An isogeometric finite element formulation of electromechanically coupled beams with cross-sectional deformations and frictional contact for dielectric elastomer smart textiles

用于介电弹性体智能纺织品的具有横截面变形和摩擦接触的机电耦合梁的等几何有限元公式

• 批准号: 523829370
• 负责人: Dr. Myung-Jin Choi, Ph.D.
• 金额: --
• 依托单位: Lehrstuhl für Baustatik und Baudynamik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/523829370?language=en
• 关键词: isogeometric; finite; element; formulation; electromechanically

Textile-based capacitive pressure sensors have been developed for many applications including wearable electronics, artificial skin, and structural health monitoring. For developing an innovative design or mechanism of the sensors, an efficient and accurate simulation method is necessary. This project aims at developing a new finite element formulation of beams for a direct numerical simulation of electromechanically coupled textile structures at the level of individual fibers. Each fiber is modeled by a beam formulation, which requires much less degrees-of-freedom, compared with the brick element formulation. We consider a circular cross-section having multiple layers of material in the radial direction: a conductor surrounded by a dielectric elastomer. The operation of our envisioned capacitive pressure sensors can be simply explained by an equivalent capacitor generated at the crossing point of the fibers. The conductors are charged oppositely, so that an electrical field is generated between them, which polarizes the charges in the elastomer layer in between. The elastomer is compressed by an external load, and the capacitance changes due to the change of the distance between crossing conductors, and the contact area. Therefore, in the simulation of the capacitive sensors, it is significant to incorporate the cross-sectional strains in the new beam formulation, which is in contrast to the conventional methods, which typically assume rigid cross-sections. We employ a Cosserat beam formulation with unconstrained directors, where the stretching and rotation of directors represent the cross-sectional strains efficiently. We further enrich the cross-sectional strains as incompatible modes, using an enhanced assumed strain (EAS) method. The electromechanical coupling may occur in several parts including constitutive laws, electrostatic force between conductors, and contact conditions. We employ a constitutive law from a free energy function, which consists of three parts; mechanical, electrical, and polarization. The new beam formulation does not assume any zero stress conditions, and represent 3-D stress, strain, and electrical fields, which enables a straightforward application of 3-D constitutive laws. In the beam-to-beam contact formulation, we employ a Gauss point-to-surface contact algorithm. An isogeometric analysis using NURBS (Non-uniform rational B-spline) basis functions gives a higher order continuity along the beam’s longitudinal and circumferential directions, which yields a robust local Newton-Raphson process for the closest point projection. In the electrical contact, we also investigate the effect of the electrostatic force between polarized elastomers, and charged conductors. The research project is intended to contribute to a deeper understanding of how smart textiles work.

基于纺织品的电容式压力传感器已经被开发用于许多应用，包括可穿戴电子设备、人造皮肤和结构健康监测。为了开发传感器的创新设计或机制，需要一种有效且准确的仿真方法。该项目旨在开发一种新的梁有限元公式，用于在单个纤维水平上直接数值模拟机电耦合的纺织结构。每根纤维由梁公式建模，与砖单元公式相比，它需要更少的自由度。我们考虑一个圆形的横截面，在径向方向上有多层材料：一个导体包围的介电弹性体。我们设想的电容式压力传感器的操作可以简单地通过在纤维的交叉点处产生的等效电容器来解释。导体带相反的电荷，从而在它们之间产生电场，该电场使其间的弹性体层中的电荷极化。弹性体被外部负载压缩，并且电容由于交叉导体之间的距离和接触面积的变化而变化。因此，在电容传感器的模拟中，将横截面应变纳入新的梁公式中非常重要，这与通常假设刚性横截面的传统方法相反。我们采用Cosserat梁配方与不受约束的董事，其中的拉伸和旋转的董事代表的横截面应变有效。我们进一步丰富的横截面应变不兼容模式，使用增强的假设应变（EAS）方法。机电耦合可以发生在几个部分，包括本构律，导体之间的静电力，和接触条件。我们采用的本构关系从自由能函数，其中包括三个部分：机械，电气和极化。新的梁公式不假设任何零应力条件，而是代表三维应力、应变和电场，这使得可以直接应用三维本构律。在梁-梁接触公式中，我们采用高斯点-面接触算法。使用NURBS（非均匀有理B样条）基函数的等几何分析给出了沿着梁的纵向和周向的高阶连续性，这产生了用于最近点投影的鲁棒局部Newton-Raphson过程。在电接触中，我们也研究了极化弹性体和带电导体之间的静电力的影响。该研究项目旨在加深对智能纺织品工作原理的理解。