Fiber networks are the building blocks of many biological and non-biological systems and appear in many industries and products such as paper, battery substrates, tissue templates and cytoskeleton of cells. The relation between the mechanical behavior of fiber networks and their microstructure is of great interest. The mechanics of any disordered system including that of fiber networks is non-affine. Therefore, a proper understanding of the non-affinity is required to express their macroscopic behavior in terms of their multi scale microstructure. In these structures and at scales close to the characteristic length scales of the problem, ordinary homogenization techniques are not applicable due to the absence of a well-defined unit cell. In order to understand the intrinsic non-affinity of fiber networks and employ this concept in predicting their elastic behavior, two different boundary value problems are addressed in this thesis (a) regular fiber networks populated with randomly located defects and (b) random fiber networks. We study non-affinity in both structures and present novel methodologies to obtain their macroscopic behavior based on their microstructure. A semi-analytical model is developed using singular field decomposition in order to predict the non-affine behavior of highly defected regular network. A new strain-based measure of non-affine deformation is introduced in order to quantify non-affinity. We also study and probe the microstructure and mechanics of random fiber networks on various length scales. Based on our analyses, we conclude that dense random fiber networks are stochastic fractal objects. The stochastic finite element method is used to solve mechanics boundary value problems on these networks.In the first problem studied, we consider a regular network populated by a large number of elementary defects. Therefore, the non-affinity is introduced into the structure in a controlled way, i.e. by placing defective sites in the network. We present a methodology to predict the elasticity of arbitrarily defective regular networks based on the stiffness of individual filaments and the location of defects. The method requires a preliminary calibration step in which the eigenstrains associated with elementary defects of the network are fully characterized. The eigenfield of each type of defect is expressed as a superposition of fields of singular point sources in 2D elastostatics. The amplitude of point sources is determined by probing the eigenstrain with a series of path independent integrals. Once the representation of each elementary defect is determined, any distribution of defects in the network can be mapped into a distribution of point sources in an equivalent continuum. The non-affine elastic behavior of a defective network with any distribution and concentration of defects is inferred from its associated continuum map.The non-affine response of random fiber networks and their scaling properties are investigated in the second part of the thesis. A new measure of non-affinity is introduced and used to quantify non-affine response of these networks at various length scales. It is seen that all components of the strain tensors and the rotation are non-affine and the degree of non-affinity decreases as the scale of observation increases. The influence of network characteristic length scales, type of far-field loading and initial fiber orientations on the degree of non-affinity is thoroughly investigated. Moreover, the microstructure and elasticity of these networks are studied by overlying a regular mesh on the network. In all cases considered, a power law scaling with an exponent independent of the fiber number density and probing length scale is observed. Based on this observation, we conclude that dense random fiber networks deform in a manner similar to highly heterogeneous continuum domains with stochastic fractal distribution of moduli. We use a stochastic finite element formulation to solve mechanics boundary value problem defined on domains with this type of structure.The main contribution of the thesis is identifying the fact that random fiber networks are stochastic fractal objects from a mechanics point of view (i.e. they deform in a manner similar to heterogeneous media with stochastic fractal distribution of moduli) and in developing a methodology that can be used to solve boundary value problems on domains with such microstructure. It is noted that classical homogenization techniques do not apply to (discrete or continuum) microstructures of the type discussed here.
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