Complex coupling of brittle and stretchable networks in double-network (DN) gel has been a hot research topic to understand working principle of ultra-high mechanical toughness, in comparison with the conventional gels. In this study, both the percolation theory and phantom network model were employed to formulate a Brauer diagram model, which was used to describe the suppositional phantom double networks and explore their coupling effects in DN gel. The mechanochemical coupling was investigated using the proposed Brauer diagram model, in which three critical parameters of coupling fraction, surviving probability and phantom degree, were proposed to formulate a constitutive relationship among rubber elasticity, mechanochemical coupling and stress-elongation ratio. Finally, effectiveness of the Brauer diagram model was verified using analytical data from the finite element analysis and molecular dynamics, as well as experimental results of DN gels reported in the literature.

中文翻译：

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力化学耦合双网络凝胶中虚拟网络的布劳尔图模型

与传统凝胶相比，双网络（DN）凝胶中脆性和可拉伸网络的复杂耦合一直是了解超高机械韧性工作原理的热门研究课题。本研究采用渗流理论和幻影网络模型建立布劳尔图模型，用于描述虚拟幻影双网络并探讨其在DN凝胶中的耦合效应。使用所提出的布劳尔图模型对机械力化学耦合进行了研究，其中提出了耦合分数、存活概率和幻像度这三个关键参数，以建立橡胶弹性、机械力化学耦合和应力伸长比之间的本构关系。最后，利用有限元分析和分子动力学的分析数据以及文献报道的 DN 凝胶的实验结果验证了 Brauer 图模型的有效性。