Mechanism of reinforcement in soft composites: random fiber networks with inclusions*

The mechanical behavior of athermal random fiber networks embedding particulate inclusions is studied in this work. Composites in which the filler size is comparable with the mean segment length of the network are considered. In presence of inclusions, the small strain modulus increases, while the ability of the network to strain stiffen decreases relative to the unfilled network case. The reinforcement induced by fillers is most pronounced in sparse networks of floppier filaments that deform in the bending-dominated mode in the unfilled state. As the unfilled network density or the bending stiffness of fibers increase, the effect of filling diminishes rapidly. Fillers lead to a transition from the soft, bending-dominated, to the stiffer, axial-dominated, deformation mode of the network, transition which is primarily responsible for the observed overall reinforcement. These results provide a justification for the broadly observed difference in reinforcement in sparsely versus densely cross-linked networks at given filling fraction, and provide guidance for the further development of network-based materials.