论文标题
理想液晶弹性体的通用变形
Universal deformations of ideal liquid crystal elastomers
论文作者
论文摘要
液晶弹性体是橡胶状的固体，其液晶中性成分（刚性，棒状分子）掺入主链或作为聚合物的侧链中。由于橡胶的熵弹性与液晶的定向相变之间的耦合，这些固体显示了一系列不寻常的热机电特性。这些有趣的特性之一是软行为，它能够在几乎没有压力的情况下经历重大变形。尽管该现象是众所周知的，但在同质变形的背景下，它在很大程度上进行了检查。本文研究了复杂不均匀变形的软行为。我们将这些材料建模为超弹性，各向同性，不可压缩的固体，并利用埃里克森（Ericksen）的开创性工作，后者确定了非平凡的通用变形的存在，这些变形的存在，那些满足每个高弹性，等同于等同于等同于等于的固体的平衡方程。我们研究球形和圆柱气球，气蚀和弯曲的通胀。
Liquid crystal elastomers are rubber-like solids with liquid crystalline mesogens (stiff, rod-like molecules) incorporated either into the main chain or as a side chain of the polymer. These solids display a range of unusual thermo-mechanical properties as a result of the coupling between the entropic elasticity of rubber and the orientational phase transitions of liquid crystals. One of these intriguing properties is the soft behavior, where it is able to undergo significant deformations with almost no stress. While the phenomenon is well-known, it has largely been examined in the context of homogenous deformations. This paper investigates soft behavior in complex inhomogeneous deformations. We model these materials as hyperelastic, isotropic, incompressible solids and exploit the seminal work of Ericksen, who established the existence of non-trivial universal deformations, those that satisfy the equations of equilibrium in every hyperelastic, isotropic, incompressible solid. We study the inflation of spherical and cylindrical balloons, cavitation and bending.
