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The purpose of this paper is to study the mechanochemical effect and self-growth mechanism of double-network (DN) gel and to provide a quasiperiodic model for rubber elasticity.

The chemical reaction kinetics is used to identify the mechanochemical transition probability of host brittle network and to explore the mechanical behavior of endosymbiont ductile network. A quasiperiodic model is proposed to characterize the cooperative coupling of host–endosymbiont networks using the Penrose tiling of a 2 × 2 matrix. Moreover, a free-energy model is formulated to explore the constitutive stress–strain relationship for the DN gel based on the rubber elasticity theory and Gent model.

In this study, a quasiperiodic graph model has been developed to describe the cooperative interaction between brittle and ductile networks, which undergo the mechanochemical coupling and mechanical stretching behaviors, respectively. The quasiperiodic Penrose tiling determines the mechanochemistry and self-growth effect of DNs.

It is expected to formulate a quasiperiodic graph model of host–guest interaction between two networks to explore the working principle of mechanical and self-growing behavior in DN hydrogels, undergoing complex mechanochemical effect. The effectiveness of the proposed model is verified using both finite element analysis and experimental results of DN gels reported in literature.