Biological catch bonds display the distinctive attribute that the bond lifetime can increase under an applied force. Insertion of biomimetic catch bonds into hybrid materials could lead to composites that exhibit remarkable mechanical properties. We model the tensile behavior of polymer-grafted nanoparticle (PGN) networks interconnected by a mixture of catch bonds and conventional slip bonds, whose lifetimes decrease with force. We formulate a kinetic master equation that provides the complete probabilistic description of a system of two PGNs. The master equation is used to analyze the parameter space that determines the rupture behavior of the catch bonds in the two-particle system. We then utilize two exemplary sets of catch bond parameters in three-dimensional computer simulations of larger PGN networks under strain-controlled tensile deformation. We demonstrate that the strain at break and toughness of the networks can be altered by tuning the attributes of the catch bonds and varying the fraction of catch bonds in the network. We show that networks encompassing the catch bonds could exhibit a several-fold increase in the strain-at-break and toughness relative to those interconnected solely by the slip bonds. Our studies can provide valuable guidelines for tailoring the mechanical properties of novel, bio-inspired nanocomposites. (c) 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018, 56, 105-118