A numerical model for the analysis and simulation of electro-active paper

近年来，电活性纸（EAPap）已成为驱动装置领域的一个有趣的替代方案。与压电材料和介电弹性体类似，这种材料在电场的影响下会发生变形。与这些材料相比，为了实现弯曲驱动，执行器装置不需要建立层。由于离子扩散过程通过纸张的厚度发生，致动器主要是弯曲的，而不是像在压电陶瓷和介电弹性体中那样被压缩。该技术的主要优点是在低压应用中可以获得大的弯曲变形。其他显著的特性是重量轻和可生物降解性，这为智能执行器领域的实际应用开辟了许多可能性。EAPap是一种由壳聚糖链组成的有序区域的压电型纤维素。在制备过程中，将氯化氢注入到材料中，使材料附着在有序的壳聚糖链上。在外加电场的作用下，氯离子从壳聚糖链上分离并向阳极迁移，向离子质量和电荷的非均匀分布方向收敛。因此，静电力和流体静力应力在EAPap的厚度上分布不均，导致执行器弯曲。在文献中，相对于压电模型的结构分析，现象学行为是高度简化的。本研究项目旨在建立一个数值和现象学模型，通过考虑压电效应和离子扩散来捕捉EAPap的物理弯曲行为。由于EAPap是一个相当薄的结构，因此推导出一个外壳公式作为建模的起点。我们寻求一个模型，结合不均匀离子分布的所谓的缩放边界壳公式。此外，它还便于通过结构厚度计算高度非线性应变。提供了机电耦合问题的扩展。我们的目标是建立一个模型，通过描述EAPap的变形作为离子分布的函数来解释弯曲驱动机制。该模型包括静电力和体积变化。此外，与时间相关的行为是项目的额外焦点。特别地，提出了离子随时间迁移的模型。为此，离子的扩散被认为是外加电场的函数。最后，该项目为EAPap执行器的开发和改进提供了一种仿真方法，以适应实际应用。这种方法也可以方便地适用于类似的驱动原理，例如离子聚合物金属复合材料。

In recent years, electro-active paper (EAPap) has emerged as an interesting alternative in the field of actuation devices. Similar to piezoelectric materials and dielectric elastomers, the material is deformed under the influence of an electric field. In contrast to these materials, no build-up of layers is necessary for an actuator device in order to enable a bending actuation. Since an ionic diffusion process occurs through the thickness of the paper, the actuator is mainly bent instead of being compressed as in piezo-ceramics and dielectric elastomers. The main advantage of this technology is that large bending deformations can be obtained for low voltage application. Other remarkable properties are lightweight and biodegradability, which opens up many possibilities for practical applications in the field of smart actuators.EAPap is a piezoelectric cellulose which is characterized by ordered regions consisting of chitosan chains. During the fabrication process, hydrogen chloride is injected in the material which gets attached to the ordered chitosan chains. Under the influence of an applied electric field, the chloride anions detach from the chitosan chains and migrate to the anode, converging towards a heterogeneous distribution of ionic mass and charge. Consequently, electrostatic forces and hydrostatic stresses are heterogeneously distributed over the thickness of the EAPap, which results in the bending of the actuator. In the literature, the phenomenological behavior is highly simplified with respect to the structural analysis by piezoelectric models. This research project aims for a numerical and phenomenological model, which captures the physical bending behavior of EAPap by considering the piezo effect as well as the diffusion of ions. Since EAPap is a rather thin structure, a shell formulation is derived as a starting point for the modeling. We seek for a model that incorporates the inhomogeneous ionic distribution by a so-called scaled boundary shell formulation. Additionally, it facilitates the computation of the highly non-linear strains through the thickness of the structure. An extension to electro-mechanical coupled problems is provided. We are aiming for a model that accounts for the bending actuation mechanism by describing the deformation of EAPap as a function of the ionic distribution. The model includes electrostatic forces as well as volumetric changes. Moreover, the time-dependent behavior is an additional focus of the project. In particular, a model for the ionic migration over time is proposed. For this purpose, the diffusion of ions is considered as a function of the applied external electric field. Finally, the project provides a simulation method for the development and refinement of EAPap actuators for realistic applications. This method may also be adapted conveniently to similar actuation principles as e.g. ionic polymer metal composites.