Rigidity and fracture of biopolymer double networks

Composite biopolymer networks in soft tissues such as cartilage have remarkable tunable mechanics and resistance to failure. To achieve these properties in engineered materials, we need a mechanistic understanding of the structure-function properties that determine the workable range of strains and stresses over which the system maintains its integrity and mechanisms that facilitate protection against fracture. We study a model that combines two structure-function frameworks - a double network (DN) made of a stiff network and a flexible network, and rigidity percolation theory. We find that the rigidity percolation threshold for the stiff network can be varied, even significantly lowered by changing the flexible network's concentration. Second, the flexible network can modulate the mechanics of the DN (strength, extensibility, and toughness) far more efficiently when the stiff network is just above its rigidity percolation threshold. Third, the DN can further be tuned to either be more extensible for low concentrations of the flexible network, breaking gradually, or be stronger, breaking in a more brittle fashion for high concentrations of the flexible network. Our results show how structure and composition can be tuned to resist cracks.