Different from the conventional single-network hydrogels, double-network (DN) hydrogels have attracted great research interest due to their ultra-high toughness, however, their working principles behind complex mechanochemical coupling have not been fully understood. In this study, an extended potential well model is formulated to investigate host-guest chemistry and free-energy trap effect, coupled in the DN hydrogels undergoing mechanochemical toughening. According to the Morse potential and mean field model, the newly established potential well model can describe the coupled binding of host brittle network and guest ductile network in the DN hydrogels. A free-energy equation is further proposed to describe working principles of mechanochemical coupling and toughening mechanisms using the depth, width and trap number of potential wells, which determine the barrier energy of host brittle network, mesh size of guest ductile network and mechanochemical host-guest interactions of these two networks, respectively. Finally, effectiveness of the proposed model is verified using finite-element analysis and experimental results of various DN hydrogels reported in literature. This study clarifies the linking of mechanochemical coupling and toughening mechanisms in DN hydrogels having the host-guest chemistry from both brittle and ductile networks using the potential well model.