Simulation of Liquid Crystal Elastomers

液晶弹性体（LCEs）是由具有定向有序侧链和主链介生棒的弱交联液晶聚合物组成的橡胶。LCEs的显著特性是取向顺序和机械变形之间的耦合，这使得这些橡胶对外界刺激（如照明和其他应用领域）非常敏感，导致大而快速的形状变形。在过去的十年里，人们已经获得了大量关于LCEs的实验和理论结果。然而，lce的完整表征仍然是难以捉摸的，特别是对lce的动态响应。最近，研究者和他的合作者提出了一个非局部连续体模型来理解向列LCEs的动力学。仿真结果表明，该模型能够较好地捕捉到实际实验中观察到的lce的形状变化现象和其他一些特征。因此，该模型为进一步探索lce的动力学提供了坚实的基础。然而，由于lce剧烈响应背后的物理过程的内在复杂性，该模型的数值处理非常具有挑战性。在这个项目中，研究者专注于开发有效和可靠的数值方法来求解源自向列LCEs模型的推导方程。该项目的成功将为加强对LCEs的理解提供一个重要的工具。此外，深入了解液晶弹性体的动态响应对于其在传感器、执行器、可变形自适应光学元件、微流体泵等技术应用至关重要。液晶弹性体是一种柔软的复杂材料。lce的显著特征是相对较小的外部影响，如温度变化或照明的开始，可以导致大而快速的形状变形。由于这种显著的特性，LCEs具有实际技术应用的潜力，包括传感器，执行器，可变形自适应光学元件，微流体泵等。为了充分利用这些材料，研究者和他的合作者已经提出了一个数学模型，可以成功地捕捉LCEs的许多动态特征，如形状变化现象。然而，由于lce剧烈响应背后的物理过程的内在复杂性，所提出的模型的理论研究和模拟都非常具有挑战性。在这个项目中，研究者寻求开发有效和可靠的数值模拟方法。该研究的成功将为提高对lce的认识提供有力的工具，而深入的理解对于这些材料的实际技术应用至关重要。此外，研究中开发的方法将有助于其他相关复杂软物质系统的建模，因此将在计算材料科学界具有持久的价值。

Liquid crystal elastomers (LCEs) are rubbers that are comprised of weakly cross-linked liquid crystal polymers with orientationally ordered side-chain and main-chain mesogenic rods. The remarkable property of LCEs is the coupling between orientation order and mechanical deformation, which makes these rubbers very sensitive to external stimuli, such as illumination and other applied fields, leading to large and fast shape deformations. A great deal of the experimental and theoretical results on LCEs has been obtained during the last decade. However, a full characterization of LCEs still remains elusive, especially for the dynamic responses of LCEs. Recently, the investigator and his collaborators proposed a non-local continuum model to understand the dynamics of nematic LCEs. The simulation of the model demonstrated that the proposed model can successfully capture shape changing phenomena and some other features of LCEs that were observed from real experiments. The model thus provides a solid basis for further exploration of the dynamics of LCEs. However, due to the intrinsic complexity of the physical processes underlying the dramatic responses of LCEs, the numerical treatment of the model is very challenging. In this project, the investigator focuses on developing efficient and reliable numerical methods for solving the derived equations originating from the proposed model on nematic LCEs. The success of this project will provide an important tool to enhance the understanding of LCEs. Further, the deep understanding of the dynamic responses of LCEs is crucial to their technological applications including sensors, actuators, deformable adaptive optical elements, micro-fluidic pumps, etc.Liquid crystal elastomers (LCEs) are soft complex materials. The salient feature of LCEs is that relatively small external effects, such as changes in temperature or onset of illumination, can result in large and fast shape deformations. Due to this remarkable property, LCEs have the potential for real technological applications including sensors, actuators, deformable adaptive optical elements, micro-fluidic pumps, etc. To fully exploit these materials, the investigator and his collaborators have already proposed a mathematical model that can successfully capture many dynamic features of LCEs, such as shape changing phenomena. However, due to the intrinsic complexity of the physical processes underlying the dramatic responses of LCEs, both theoretical study and simulation of the proposed model are very challenging. In this project, the investigator seeks to develop efficient and reliable numerical methods for the simulation. The success of the research will provide a powerful tool to improve the understanding of LCEs, and the deep understanding is essential to the real technological applications of these materials. Moreover, the methods developed in the research will be useful for the modeling of other related complex soft matter systems, and will therefore have a lasting value in the computational materials science community.