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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.

This study aims to interrogate and expand on the flexible citizenship framework by illuminating students' emergent identities and imagined future mobilities in China's expanding international school sector.

In-depth semistructured interviews were conducted with international school students and their parents in Shenzhen, covering their motivations for overseas higher education, experience with international schooling, self-perceived identities and imagined futures.

The participants aspired to overseas higher education for both symbolic capital attainment and embodied cultural cultivation to thrive in a globalised world. They expressed confidence that international schooling experiences prepared students for mobility to Western higher education and cultivated globally-oriented identities while not undermining their Chinese roots. They imagined their futures in terms of considerable flexibility, with a rising China viewed as an attractive and feasible option for career development.

This research provides an enriched understanding of a new generation of globally mobile Chinese students. The participants held distinctively different outlooks, aspirations and attitudes than depicted in the flexible citizenship framework, which emphasised a one-dimensional and instrumentalist portrayal of Chinese international students. This study discusses cross-generational changes in the desire for overseas education and a global-national outlook among young people in the context of significant social transformations in urban China.

The originality of this study is in expanding the flexible citizenship framework with reference to the emergent identities and pathways of students in the international schooling sector in China.