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1. An integral model based on slender body theory, with applications to curved rigid fibers

   https://doi.org/10.1063/5.0041521  

   Andersson, Helge I; Celledoni, Elena; Ohm, Laurel; Owren, Brynjulf; Tapley, Benjamin K (April 2021, Physics of Fluids)

   We propose a novel integral model describing the motion of both flexible and rigid slender fibers in viscous flow and develop a numerical method for simulating dynamics of curved rigid fibers. The model is derived from nonlocal slender body theory (SBT), which approximates flow near the fiber using singular solutions of the Stokes equations integrated along the fiber centerline. In contrast to other models based on (singular) SBT, our model yields a smooth integral kernel which incorporates the (possibly varying) fiber radius naturally. The integral operator is provably negative definite in a nonphysical idealized geometry, as expected from the partial differential equation theory. This is numerically verified in physically relevant geometries. We discuss the convergence and stability of a numerical method for solving the integral equation. The accuracy of the model and method is verified against known models for ellipsoids. Finally, we develop an algorithm for computing dynamics of rigid fibers with complex geometries in the case where the fiber density is much greater than that of the fluid, for example, in turbulent gas-fiber suspensions. 

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2. Sub-microscale speckle pattern creation on single carbon fibers for scanning electron microscope-digital image correlation (SEM-DIC) experiments

   https://doi.org/10.1016/j.compositesa.2022.107331  

   Shah, Karan; Sockalingam, Subramani; O'Brien, Hannah; El Loubani, Mohammad; Lee, Dongkyu; Sutton, Michael (November 2022, Composites Part A Applied science and manufacturing)

   High performance carbon fibers are widely used as fiber reinforcements in composite material systems for aerospace, automotive, and defense applications. Longitudinal tensile failure of such composite systems is a result of clustering of single fiber tensile failures occurring at the microscale, on the order of a few microns to a few hundred microns. Since fiber tensile strength at the microscale has a first order effect on composite strength, it is important to characterize the strength of single fibers at microscale gage lengths which is extremely challenging. An experimental technique based on a combination of transverse loading of single fibers under SEM with DIC is a potential approach to access microscale gage lengths. The SEM-DIC technique requires creation of uniform, random, and contrastive sub-microscale speckle pattern on the curved fiber surface for accurate strain measurements. In this paper, we investigate the formation of such sub-microscale speckle patterns on individual sized IM7 carbon fibers of nominal diameter 5.2 µm via sputter coating. Various process conditions such as working pressure, sputtering current, and coating duration are investigated for pattern creation on fiber surface using a gold-palladium (Au-Pd) target. A nanocluster type sub-microscale pattern is obtained on the fiber surface for different coating conditions. Numerical translation experiments are performed using the obtained patterns to study image correlation and identify a suitable pattern for SEM-DIC experiments. The pattern obtained at a working pressure of 120–140 mTorr with 50 mA current for a duration of 10 min is found to have an average speckle size of 53 nm and good contrast for image correlation. Rigid body translation SEM experiments for drift/distortion correction using a sized IM7 carbon fiber coated with the best patterning conditions showed that Stereo-SEM-DIC is needed for accurately characterizing fiber strain fields due to its curved surface. The effect of sputter coating on fiber tensile strength and strain is investigated via single fiber tensile tests. Results showed that there is no significant difference in the mean tensile strength and failure strain between uncoated and coated fibers (average increment in fiber diameter of ∼221 nm due to coating) at 5% significance level. SEM images of failure surfaces for uncoated and coated fibers also confirmed a tensile failure of fibers as observed for polyacrylonitrile PAN-based fibers in literature. 

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3. Sub-microscale speckle pattern creation on single carbon fibers for in-situ DIC experiments

   https://doi.org/10.12783/asc36/35902  

   Shah K, Yang G (September 2021, Proceedings of the American Society for Composites Technical Conference)

   High performance carbon and glass fibers are widely used as reinforcements in composite material systems for aerospace, automotive, and defense applications. Modifications to fiber surface treatment (sizing) is one of the ways to improve the strength of fibers and hence the overall longitudinal tensile strength of the composite. Single fiber tensile tests at the millimeter scale are typically used to characterize the effect of sizing on fiber strength. However, the characteristic length-scale governing the composite failure due to a cluster of fiber breaks is in the micro-scales. To access such micro-scale gage-lengths, we aim to employ indenters of varying radii to transversely load fibers and use scanning electron microscope (SEM) with digital image correlation (DIC) to measure strains at these lengthscales. The use of DIC technique requires creation of a uniform, random, and high contrast speckle pattern on the fiber surface such as that shown in Figure 1. In this work, we investigate the formation of sub-microscale speckle pattern on carbon fiber surface via sputter deposition and pulsed laser deposition techniques (PLD) using Gold-Palladium (Au-Pd) and Niobium-doped SrTiO3 (Nb:STO) targets respectively. Different processing conditions are investigated for both sputter deposition: sputtering current and coating duration, and PLD: number of pulses respectively to create sub-micron scale patterns viable for micro-DIC on both sized and unsized carbon fibers. By varying the deposition conditions and SEM-imaging the deposited patterns on fibers, successful pattern formation at sub-micron scale is demonstrated for both as-received sized and unsized IM7 carbon fibers of average diameter 5.2 µm via sputter deposition and PLD respectively. 

