AI 中文总结
本文构建向列弹性体的有效二维模型，研究带贯穿厚度扭转的圆柱，发现其对长波螺旋扁平化模式不稳定并确定临界参数，揭示指向矢与几何的耦合作用。
AI 中文摘要
液晶弹性体（LCE）会沿预设的向列指向矢场发生各向异性形变，是可编程形状变化的理想候选材料。现有研究主要聚焦于平板上的指向矢图案或曲面上的简单图案，而曲面上的非平凡指向矢情况仍未被充分探索。许多生物系统同时具有复杂几何结构和复杂螺旋纤维架构，为探究指向矢与底层几何的相互作用，我们采用向列弹性体的非欧平板理论，结合贯穿厚度的扭转指向矢，构建了有效二维模型。在固定扭转角下，模型显示中面曲率与指向矢扭转存在反常耦合，该耦合项源于取向序与弹性的相互作用，且主导传统弯曲贡献。为阐释该通用理论，我们研究了具有贯穿厚度扭转的圆柱形状的稳定性，发现圆柱对长波螺旋扁平化模式不稳定，并确定了失稳起始的临界参数。
英文摘要
Liquid Crystal elastomers (LCEs) deform anisotropically along a prescribed nematic director field, making them promising candidates for programmable shape change. Existing studies have primarily focused on either director patterns on flat sheets or simple patterns on curved geometries, leaving the case of a non-trivial director on a non-trivial geometry still largely unexplored. Many biological systems, however, have both complex geometries and complex helical fiber architectures. To explore the interplay between director and underlying geometry, we use a non-Euclidean plate theory for nematic elastomers with a through-thickness twisted director to develop an effective 2D model. With a fixed twist angle, our model shows an anomalous coupling between mid-surface curvature and director twist. This emergent term arises from the interplay between orientational order and elasticity, and dominates traditional bending contributions. To illustrate the general theory, we study the stability of cylindrical shapes with through-thickness twist. We find that the cylinder is unstable to a long-wavelength helical flattening mode and determine the critical parameter for the onset of instabilities.
