Elasticity of randomly distributed sheet networks

Plate-like sheet networks assembled by randomly distributed sheets are commonly found in artificial nacre-like materials. However, the effects of spatial randomness and porosity of the network on its mechanical properties still remain largely unrevealed. To make a comprehensive understanding on the elasticity of these networks, a mechanics model is established based on the effective medium method where the intralayer spatial randomness of the sheets and porosity of the network are considered. An analytical expression of the effective Young's modulus of random sheet networks is derived and verified by FE simulation. The effective elastic modulus of the network is a quadratic function of the effective sheet area fraction that can be obtained by the real sheet area fraction minus a threshold. The threshold is ineffective sheet area fraction that cannot contribute to load bearing, and found to be a constant as 0.25. Besides, the effects of sheet size dispersion and sheet shape on the effective Young's modulus are investigated. The modulus can be improved by increasing the diameter variance or replacing the circular sheets with square sheets. This work provides a method to estimate the effect of randomness of arrangement, size and shape of sheets on the elasticity of network materials.