In-plane and out-of-plane stiffness of 2D random fiber networks: Micromechanics and non-classical stiffness relation

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. (c) 2020 Elsevier Ltd. All rights reserved.