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以模糊系统理论观点建立了一套高聚物模糊随机网络统计力学框架,引入缠结张量和隶属函数对分子链间的缠结进行定量表征,把高聚物非晶态结构看成是由无规缠结的分子线团构成的模糊随机网络,选取随机四面体缠结-交联体胞作为网络结构的平均代表单元,利用模糊概率论和统计力学给出了弹性形变自由能表达式,可以描绘不同形变方式下的橡胶弹性实验数据,经典分子网理论和Mooney-Rivlin方程都是本文结果的特例。
A set of statistic mechanics framework of fuzzy random network of polymer is established from the viewpoint of fuzzy system theory. The entanglement tensor and membership function are introduced to quantitatively characterize the entanglement between molecular chains. The amorphous structure of polymer is considered as Randomly entangled molecular strands of fuzzy random network, selected random tetrahedron intertwined - crosslinked somatic cells as the average network structure of the representative units, the use of fuzzy probability theory and statistical mechanics given elastic deformation free energy expression, The experimental data of rubber elasticity under different deformation modes can be depicted. The classical molecular net theory and the Mooney-Rivlin equation are all special cases of the results in this paper.