Mechanics of random fiber networks—a review

Abstract

This article presents a review of the current understanding of the mechanics of random fiber networks. The discussion refers to athermal fiber networks, for which the governing functional is the system enthalpy, as well as to molecular networks, in which thermal fluctuations are important. Fiber networks are broadly encountered in everyday life as paper, insulation and damping materials, and as the essential component of some consumer products, while molecular networks form the structure of biological and non-biological materials such as the cytoskeleton, connective tissue, gels and rubber. The mechanics of these materials is defined by the structure of the network and by the mechanical behavior of individual filaments. The structure is characterized by a number of parameters, such as the density, filament orientation, fiber waviness, density and nature of cross-links, which are discussed in the first part of the article. The constitutive behavior of individual filaments is defined by their bending and axial stiffness, and by the response to thermal fluctuations. The constitutive response of the cross-links plays a central role in defining the system-scale mechanical behavior. The analysis of the network mechanics is divided into two parts addressing cross-linked and entangled (non-cross-linked) networks. Both molecular and athermal cross-linked networks are discussed, while only the literature on athermal entangled networks is included. Flexible and semi-flexible fibers are considered, with special attention given to the second category. The constitutive behavior under small and large deformations, including attempts to define continuum representations of the discrete system, is reviewed. A number of open issues are discussed in closure.