论文标题
弯曲诱导的主导演的重新定向在与超弹性底物键合的列液晶弹性体中
Bending-induced director reorientation in a nematic liquid crystal elastomer bonded to a hyperelastic substrate
论文作者
论文摘要
在本文中，在非线性弹性框架内研究了由列液晶弹性体（缩写为NLCE）覆盖的超弹性底物的二维纯弯曲。由变形动量平衡，定向动量平衡和机械约束而产生的管理系统，并为给定的组成型模型得出相应的精确解决方案。发现存在两种不同的弯曲解决方案。为了确定哪个首选是，我们比较两种溶液的总势能，并发现两条能曲线可能具有弯曲角$α_c$的临界值的相交点，对于某些材料参数。特别是，主管$ \ bm n $突然将$ \dfracπ{2} $从一个解决方案旋转到另一个解决方案，以$α_c$为$α_c$，这表明导演重新定位（或跳跃）。此外，可以使用获得的弯曲溶液揭示不同材料和几何参数对弯曲变形和过渡角$α_C$的影响。同时，精确的解决方案可以提供基准问题，以验证液晶弹性体近似板模型的准确性。
In this paper, the two-dimensional pure bending of a hyperelastic substrate coated by a nematic liquid crystal elastomer (abbreviated as NLCE) is studied within the framework of nonlinear elasticity. The governing system, arising from the deformational momentum balance, the orientational momentum balance and the mechanical constraint, is formulated, and the corresponding exact solution is derived for a given constitutive model. It is found that there exist two different bending solutions. In order to determine which the preferred one is, we compare the total potential energy for both solutions and find that the two energy curves may have an intersection point at a critical value of the bending angle $α_c$ for some material parameters. In particular, the director $\bm n$ abruptly rotates $\dfracπ{2}$ from one solution to another at $α_c$, which indicates a director reorientation (or jump). Furthermore, the effects of different material and geometric parameters on the bending deformation and the transition angle $α_c$ can be revealed using the obtained bending solutions. Meanwhile, the exact solution can offer a benchmark problem for validating the accuracy of approximated plate models for liquid crystal elastomers.
