogenization theory (LEHT) with thermal conductive capability is developed to investigate the morphological effect of carbon/graphite fibers on the effective and localized thermal responses of periodic composites. Based on the orientations of basal planes, the material properties of carbon fibers can be transversely isotropic, radially orthotropic or circumferentially orthotropic, possibly influencing the microscopic behavior of thermal conductive composites. By taking fiber-fiber interactions into account, repeating unit cells (RUCs) of hexagonal and rectangular geometries are considered with large fiber volume fractions. The efficiency and stability of the LEHT are guaranteed by solving the complete internal eigenvalue functions, imposing point-wise continuity conditions, as well as implementing the generalized variational principle. It is demonstrated that the present theory exhibits good agreement with the independently developed Eshelby solutions and Hashin's formula. The morphological effects are also tested by generating effective coefficients over a wide range of fiber volume fractions and recovering the local thermal field concentrations within the composite microstructures. The results clearly indicate that even if the homogenized properties are not significantly affected by the morphologies of carbon fibers by satisfying the replacement scheme, the large heat-flux gradients within the orthotropic fibers could still lead to the split of carbon reinforcement.

Numerical simulation and modeling of the die swell for fiber suspension flows

A numerical model is developed to examine the die swell for fiber suspensions, which occurs in 3D printing extrusion processes. More specifically, it focuses on the fiber orientation distribution in a Newtonian suspending fluid and its effects on the shape of the free surface. In a first step, the flow in a 2D axisymmetric capillary die is explored in order to validate the numerical implementation for the fiber orientation model. It is found that the coupling effect flattens the velocity profile but has a small impact on the fiber orientation distribution in the suspension flow. In a second step, the modeling of die swell is considered and result from the literature for the final swelling height is obtained for an uncoupled flow. For fully coupled flows, different values for the coupling parameter and the fiber-fiber interaction coefficient have been tested in order to observe their effects on the free surface shape and on the final fiber orientation distribution. The increase of the fiber coupling parameter increases the die swell ratio when fibers are randomly distributed at the flow inlet, but the opposite behavior, i.e., a decrease of the swelling ratio, is noticed when a perfect fiber alignment condition is imposed at the entrance for low fiber interaction coefficients. The Tanner model, initially developed for viscoelastic fluids, is updated to estimate extrudate swell for fibers suspended in a Newtonian fluid in terms of the coupling parameter and the interaction coefficient. Although this analytical approach used a quadratic closure approximation, it gives qualitative results when compared with the numerical simulations.

Direct simulation of glass fiber breakage in simple shear flow considering fiber-fiber interaction

This study simulates the breakage behavior of glass fibers subjected to simple shear flow by modeling an individual fiber as a chain of connected spheres and considering fiber-fiber interaction. The simulation results show that the fiber length decreases as viscosity, shear rate, and fiber volume fraction increases. In contrast, with increasing time, the fiber lengths obtained from different initial fiber lengths converge to nearly the same value. These trends are in qualitative agreement with those observed in an existing experiment, revealing that the simulation methodology in this study is applicable to the prediction of fiber length degradation. Concerning the breakage mechanism due to the fiber-fiber interactions, it is suggested that the fiber bending caused by the interactions not only directly results in breakage but also easily triggers the flow-induced fiber deformation that leads to breakage. In addition, the fiber-wall interactions are found to affect the breakage of fibers near walls.

Contribution of nascent cohesive fiber-fiber interactions to the non-linear elasticity of fibrin networks under tensile load

Fibrin is a viscoelastic proteinaceous polymer that determines the deformability and integrity of blood clots and fibrin-based biomaterials in response to biomechanical forces. Here, a previously unnoticed structural mechanism of fibrin clots' mechanical response to external tensile loads is tested using high-resolution confocal microscopy and recently developed three-dimensional computational model. This mechanism, underlying local strain-stiffening of individual fibers as well as global stiffening of the entire network, is based on previously neglected nascent cohesive pairwise interactions between individual fibers (crisscrossing) in fibrin networks formed under tensile load. Existence of fiber-fiber crisscrossings of reoriented fibers was confirmed using 3D imaging of experimentally obtained stretched fibrin clots. The computational model enabled us to study structural details and quantify mechanical effects of the fiber-fiber cohesive crisscrossing during stretching of fibrin gels at various spatial scales. The contribution of the fiber-fiber cohesive contacts to the elasticity of stretched fibrin networks was characterized by changes in individual fiber stiffness, the length, width, and alignment of fibers, as well as connectivity and density of the entire network. The results show that the nascent cohesive crisscrossing of fibers in stretched fibrin networks comprise an underappreciated important structural mechanism underlying the mechanical response of fibrin to (patho)physiological stresses that determine the course and outcomes of thrombotic and hemostatic disorders, such as heart attack and ischemic stroke. Statement of SignificanceFibrin is a viscoelastic proteinaceous polymer that determines the deformability and integrity of blood clots and fibrin-based biomaterials in response to biomechanical forces. In this paper, a novel structural mechanism of fibrin clots’ mechanical response to external tensile loads is tested using high-resolution confocal microscopy and newly developed computational model. This mechanism, underlying local strain-stiffening of individual fibers as well as global stiffening of the entire network, is based on previously neglected nascent cohesive pairwise interactions between individual fibers (crisscrossing) in fibrin networks formed under tensile load. Cohesive crisscrossing is an important structural mechanism that influences the mechanical response of blood clots and which can determine the outcomes of blood coagulation disorders, such as heart attacks and strokes.

