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1. Structural evolution and stability of non-crosslinked fiber networks with inter-fiber adhesion

   https://doi.org/DOI: 10.1039/c7sm02555f  

   Picu, R.C.; Sengab, A. (April 2018, Soft matter)

   Adhesion plays an important role in the mechanics of nanoscale fibers such as various biological filaments, carbon nanotubes and artificial polymeric nanofibers. In this work we study assemblies of non-crosslinked filaments and characterize their adhesion-driven structural evolution and their final stable structure. The key parameters of the problem are the network density, the fiber length, the bending stiffness of fibers and the strength of adhesion. The system of fibers self-organizes in one of three types of structures: locked networks, in which fibers remain in the as-deposited state, cellular networks, in which fibers form bundles and these organize into a larger scale network, and disintegrated networks, in which the network of bundles becomes disconnected. We determine the parametric space corresponding to each of these structures. Further, we identify a triangular structure of bundles, similar to the Plateau triangle occurring in foams, which stabilizes the network of bundles and study in detail the stabilization mechanism. The analysis provides design guidelines and a physical picture of the stability and structure of random fiber networks with adhesion. 

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2. Mechanical behavior of cellular networks of fiber bundles stabilized by adhesion

   https://doi.org/10.1016/j.ijsolstr.2019.11.003  

   Negi, V (November 2019, International journal of solids and structures)

   In this work, we study the mechanical behavior of non-crosslinked networks of fibers that interact adhe- sively. Adhesion drives fiber organization into bundles and a network of fiber bundles forms as a result of this process. Bundles split and re-connect forming specific triangular features at all bundle intersections, with role in network stabilization. The structure of such networks has been discussed in the literature, but their mechanics remains largely unexplored. We show here that such networks are exceptionally sta- ble, and despite the absence of crosslinks between fibers behave, at relatively small strains, essentially similar to crosslinked networks, in which the role of crosslinks is played by the triangular structures at bundle intersections. We also provide new results regarding the effect of the network architecture on the type of strain stiffening observed in tension. The results apply to carbon nanotube structures, such as buckypaper, and various connective biological tissue in which collagen fibrils form bundles and the tissue is a network of collagen fibril bundles. 

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3. Myosin and Alpha-actinin regulation of stress fiber contractility under tensile stress

   https://doi.org/10.1038/s41598-023-35675-7  

   Ni, Haoran; Ni, Qin; Papoian, Garegin A; Trache, Andreea; Jiang, Yi (December 2023, Scientific Reports)

   Abstract Stress fibers are actomyosin bundles that regulate cellular mechanosensation and force transduction. Interacting with the extracellular matrix through focal adhesion complexes, stress fibers are highly dynamic structures regulated by myosin motors and crosslinking proteins. Under external mechanical stimuli such as tensile forces, the stress fiber remodels its architecture to adapt to external cues, displaying properties of viscoelastic materials. How the structural remodeling of stress fibers is related to the generation of contractile force is not well understood. In this work, we simulate mechanochemical dynamics and force generation of stress fibers using the molecular simulation platform MEDYAN. We model stress fiber as two connecting bipolar bundles attached at the ends to focal adhesion complexes. The simulated stress fibers generate contractile force that is regulated by myosin motors and$$\alpha$$ $\alpha$-actinin crosslinkers. We find that stress fibers enhance contractility by reducing the distance between actin filaments to increase crosslinker binding, and this structural remodeling ability depends on the crosslinker turnover rate. Under tensile pulling force, the stress fiber shows an instantaneous increase of the contractile forces followed by a slow relaxation into a new steady state. While the new steady state contractility after pulling depends only on the overlap between actin bundles, the short-term contractility enhancement is sensitive to the tensile pulling distance. We further show that this mechanical response is also sensitive to the crosslinker turnover rate. Our results provide new insights into the stress fiber mechanics that have significant implications for understanding cellular adaptation to mechanical signaling. 

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4. Mechanical behavior of cross-linked random fiber networks with inter-fiber adhesion

   https://doi.org/10.1016/j.jmps.2018.09.027  

   Negi, V (September 2018, Journal of the mechanics and physics of solids)

   We study the effect of inter-fiber adhesion on the mechanical behavior of cross-linked ran- dom fiber networks in two dimensions. To this end, we consider networks with connectiv- ity number, z , below, at, and above the isostaticity limit of the structure without adhesion, z c . Fibers store energy in the axial and bending deformation mode and the cross-links are of freely rotating type. Adhesive forces lead to fiber bundling and to a reduction of the total volume of the network. The degree of shrinkage is determined as a function of the strength of adhesion and network parameters. The mechanical response of these struc- tures is further studied in uniaxial tension and compression. The stress-strain curves of networks without inter-fiber adhesion exhibit an initial linear regime, followed by strain stiffening in tension and strain softening and strain localization in compression. In pres- ence of adhesion, the response becomes more complex. The initial linear regime persists, with the effective modulus decreasing and increasing with increasing adhesion in cases with z > z c and z < z c , respectively. The strain range of the linear regime increases signif- icantly with increasing adhesion. Networks with z > z c subjected to tension strain-stiffen at rates that depend on the adhesion strength, but eventually enter a large strain/stress regime in which the response is independent of this parameter. Networks with z < z c are stabilized by adhesion in the unloaded state. Beyond the initial linear regime their tangent modulus gradually decreases, only to increase again at large strains. Adhesive interactions lead to similar effects in compression. Specifically, in the z > z c case, increasing the adhe- sion strength reduces the linear elastic modulus and significantly increases the range of the linear regime, delaying strain localization. This first investigation of the mechanics of cross-linked random networks with inter-fiber adhesion opens the door to the design of soft materials with novel properties. 

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5. Evolution of Force Chains Explains the Onset of Strain Stiffening in Fiber Networks

   https://doi.org/10.1115/1.4055586  

   Sarkar, Mainak; Notbohm, Jacob (November 2022, Journal of Applied Mechanics)

   Abstract Fiber networks are the primary structural components of many biological structures, including the cell cytoskeleton and the extracellular matrix. These materials exhibit global nonlinearities, such as stiffening in extension and shear, during which the fibers bend and align with the direction of applied loading. Precise details of deformations at the scale of the fibers during strain stiffening are still lacking, however, as prior work has studied fiber alignment primarily from a qualitative perspective, which leaves incomplete the understanding of how the local microstructural evolution leads to the global mechanical behavior. To fill this gap, we studied how axial forces are transmitted inside the fiber network along paths called force chains, which continuously evolve during the course of deformation. We performed numerical simulations on two-dimensional networks of random fibers under uniaxial extension and shear, modeling the fibers using beam elements in finite element software. To quantify the force chains, we identified all chains of connected fibers for which the axial force was larger than a preset threshold and computed the total length of all such chains. To study the evolution of force chains during loading, we computed the derivative of the total length of all force chains with respect to the applied engineering strain. Results showed that the highest rate of evolution of force chains coincided with the global critical strain for strain stiffening of the fiber network. Therefore, force chains are an important factor connecting understanding of the local kinematics and force transmission to the macroscale stiffness of the fiber network. 

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