The elasto-plastic behaviour of three-dimensional stochastic fibre networks with cross-linkers

Fibre network materials constitute a class of highly porous materials with low density, promising for functional and structural applications; however, very limited research has been conducted, especially on simulation and analytical models. In this paper, a continuum mechanics-based three-dimensional periodic beam-network model has been constructed to describe the stochastic fibre network materials. In this model, the density of the cross-linkers is directly related to the relative density of the fibre network materials, and the cross-linkers are represented by equivalent beam elements. The objective of this work was to delineate the elasto-plastic behaviour of the stochastic fibre network materials. Characteristic stress and strain derived from the total strain energy density have been adopted to reveal the yielding behaviour of the fibre networks. The results indicate that the stochastic fibre network materials are transversely isotropic. The in-plane stiffness and strength are much larger than those in the out-of-plane direction. For the fibre network materials with a small relative density, the relationship between the uniaxial yield strength and the relative density is a quadratic function in the x direction and is a cubic function in the z direction, which agree well with our dimensional analysis and are consistent with the relevant experimental results in literature. The yield surface depends strongly on the relative density and the connection between fibres.