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

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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.