On nonlinear thermo-electro-mechanics in the context of electro-active polymers

在过去20年里，对功能材料不断增长的需求，同时确保了低生产成本，导致了对智能材料的强烈关注。这类材料的突出例子是电活性聚合物，它可以由于外加电场的刺激而改变其形状和机械性能。由于感应电场所需的高电压，但也由于在应用电活性聚合物期间的其他外部影响，材料的温度可能会发生显著变化。因此，考虑这些热对材料行为的影响也是至关重要的。因此，在这个项目的第一阶段，我们用解析和数值方法发展和求解了热-机电耦合问题的基础知识。在这个项目的第二阶段，我们最初的目标是对各种(速率相关的)电活性材料进行实验研究。为此，我们将扩展厄兰根-纽伦堡大学应用力学教席现有的测试设备。这些测试的结果将用于验证本项目第一阶段开发的理论框架。在实验中，将测试两种类型的电活性材料。我们将使用商业上可用的材料VHB 4910和由纽伦堡大学聚合物材料教席为我们的实验定制并提供的填充了压电颗粒的硅胶。随后，将使用经过验证的数值实施来分析一些内部和外部效应对材料的影响。例如，我们将研究材料样品周围的自由空间如何影响数值模拟的结果。此外，将更详细地研究材料的微观结构所起的作用。为此，我们将引入两种不同的尺度来观察材料。这将包括描述材料的确切微观结构的微观尺度和材料被认为是均质的宏观尺度。微观尺度和宏观尺度之间的尺度转换的表述最终将导致对物质行为的更现实的描述。对于内部结构不能被认为是均匀的材料，这一点尤其重要。例如，实验中使用的填充颗粒的有机硅复合材料就是这种情况。最后，将建立一个新的公式来描述材料中缺陷的驱动力。因此，对于电活性聚合物，有机硅复合材料中的压电性颗粒可以被认为是这样的缺陷。

The ever increasing demand for functional materials while simultaneously assuring low production costs has led to a strong focus on smart materials in the past two decades. Prominent examples of this class of materials are electro-active polymers that can change their form and mechanical properties due to external stimulation by an applied electric field.As a result of the high electric voltages that are needed to induce the electric field but also due to other external influences during the application of electro-active polymers, significant changes in the temperature of the material may occur. Therefore it is crucial to consider these thermal influences on the material behavior as well. Thus in the first phase of this project the basics of the coupled thermo-electro-mechanical problem were developed and solved using both analytical and numerical methods.In the second phase of this project we initially aim to conduct experimental investigations on various (rate-dependent) electro-active materials. To this end we will extend the testing equipment that is available at the Chair of Applied Mechanics of the University Erlangen-Nuremberg. The results of these tests will be used to validate the theoretical framework that was developed in the first phase of this project. In the experiments two types of electro-active materials will be tested. We will use the commercially available material VHB 4910 and a silicone, filled with piezoactive particles, that is custom made and provided for our experiments by the Chair of Polymeric Materials at the University Erlangen-Nuremberg.Subsequently the validated numerical implementation will be used to analyze the influence of a number of internal and external effects on the material. We will investigate for example how the free space surrounding a material sample influences the results of the numerical simulation. Furthermore the role of the microstructure of the material will be investigated in more detail. For this we will introduce two different scales on which the material is observed. This will include the microscale where the exact microscopic structure of the material is depicted and the macroscale where the material is considered to be homogeneous. The formulation of a scale transition between the micro- and the macroscale will eventually lead to a more realistic description of the material behavior. This is especially important for materials for which the internal structure cannot be considered to be homogeneous. This is for example the case for the particle filled silicone composite used in the experiments. Finally a novel formulation for the driving forces at defects in the material will be established. Thereby, with respect to electro-active polymers, the piezoactive particles in the silicone composite can be considered as such defects.