Structure and mechanics of athermal fiber networks with interfiber adhesion and excluded volume interactions

Abstract

The thrust of this thesis is on evaluating the role of nonbonded interactions, namely adhesion, excluded volume interactions, and friction at the interfiber contacts, in defining the mechanical behavior of the network. This physics is studied in (a) fiber networks where strong adhesion results in bundling of fibers and the formation of a network of branched bundles, and (b) quasiplanar fibrous mats where weak adhesion provides stability to point contacts between fibers but does not lead to fiber bundling. Additionally, the coupled effects of the nonbonded interactions and tortuous fiber morphologies, which is commonly observed in many naturally occurring fibrous materials, are explored in the context of fibrous mats with point contacts.

Analysis of 2D adhesion stabilized networks of branched bundles derived from crosslinked networks, namely Delaunay and Voronoi, revealed that the crosslinked networks undergo large volumetric shrinkage due to bundling, and the scaling of this volumetric shrinkage to the magnitude of adhesion is revealed. In this thesis, it is found that the mechanics of the network of bundles depends largely on the level of crosslinking in the parent crosslinked network. Networks derived from highly crosslinked networks, like Delaunay, show a strain-stiffening response while strain-softening response is observed for networks derived from sub-isostatic Voronoi networks. Additionally, it is demonstrated that tuning the level of crosslinking in the parent network can result in adhesion stabilized network of bundles, which show initial strain-softening response followed by a rapid strain-stiffening — a behavior similar to that of elastomers.

Small-strain mechanics of cellular networks of bundles formed from extensive adhesion driven self-organization in non-crosslinked fibers is also studied in this thesis. In these networks, typically three bundles exchange fibers between them to form a triangular nodal structure. It is shown that these nodal structures are highly stable and the movement of bundle branching points during loading is limited. However, it is found that the peculiar geometrical features associated with these triangular nodal structures provide these networks with an unexpected non-exponential strain-stiffening at larger strains.

In the later part of this thesis, we investigate quasiplanar fibrous mats with adhesion stabilized point contacts. Additionally, friction is also applied at the contacts. These mats show a bilinear elastic-plastic behavior when subjected to uniaxial tensile loading, with plasticity emerging from frictional sliding at interfiber contacts. It is shown that the nonaffine deformations during straightening of tortuous fibers couples with the frictional sliding to provide the observed non-zero tangent modulus in the post-yielding regime. This could potentially explain the post-yielding tangent modulus of the bilinear elastic-plastic response observed in many dry nonbonded nonwovens, like cellulose nanofibril paper, electrospun nanofiber mats etc.

Finally, this thesis also addresses the issue of fiber entanglement in athermal semi-flexible fibers. We study the structure-property relationship of 3D tortuous fiber mats with Coulombic friction and no adhesion. The effect of entanglement on the stress-strain response of these mats is demonstrated by eliminating the potential effects of other geometrical properties of the fibers. Furthermore, we propose a concept of entanglement length based on interwovenness of the fibers, and we show that this length-scale correlates well with the observed entanglement effect on the tensile stress-strain response.

In summary, the key contribution of this dissertation is to further the understanding of the effects of nonbonded interactions, particularly adhesion, in networks of branched fiber bundles and nonwoven mats without bundling and, consequently, open avenues to designing fiber networks with tuned architecture and mechanical properties.

In the presence of strong adhesion, fibers bundle leading to the formation of a non-crosslinked network of fiber bundles. The structure of these networks is defined by the interplay of adhesion and bending energies. To determine the structure of self-organized networks in the presence of adhesion, the evolution of bundling and junctions between bundles has to be traced in time. To this end, a semi-analytical expression specifying the constraints on the curvature of bundles in the vicinity of a branching point at static equilibrium is derived. Based on this theoretical analysis, a novel computational method is developed to determine the stable configurations of the adhesion stabilized bundle networks and their mechanics by minimization of total energy.

Many biological and engineering soft-materials have microstructures comprising of networks of fibers, e.g. nonwovens, electrospun scaffolds, collagen networks, buckypaper etc. The mechanical properties of fiber networks depend on single fiber properties, network architecture, and interactions between fibers. The nature of interfiber interactions, whether bonded or nonbonded, have a dramatic effect on the mechanical properties of fiber networks. Thus, a detailed understanding of the various types of interfiber interactions and their effects on network mechanics will enhance the understanding of many biological materials and help design novel engineering soft-materials.