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4. Label-Free Prediction of Fluorescently Labeled Fibrin Networks

   https://doi.org/10.34133/bmr.0211  

   Eldeen, Sarah; Ramirez, Andres_Felipe Guerrero; Keresteci, Bora; Chang, Peter D; Botvinick, Elliot L (January 2025, Biomaterials Research)

   While fluorescent labeling has been the standard for visualizing fibers within fibrillar scaffold models of the extracellular matrix (ECM), the use of fluorescent dyes can compromise cell viability and photobleach prematurely. The intricate fibrillar composition of ECM is crucial for its viscoelastic properties, which regulate intracellular signaling and provide structural support for cells. Naturally derived biomaterials such as fibrin and collagen replicate these fibrillar structures, but longitudinal confocal imaging of fibers using fluorescent dyes may impact cell function and photobleach the sample long before termination of the experiment. An alternative technique is reflection confocal microscopy (RCM) that provides high-resolution images of fibers. However, RCM is sensitive to fiber orientation relative to the optical axis, and consequently, many fibers are not detected. We aim to recover these fibers. Here, we propose a deep learning tool for predicting fluorescently labeled optical sections from unlabeled image stacks. Specifically, our model is conditioned to reproduce fluorescent labeling using RCM images at 3 laser wavelengths and a single laser transmission image. The model is implemented using a fully convolutional image-to-image mapping architecture with a hybrid loss function that includes both low-dimensional statistical and high-dimensional structural components. Upon convergence, the proposed method accurately recovers 3-dimensional fibrous architecture without substantial differences in fiber length or fiber count. However, the predicted fibers were slightly wider than original fluorescent labels (0.213 ± 0.009 μm). The model can be implemented on any commercial laser scanning microscope, providing wide use in the study of ECM biology. 

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5. Magic Angles and Force Transmission in Helically Wrapped Worms

   https://doi.org/10.1093/icb/icaf106  

   Ellers, Olaf; McHenry, Matthew J; Johnson, Amy S (July 2025, Integrative And Comparative Biology)

   Synopsis Many animal structures and appendages are pressurized, cylindrical, and helically wrapped with fibers. Squid tentacles, elephant trunks, echinoderm tube feet, notochords, arteries, and the bodies of sharks, nematodes, and annelids are all helically wrapped and their structural function depends on force transmission by this wrapping. Classical understanding of helically-wrapped cylinders in biology originates with calculations and concepts developed in the context of worm bodies, particularly nemerteans, turbellarians, and nematodes. This work recognized the geometric effects of the fiber angle on the cylinder volume and the fiber stretch. Subsequent work on tongues, tentacles, trunks, and polychaete worms used cylinder geometry to infer mechanical advantage. However, these studies did not explicitly consider forces and hence are limited in developing a general understanding for the mechanics of soft skeletons. Recently, a more precise theory was developed that incorporates force transmission, enhancing an understanding of mechanical and displacement advantage in these biological hydrostats. Some general insights are derivable from this foundation. A pressurized cylinder has a hoop stress that is twice the longitudinal stress and a crossed-helical wrapping of fibers can carry all of those stresses, if the fibers are at the magic angle of 54.7°. In a variable-volume cylinder with inextensible fibers, the magic angle corresponds to the maximum enclosed volume, but in a constant-volume cylinder, shape change necessitates stretching of the helical fibers. Strain and the length-to-radius ratio (aspect ratio) are functions of fiber angle, but aspect ratio also depends on the number of fiber wrappings. A constant-volume cylinder at any other angle will generate higher pressure, stretch helical fibers, store energy, cause shape changes, and possibly generate axial or radial external forces. Due to geometry, the mechanical advantage of force transmission from longitudinal muscles to radial output forces is not the inverse of the mechanical advantage of circumferential muscles transmitting force to the axial direction. Additionally, the mechanical advantage of short, wide cylinders is higher in extension than that of longer, thinner cylinders, suggesting that short and wide earthworm and polychaete segments have a higher mechanical advantage in generating axial forces during burrowing. Helical fibers can reduce the mechanical advantage during extension and retraction because energy is stored in the fibers; stiffer fibers reduce the mechanical advantage more; and some worms have helical muscles that might allow behavioral modulation of mechanical advantage. These inferences demonstrate insights that may be gleaned from explicit considerations of the mechanical principles of hydrostatic skeletons. 

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