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. Charac- teristic 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 stochas- tic 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 rel- evant experimental results in literature. The yield surface depends strongly on the relative density and the connection between fibres. Data comprises: statistics of the relative density and normalized Young’s modulus; ratios between reaction forces over 20 models; characteristic stress-strain relations; relationship between the relative density and the uniaxial yield strength; effects of relative density on the shear strength.