Micromechanics of a Planar Hybrid Fibrous Network

A micromechanical approach is proposed in this work to predict the initial tensile response under uniaxial loading of a bonded two-dimensional fibrous network consisting of two kinds of fibers. The probabilities and statistical distributions of the hybrid bonding points and free fiber lengths between the bonding points in the structure are first derived, and the deformations of both the fiber segment and the bonding area of a typical microelement of the network are analyzed and calculated. The analysis of an arbitrary microelement is then extended statistically to an intermediate level of the structure, the mesodomain, through which the macroscopic deformations of the structure are computed. Ultimately, the general expressions of elastic moduli and Poisson's ratios for a hybrid fibrous network are obtained. A parametric study examines the relationships between fiber mechanical and dimensional properties, fiber volume fractions of the two fiber types, fiber orientation distributions and the properties of the bonding areas, and the tensile behavior of the structure for an ideal planar fiber network.