On Structure and Elastic Fields of Random Fiber Networks

Random filamentous networks and their response to the applied load can be considered as a model to study the mechanical properties of biological systems such as cytoskeleton of a cell and connective tissues. A mathematical model for the actual and complex deformation of these networks under stress is developed using a micromechanics approach. We recently studied the effect of various micro-structural parameters such as fiber length, mean segment length and fiber flexibility on the network deformation field at various length scales. The network elasticity is mapped into a two dimensional heterogeneous continuum domain in order to show that the elastic fields of dense fiber networks show long range correlations over a range of scales for which we gave the upper and lower bounds. It is concluded that the deformation of random networks is similar to that of highly heterogeneous continuum domains with stochastic distribution of moduli. We employed the stochastic finite element method to solve boundary value problems defined on the random fiber network domain. Here, we present a brief review of this methodology and report new results on scaling properties of the structure of fiber networks using box-counting method.