Traditional dielectric elastomers exhibit an unstable response when the electric field reaches a certain threshold, known as electro-mechanical instability, which significantly limits the broad application of these soft active materials. Recently, a bimodal-networked dielectric elastomer has been designed without suffering from the electro-mechanical instability due to a clear strain stiffening effect in the median strain regime (Science, 2022, 377, 228). In this work, we develop a constitutive model to fully describe the mechanical and electro-activated response of this novel dielectric elastomer. The free energy density consists of a time-independent hyperelastic component, time-dependent viscous components and an electrical component. A hyperelastic function dependent on both the first and second strain invariants is proposed to fully capture the stress response. The form of ideal dielectric elastomers is adopted for the electrical free energy. With further incorporation of viscous effects, the model is able to describe both static electro-actuated behavior as well as the frequency-dependent actuation performance upon a square wave voltage loading. The model is also implemented for finite element analysis to design tubular actuators which have been extensively used in the area of soft robotics.

中文翻译：

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新型无机电不稳定介电弹性体的连续体模型


当电场达到一定阈值时，传统的介电弹性体会表现出不稳定的响应，称为机电不稳定性，这极大地限制了这些软活性材料的广泛应用。最近，由于在中位应变状态中具有明显的应变硬化效应，人们设计了一种双峰网络介电弹性体，而不会受到机电不稳定的影响（科学，2022,377,228）。在这项工作中，我们开发了一个本构模型来充分描述这种新型介电弹性体的机械和电激活响应。自由能密度由与时间无关的超弹性分量、与时间相关的粘性分量和电分量组成。提出了一个依赖于第一和第二应变不变量的超弹性函数来完全捕获应力响应。电自由能采用理想介电弹性体的形式。通过进一步结合粘性效应，该模型能够描述静态电驱动行为以及方波电压负载下与频率相关的驱动性能。该模型还用于有限元分析，以设计已广泛用于软机器人领域的管状致动器。