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.

纤维基材料在自然界和工程应用中很普遍。从微观上看，这些材料类似于交联或缠结纤维的离散组合。为了了解有效机械性能与潜在微观结构之间的关系，我们考虑了交联长纤维的各种周期性和随机二维 (2D) 网络。周期性二维网络（例如正方形、三角形和 Kagome）的线性弹性特性是众所周知的。然而，对于低密度网络，纤维段的协同屈曲可以在小应变下发生，导致非线性、各向异性的弹性行为。对于 Kagome 和三角形网络，预测从拉伸到弯曲然后回到拉伸主导变形的转变。对于随机二维网络，弹性行为不同。在单轴拉伸下，应力-应变行为在统计上是各向同性的，并且略呈非线性，主要是与加载方向紧密对齐的纤维拉伸。同时，随机网络中不断发生随机屈曲，导致显着的横向收缩。因此，虽然有效杨氏模量相对于相对密度遵循近乎线性的比例，但有效泊松比随着相对密度的降低表现出从拉伸到弯曲主导模式的转变。执行统计分析以估计取决于计算框大小和随机实现数量的有效属性的相对误差。