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

耦合多物理场问题的建模与仿真是目前科技领域的一个活跃研究领域。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。一个例子是由于温度变化或紫外光等外部多物理作用引起的连续体变形。这种变形可以引起连续体本身的运动，也可以引起附着在连续体边界上的物体的运动。这对于液晶弹性体来说是可能的，液晶弹性体可以在温度场或紫外光下很大程度上变形，并且能够承担更昂贵和更重的运动机构的功能。在这种人工材料在器件、执行器和轻量化结构设计中的应用发展中，瞬态数值模拟越来越多地得到应用。这减少了耗时和昂贵的实验研究的次数，并有助于节约自然资源和能源。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。在这里，最好采用一种长期稳定的仿真方法，这种方法可以与现有的有限元方法相结合，从而便于多体仿真。在这种情况下，变分材料模型和辅以能量-动量一致时间积分算法的仿真方法被归类为长期稳定的。因此，本研究项目的目的是通过基于功能公式的新型广义连续体，对液晶弹性体的微观-宏观力学材料行为进行变分建模。这使得模拟具有特定材料的混合有限元方法，并导致弹性体零件的无锁空间离散化。为了在数值上稳定且高效地模拟多物理诱发运动，需要开发和实现一种能量动量一致的时间积分方法。该算法采用自动时间步长控制，辅以无锁空间离散化，计算步数少，算法精确地满足广义连续体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.