Variational modelling and simulation of thermo-optochemo-dynamical coupling in liquid crystalline elastomers

多物理场耦合问题的建模与仿真是当前科学技术领域的一个研究热点。我们的目标是尽可能精确地模拟不同物理领域之间的单边和相互作用。通过这种方式，行为预测和复杂系统的有针对性的影响是可能的。一个例子是通过温度变化或紫外光等外部多物理作用引起的连续体的诱导变形。变形可以引起连续体本身的运动，也可以引起连续体边界上物体的运动。这是可能的液晶弹性体，它可以通过温度场或紫外线很大程度上变形，并能够承担更昂贵和沉重的运动机构的功能。在开发这种人造材料的应用在设计的设备，致动器和轻型结构，瞬态数值模拟越来越多地使用。这减少了耗时和昂贵的实验研究的数量，并有助于保护自然资源和能源。特别是对于液晶弹性体等非均相聚合物材料，可以通过数值模拟来开发和优化其目标应用。这里，优选应用长期稳定的模拟方法，其可以与现有的有限元方法接口，因此便于多体模拟。在这种情况下，变分材料模型和模拟方法补充能量动量一致的时间积分算法被归类为长期稳定的。因此，本研究项目的目的是液晶弹性体的微观-宏观-力学材料行为的变分建模，通过一个新的广义连续的基础上的功能配方。这使得模拟与材料特定的混合有限元方法，并导致锁定自由空间离散化的弹性体部件。为了模拟多物理诱导运动的数值稳定和CPU的时间效率，能量动量一致的时间积分方法是发展和实施。该算法采用自动时间步长控制，并辅以无锁定空间离散，计算步骤少，在算法上能精确地满足广义连续统和耦合问题的各平衡律。

Modelling and simulation of coupled multiphysics problems in science and technology is currently an active field of research. The goal is to model as exactly as possible unilateral and mutual actions between different fields of physics. In this way, behaviour predictions and a targeted influencing of complex systems are possible. An example is the induced deformation of a continuum by means of external multiphysical actions as a temperature change or ultraviolet light. The deformation can causes the motion of the continuum itself, or the motion of bodies attached at the continuum boundary. This is possible with liquid crystalline elastomers, which can be largely deformed by a temperature field or ultraviolet light, and are able to take up functions of more expensive and heavy motion mechanisms.In the development of applications of such artifical materials during the design of devices, actuators and lightweight structures, transient numerical simulations are more and more in use. This reduce the number of time consuming and expensive experimental investigations, and contribute to the conservation of natural resources and energy. Especially for heterogeneous polymeric materials as liquid crystalline elastomers, their targeted application can be developed and optimized by numerical simulations. Here, it is preferable to apply a long-term stable simulation method, which can be interfaced with existing finite element methods and therefore facilitates multibody simulations. In this context, variational material models and simulation methods supplemented by energy-momentum-consistent time integration algorithms are classified as long-term stable. The aim of this research project is thus the variational modelling of the micro-macro-mechanical material behaviour of a liquid crystalline elastomer by means of a noval generalized continuum based on functional formulations. This enables a simulation with material specific mixed finite element methods, and leads to a locking-free space discretization of the elastomeric parts. In order to simulate multiphysically induced motions numerically stable and cpu-time efficient, an energy-momentum-consistent time integration method is to be developed and implemented. By using an automatic time step size control, such algorithms supplimented by locking-free space discretizations perform less calculation steps, and satisfy each balance law of a generalized continuum and coupled problem algorithmically exactly.