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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.more » « less
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.more » « less
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.more » « less