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首页> 外文期刊>Journal of the Mechanics and Physics of Solids >Free-energy density functions for nematic elastomers
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Free-energy density functions for nematic elastomers

机译：向列弹性体的自由能密度函数

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The recently proposed neo-classical theory for nematic elastomers generalizes standard molecular-statistical Gaussian network theory to allow for anisotropic distributions of polymer chains. The resulting free-energy density models several of the novel properties of nematic elastomers. In particular, it predicts the ability of nematic elastomers to undergo large deformations with exactly zero force and energy cost-so called soft elasticity. Although some nematic elastomers have been shown to undergo deformations with unusually small applied forces, not all do so, and none deform with zero force. Further, as a zero force corresponds to infinitely many possible deformations in the neo-classical theory, this non-uniqueness leads to serious indeter-minacies in numerical schemes. Here we suggest that the neo-classical free-energy density is incomplete and propose an alternative derivation that resolves these difficulties. In our approach, we use the molecular-statistical theory to identify appropriate variables. This yields the choice for the microstructural degrees of freedom as well as two independent strain tensors (the overall macroscopic strain plus a relative strain that indicates how the deformation of the elastomeric microstructure deviates from the macroscopic deformation). We then propose expressions for the free-energy density as a function of the three quantities and show how the material parameters can be measured by two simple tests. The neo-classical free-energy density can be viewed as a special case of our expressions in which the free-energy density is independent of the overall macroscopic strain, thus supporting our view that the neo-classical theory is incomplete.
机译：最近提出的向列弹性体的新古典理论概括了标准的分子统计高斯网络理论，以允许聚合物链的各向异性分布。所得的自由能密度模拟了向列弹性体的几种新特性。特别地，它预测了向列弹性体在恰好为零力和能源成本的情况下经历大变形的能力，即所谓的软弹性。尽管已显示某些向列弹性体会在异常小的外加力作用下发生变形，但并非全部如此，并且都不会在零力作用下变形。此外，由于零力对应于新古典理论中的无限多个可能的变形，因此这种非唯一性会导致数值方案中的严重不确定性。在这里，我们认为新古典自由能密度是不完整的，并提出了解决这些困难的另一种推导方法。在我们的方法中，我们使用分子统计理论来确定适当的变量。这样就可以选择微观结构的自由度以及两个独立的应变张量（整体宏观应变加上一个相对应变，该应变指示弹性体微观结构的变形如何偏离宏观变形）。然后，我们提出了自由能密度与三个量的关系的表达式，并显示了如何通过两个简单的测试来测量材料参数。新古典自由能密度可以看作是我们表达式的特殊情况，其中自由能密度与整体宏观应变无关，因此支持了我们新古典理论不完整的观点。

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