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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Mechanical behavior of nonwoven non-crosslinked fibrous mats with adhesion and friction
We present a study of the mechanical behavior of planar fibrous mats stabilized by inter-fiber adhesion. Fibers of various degrees of tortuosity and of infinite and finite length are considered in separate models. Fibers are randomly distributed, are not cross-linked, and interact through adhesion and friction. The variation of structural parameters such as the mat thickness and the mean segment length between contacts along given fibers with the strength of adhesion is determined. These systems are largely dissipative in that most of the work performed during deformation is dissipated frictionally and only a small fraction is stored as strain energy. The response of the mats to tensile loading has three regimes: a short elastic regime in which no sliding at contacts is observed, a well-defined sliding regime characterized by strain hardening, and a rapid stiffening regime at larger strains. The third regime is due to the formation of stress paths after the fiber tortuosity is pulled out and is absent in mats of finite length fibers. Networks of finite length fibers lose stability during the second regime of deformation. The scaling of the yield stress, which characterizes the transition between the first and the second regimes, and of the second regime's strain hardening modulus, with system parameters such as the strength of adhesion and friction and the degree of fiber tortuosity are determined. The strength of mats of finite length fibers is also determined as a function of network parameters. These results are expected to become useful in the design of electrospun mats and other planar fibrous non-cross-linked networks.
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- Award ID(s):
- 1634328
- NSF-PAR ID:
- 10160164
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 15
- Issue:
- 29
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 5951 to 5964
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Critical processes including seismic faulting, reservoir compartmentalization, and borehole failure involve high‐pressure mechanical behavior and strain localization of sedimentary rocks such as sandstone. Sand is often used as a model material to study the mechanical behavior of poorly lithified sandstone. Recent studies exploring the multi‐scale mechanics of sand have characterized the brittle, low‐pressure regime of behavior; however, limited work has provided insights into the ductile, high‐pressure regime of behavior via
in‐situ measurements. Critical features of the ductile regime, including grain breakage, grain micromechanics, and volumetric strain behavior therefore remain under‐explored. Here, we use a new high‐pressure triaxial apparatus within‐situ x‐ray tomography to provide new insights into deformation banding, grain breakage, and grain micromechanics in Ottawa sand subjected to triaxial compression under confining pressures between 10 and 45 MPa. We observed strain‐hardening at pressures above 15 MPa and strain‐neutral responses at pressures below 15 MPa. Compacting shear bands and grain breakage were observed at all pressures with no significant variation due to grain size, except for minor increases in breakage in less‐rounded sands. Grain breakage emerged at stress levels lower than the assumed yield threshold and more intense breakage was associated with thinner deformation bands. Contact sliding at inter‐grain contacts demonstrated a bifurcation into a bimodal distribution, with intense sliding within deformation bands and reduced but non‐negligible sliding outside of deformation bands, suggesting that off‐band zones remain mechanically active during strain hardening. -
Many materials of everyday use are fibrous and their strength is important in most applications. In this work we study the dependence of the strength of random fiber networks on structural parameters such as the network density, cross-link density, fiber tortuosity, and the strength of the inter-fiber cross-links. Athermal networks of cellular and fibrous type are considered. We conclude that the network strength scales linearly with the cross-link number density and with the cross-link strength for a broad range of network parameters, and for both types of networks considered. Network strength is independent of fiber material properties and of fiber tortuosity. This information can be used to design fiber networks for specified strength and, generally, to understand the mechanical behavior of fibrous materials.more » « less
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Electrospun polymer fibers can be used as templates for the stabilization of metallic nanostructures, but metallic species and polymer macromolecules generally exhibit weak interfacial adhesion. We have investigated the adhesion of model copper nanocubes on chemically treated aligned electrospun polyacrylonitrile (PAN) fibers based on the introduction of interfacial shear strains through mechanical deformation. The composite structures were subjected to distinct macroscopic tensile strain levels of 7%, 11%, and 14%. The fibers exhibited peculiar deformation behaviors that underscored their disparate strain transfer mechanisms depending on fiber size; nanofibers exhibited multiple necking phenomena, while microfiber deformation proceeded through localized dilatation that resulted in craze (and microcrack) formation. The copper nanocubes exhibited strong adhesion on both fibrous structures at all strain levels tested. Raman spectroscopy suggests chemisorption as the main adhesion mechanism. The interfacial adhesion energy of Cu on these treated PAN nanofibers was estimated using the Gibbs–Wulff–Kaischew shape theory giving a first order approximation of about 1 J/m2. A lower bound for the system’s adhesion strength, based on limited measurements of interfacial separation between PAN and Cu using mechanically applied strain, is 0.48 J/m2.more » « less
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null (Ed.)Abstract Background The pia arachnoid complex (PAC) is a cerebrospinal fluid-filled tissue conglomerate that surrounds the brain and spinal cord. Pia mater adheres directly to the surface of the brain while the arachnoid mater adheres to the deep surface of the dura mater. Collagen fibers, known as subarachnoid trabeculae (SAT) fibers, and microvascular structure lie intermediately to the pia and arachnoid meninges. Due to its structural role, alterations to the biomechanical properties of the PAC may change surface stress loading in traumatic brain injury (TBI) caused by sub-concussive hits. The aim of this study was to quantify the mechanical and morphological properties of ovine PAC. Methods Ovine brain samples (n = 10) were removed from the skull and tissue was harvested within 30 min post-mortem. To access the PAC, ovine skulls were split medially from the occipital region down the nasal bone on the superior and inferior aspects of the skull. A template was used to remove arachnoid samples from the left and right sides of the frontal and occipital regions of the brain. 10 ex-vivo samples were tested with uniaxial tension at 2 mm s −1 , average strain rate of 0.59 s −1 , until failure at < 5 h post extraction. The force and displacement data were acquired at 100 Hz. PAC tissue collagen fiber microstructure was characterized using second-harmonic generation (SHG) imaging on a subset of n = 4 stained tissue samples. To differentiate transverse blood vessels from SAT by visualization of cell nuclei and endothelial cells, samples were stained with DAPI and anti-von Willebrand Factor, respectively. The Mooney-Rivlin model for average stress–strain curve fit was used to model PAC material properties. Results The elastic modulus, ultimate stress, and ultimate strain were found to be 7.7 ± 3.0, 2.7 ± 0.76 MPa, and 0.60 ± 0.13, respectively. No statistical significance was found across brain dissection locations in terms of biomechanical properties. SHG images were post-processed to obtain average SAT fiber intersection density, concentration, porosity, tortuosity, segment length, orientation, radial counts, and diameter as 0.23, 26.14, 73.86%, 1.07 ± 0.28, 17.33 ± 15.25 µm, 84.66 ± 49.18°, 8.15%, 3.46 ± 1.62 µm, respectively. Conclusion For the sizes, strain, and strain rates tested, our results suggest that ovine PAC mechanical behavior is isotropic, and that the Mooney-Rivlin model is an appropriate curve-fitting constitutive equation for obtaining material parameters of PAC tissues.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/c9sm00658c
