Effective Properties of Random Composites and Fiber Networks

Random fiber networks are assemblies of one-dimensional mechanical elements used to model the mechanics of various natural and man-made materials such as biopolymer gels and synthetic nonwovens. The small-strain mechanics of identical straight fibers has been subjected to detailed investigation, resulting in homogenization relations that express relations between network stiffness and microstructural properties. Chapters 2 and 3 of this dissertation extend such studies to account for situations where non-identical fibers or crimped fibers are present in the network. Such situations are ubiquitously observed in various systems, e.g. in collagenous soft tissue where fibers might be crimped and multiple types of fibers can be present.;Chapter 2 addresses the mechanics of networks with non-identical fibers where fiber properties are sampled from statistical distributions. Finite element simulations and theoretical arguments are used to show that irrespective of network geometry, increasing the variance of fiber properties decreases the small strain network stiffness on average and the amount of network softening is proportional to the variance of fiber properties. It is further shown that the variance of small strain network stiffness scales linearly with the variance of fiber properties and inversely with the number of fibers. This chapter reports simulation results using 2D Mikado and 3D Voronoi and Delaunay networks. The analytical arguments used to prove the scaling laws include deriving a relation between fiber stiffness and network stiffness and ensemble averaging of a series approximation. Chapter 2 concludes with an extension to finite deformation behavior of networks with non-identical fibers. Estimating the effective stiffness of networks is followed in chapter 3 where the effect of fiber crimp (tortuosity) on network properties is addressed. In addition to numerical results for 3D Voronoi networks, semi-analytical arguments are provided to derive lower bounds for softening due to fiber crimp and also a series estimation for effective modulus. Implicit finite element analysis are performed to study the finite strain network behavior in the presence of crimp and finally the effect of fiber crimp is studied in a coupled fiber-matrix model for soft tissue.;Chapter 4 introduces two models for simulating the mechanics of cross-linked networks of ribbon-like fibers: a coarse-grained bead-spring model and a finite element model. The coarse-grained model is used to prepare geometric models mimicking those observed in experiments using cellulose fibers and then the two models are used to test the small-strain mechanical behavior of the prepared network geometries. The models predict qualitatively similar mechanical behavior predicting linear dependence of network stiffness on the density of cross-links. Chapter 4 concludes with analyzing the computational parallel performance of the two models.;The 5th chapter is an extension of the micromechanical results pertaining to random fiber networks to random continuum composites. The effective elasticity and conductivity of composites with random microstructural properties are studied using finite element models. The composite systems consist of isotropic homogeneous subdomains having properties sampled from a statistical distribution. It is shown numerically and analytically that the effective Young's modulus and heat conduction of the random composites linearly decrease with increasing the variance of microstructural properties. Also the variances of these effective properties scale linearly with the variance of microstructural properties and inversely with the number of considered subdomains. The analytical arguments in this chapter are a generalization of the relations introduced for fiber networks in chapter 2, introducing relations between effective composite properties and the properties of an inhomogeneity.;The conclusions are outlined in chapter 6, along with an outline of the principal advances made in this work and a discussion of the suggested future directions of research immediately related to the contents of this thesis.