2-dimensional (2D) random fiber networks are extremely thin plate-like structures constructed by randomly distributed fibers, and have been widely used in many fields from nano to macroscales due to their excellent properties. To make a comprehensive understanding on their in-plane and especially out-of-plane elastic properties, a mechanics model is established and analytical expressions for the in-plane and out-of-plane stiffnesses are derived based on micromechanics analysis. It is revealed that the fiber networks carry in-plane loads by axial stretching/compression of the fibers in the networks and resist out-of-plane loading by bending and torsion of the fibers. Due to the discreteness and randomness of the networks, the in-plane and out-of-plane stiffnesses present a non-classical relation, which can be described by a newly proposed formula. This work gives an insight into the understanding and designing of the mechanical properties of discrete materials/structures ranging from nanoscale to macroscale.

二维（2D）随机纤维网络是由随机分布的纤维构成的极薄的板状结构，由于其优异的性能已广泛用于从纳米到宏观的许多领域。为了全面了解它们的平面内，尤其是平面外的弹性特性，建立了力学模型，并基于微力学分析得出了平面内和平面外刚度的解析表达式。揭示了纤维网络通过网络中纤维的轴向拉伸/压缩来承受平面内载荷，并且通过纤维的弯曲和扭转来抵抗平面外载荷。由于网络的离散性和随机性，面内和面外刚度呈现出非经典关系，可以用新提出的公式来描述。