Hydroentanglement of polymer nonwovens. 1: Experimental and theoretical/numerical framework

Hydroentanglement is a versatile and important process used to form highly entangled nonwoven materials comprised of polymer fibers. It is a key element of polymer processing in the world, with the nonwovens market worth of tens of billions of the US dollars. No fundamental theoretical models of hydroentanglement were available so far, even though such modeling is required to facilitate the entirely empirical efforts to optimize the process. No model experiments on hydroentanglement aiming at its underlying physics were conducted either. These challenging problems are in focus in the present work. A model experiment is conducted and a quasi-one-dimensional model of individual polymer fibers is proposed and implemented for a number of fibers subjected to water jets impacting as a curtain normally to the nonwoven surface and undergoing filtration motion in the inter-fiber pores. The nonwoven is assumed to be located on a moving substrate with water suction through it. The model allows for a number of two-dimensional water jets and a number of suction ports in the substrate. The quasi-one-dimensional model allows for the three-dimensional motion of individual viscoelastic polymer fibers and the fiber-fiber interaction, which makes them non-self-intersecting. Then, the governing quasi-one-dimensional equations of fiber motion are discretized and solved numerically by using a discrete element method with mesh refinement of the Lagrangian mesh during the time marching. Using the developed code, several basic model problems were solved. Specifically, the behavior of several viscoelastic polymer fibers under the action of water jets with and without fiber-fiber interaction is described. Accordingly, a quantitative measure of the fiber-fiber entanglement is introduced based on the observed morphologies in the accompanying second part of this work.

Improved approximation of transverse and shear stiffness for high volume fraction uniaxial composites

With uniaxial composites, the matrix material properties dominate the overall transverse and shear composite stiffness. Knowledge of these quantities are of practical importance in composite structures such as large wind turbine blades, which despite having a predominantly uniaxial layup, have both their torsional response and buckling behavior as critical design considerations. Accurate estimations of transverse and torsional rigidity for high volume fraction composites are currently dependent on extensive experimental work due to the low reliability and precision of transverse/shear micromechanical models. The Continuous Periodic Fiber Model is proposed to improve these predictions by considering fiber-fiber interactions through the use of periodic boundary conditions. Experimental data and standard models are used to validate the results and quantify the predictive improvements relative to traditional methods. The Continuous Periodic Fiber Model offers greatly improved accuracy for transverse stiffness estimations, reducing the average difference from the experiments by a factor of 1.7 (an average difference with experiment of 14% compared to the next best approach value of 24%) as well as modest improvements for the shear moduli.

CFD simulations of fiber-fiber interaction in a hollow fiber membrane bundle: Fiber distance and position matters

This CFD study aims to simulate the impact of fiber distance and position on fiber-fiber interaction within a bundle. In order to display the filtration performance of fibers at different positions, a hollow fiber membrane filtration setup based on nine fibers arranged in a 3 × 3 square array was constructed. A CFD porous media model approach was employed using the liquid phase as the main phase. The numerical simulation of multiphase flow on the average velocity of each fiber is validated by the experimental results. The presence of “bundle resistance” and “permeate competition” among fibers was confirmed by the axial liquid velocity simulation. When fiber distance was less than the fiber diameter, the interaction between fibers became notable due to “permeate competition”. When fiber distance was equal to fiber diameter, the “permeate competition” effect disappeared, while the “bundle resistance” became dominant within the bundle. When the fiber distance was larger than the fiber diameter, both “permeate competition” and “bundle resistance” could be neglected. The variations of fiber flux at different positions along the fiber height also proved the distribution of axial liquid velocity and sludge density in the bundle. These results highlight the difference between fiber distance and position in the bundle that ensured the fouling deposition.