Crack propagation in Articular Cartilage modeled as a biopolymer double network

Articular cartilage (AC) is a soft tissue that covers the ends of bones providing a smooth cushion at the joints. It has very few cells, and its extracellular matrix can be primarily thought of as a double network of stiff collagen fibers and flexible proteoglycans. As a material, AC is remarkable. It is only a few millimeters thick, yet can withstand large forces over 100-200 million loading cycles without fracturing. Here we investigate the structure-function properties underlying the fracture toughness of AC by using a framework that combines a double network model of cartilage with rigidity percolation theory. We study how the stress-strain properties and crack propagation in the double network depend on its composition and on loading conditions. Our results may help to formulate a quantitative criterion for crack propagation and fracture in soft tissues akin to the Griffith criterion for fracture of brittle materials.