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Instability of compressible soft electroactive plates
International Journal of Engineering Science ( IF 6.6 ) Pub Date : 2021-04-02 , DOI: 10.1016/j.ijengsci.2021.103474
Guozhan Xia , Yipin Su , Weiqiu Chen

In this paper, we investigate the formation of two-dimensional surface wrinkles in a pre-deformed compressible soft electroactive (SEA) plate. Two common electrical loading protocols are considered: one is the so-called voltage-control where the plate is applied with a constant voltage across the thickness; the other is named as charge-control where the plate is activated by uniformly spraying electrical charges on its main faces. By developing the surface impedance matrix method with the Stroh formulation for compressible SEA materials, we decouple the resulting dispersion equations into symmetric and antisymmetric modes and obtain the associated closed-form expressions, respectively. These analytical expressions of the critical stretch are crucial to the quantitative understanding of wrinkling in the SEA plate. For illustration, we treat examples of compressible Gent and neo-Hookean ideal dielectric elastomers. Results show that the symmetric wrinkles may appear prior to the antisymmetric ones in a sufficiently stretched compressible SEA plate. This phenomenon is in principle caused by the release of incompressibility constraint, upon which the variation of the material chain extension limit only mildly affects the magnitude of the critical stretch. Especially, for charge-controlled plates, a compressibility-driven competition mechanism is revealed that with the increase of compressibility, the symmetric wrinkling is promoted while the antisymmetric one is suppressed. Moreover, enhancing compressibility significantly stabilizes the intrinsic instability of charge-controlled plate while makes the voltage-controlled plate more unstable. These findings, for the first time, systematically demonstrate the great significance of material compressibility on the nonlinear response and stability performance of SEA elastomers and can serve a quantitative guidance for the industrial design of new-generation SEA-based devices by exploring the material compressibility.



中文翻译:

可压缩软电活性板的不稳定性

在本文中,我们研究了预变形的可压缩软电活性(SEA)板中二维表面皱纹的形成。考虑了两种常见的电加载规程:一种是所谓的电压控制,其中在整个厚度方向上以恒定电压施加金属板;另一个被称为电荷控制,其中通过在板的主表面上均匀地喷洒电荷来激活板。通过使用Stroh公式开发可压缩SEA材料的表面阻抗矩阵方法,我们将得到的色散方程解耦为对称和反对称模式,并分别获得相关的闭式表达式。临界拉伸的这些分析表达式对于定量理解SEA板中的皱纹至关重要。为了说明,我们以可压缩的Gent和新霍克理想的介电弹性体为例。结果表明,在充分拉伸的可压缩SEA板中,对称皱纹可能先于反对称皱纹出现。该现象原则上是由不可压缩约束的释放引起的,在该约束下,材料链延伸极限的变化仅轻微地影响临界拉伸的大小。特别是,对于电荷控制板,揭示了一种压缩性驱动的竞争机制,即随着压缩率的增加,对称起皱被促进,而反对称被抑制。此外,提高可压缩性显着地稳定了电荷控制板的固有不稳定性,同时使电压控制板更加不稳定。这些发现,结果表明,在充分拉伸的可压缩SEA板中,对称皱纹可能先于反对称皱纹出现。该现象原则上是由不可压缩约束的释放引起的,在该约束下,材料链延伸极限的变化仅轻微地影响临界拉伸的大小。特别是,对于电荷控制板,揭示了一种压缩性驱动的竞争机制,即随着压缩率的增加,对称起皱被促进,而反对称被抑制。此外,提高可压缩性显着地稳定了电荷控制板的固有不稳定性,同时使电压控制板更加不稳定。这些发现,结果表明,在充分拉伸的可压缩SEA板中,对称皱纹可能先于反对称皱纹出现。该现象原则上是由不可压缩约束的释放引起的,在该约束下,材料链延伸极限的变化仅轻微地影响临界拉伸的大小。特别是,对于电荷控制板,揭示了一种压缩性驱动的竞争机制,即随着压缩率的增加,对称起皱被促进,而反对称被抑制。此外,提高可压缩性显着地稳定了电荷控制板的固有不稳定性,同时使电压控制板更加不稳定。这些发现,该现象原则上是由不可压缩约束的释放引起的,在该约束下,材料链延伸极限的变化仅轻微地影响临界拉伸的大小。特别是,对于电荷控制板,揭示了一种压缩性驱动的竞争机制,即随着压缩率的增加,对称起皱被促进,而反对称被抑制。此外,提高可压缩性显着地稳定了电荷控制板的固有不稳定性,同时使电压控制板更加不稳定。这些发现,该现象原则上是由不可压缩约束的释放引起的,在该约束下,材料链延伸极限的变化仅轻微地影响临界拉伸的大小。特别是,对于电荷控制板,揭示了一种压缩性驱动的竞争机制,即随着压缩率的增加,对称起皱被促进,而反对称被抑制。此外,提高可压缩性显着地稳定了电荷控制板的固有不稳定性,同时使电压控制板更加不稳定。这些发现,揭示了一种可压缩性驱动的竞争机制,即随着可压缩性的增加,对称起皱被促进,而反对称被抑制。此外,提高可压缩性显着地稳定了电荷控制板的固有不稳定性,同时使电压控制板更加不稳定。这些发现,揭示了一种可压缩性驱动的竞争机制,即随着可压缩性的增加,对称起皱被促进,而反对称被抑制。此外,提高可压缩性显着地稳定了电荷控制板的固有不稳定性,同时使电压控制板更加不稳定。这些发现,首次系统地证明了材料可压缩性对SEA弹性体的非线性响应和稳定性能的重大意义,并且可以通过探索材料的可压缩性为新一代基于SEA的设备的工业设计提供定量指导。

更新日期:2021-04-02
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