A numerical study on elastic properties of low-density two-dimensional networks of crosslinked long fibers

Fiber-based materials are prevalent in nature and in engineering applications. Microscopically, these materials resemble a discrete assembly of crosslinked or entangled fibers. To understand the relationship between the effective mechanical properties and the underlying microstructures, we consider a variety of periodic and random two-dimensional (2D) networks of crosslinked long fibers. The linearly elastic properties of periodic 2D networks (e.g., square, triangular and Kagome) are well understood. However, for low-density networks, cooperative buckling of the fiber segments can take place at small strains, leading to nonlinear, anisotropic elastic behaviors. A transition from stretch to bending and then back to stretch dominated deformation is predicted for the Kagome and triangular networks. For random 2D networks, the elastic behaviors are different. Under uniaxial tension, the stress–strain behavior is statistically isotropic and slightly nonlinear, dominated by stretch of the fibers aligned closely to the loading direction. Meanwhile, stochastic buckling occurs continuously in the random networks, leading to significant lateral contraction. Consequently, while the effective Young’s modulus follows a nearly linear scaling with respect to the relative density, the effective Poisson’s ratio exhibits a transition from stretch to bending dominated mode as the relative density decreases. A statistical analysis is performed to estimate the relative errors of the effective properties that depend on both the computational box size and the number of random realizations. The comparison between the periodic and random 2D networks highlights the profound effects of the network topology on the effective elastic properties.