Fibrous materials are promising for a wide range of engineering applications due to their low density and high stiffness and strength. Stochastic filamentous networks can be widely found in biomaterials at the micro- and nano-scales. The objective of this study is to investigate the mechanical properties of macro-sized, micro-sized and nano-sized stochastic fibrous networks with cross-linking.
A continuum mechanics-based three-dimensional periodic beam model has been developed to describe stochastic fibrous materials by the Finite Element Method (FEM). Relative density is a key parameter to elucidate the mechanical properties of porous fibrous materials. The relative density of the beam model developed in this study can be adjusted by changing the concentration of the cross-linker, the fibre aspect ratio and the coefficient of overlap. In general, the non-dimensional Youngโs moduli and shear moduli increase with increasing relative density. The simulation and analytical model have suggested that strut bending is the dominant deformation mechanism for stochastic fibrous materials.
Based on the total strain energy density, scalar measures of characteristic stress and strain have been applied to reveal the yielding of stochastic fibrous materials. The effect of relative density on uniaxial yield strength of stochastic fibrous materials shows a quadratic function in the x direction and a cubic function in the z direction.
When the dimensions of fibrous structures are reduced to the micro- or nano-scale, the stiffness is much different from that of their macro-sized counterparts. Strain gradient effects at the micro-meter scale, and the surface elasticity and initial stress effects at the nano-meter scale have been incorporated into the deformation mechanism of fibrous materials. For both of the micro- and nano-sized fibrous structure, the smaller the diameter, the larger the non-dimensional Youngโs moduli and shear moduli. Generally speaking, the dimensionless stiffness of nano-sized stochastic fibrous structures is larger than their micro-sized counterparts. The size-dependent effects investigated in this study could provide good reference points for scientists in tissue engineering and serve as a guide in the design of MEMS and NEMS
