In this work, aspects considering material modeling of electro‐mechanical coupling in fiber reinforced electro‐active polymers (EAP) and the corresponding finite element implementation are considered. We propose a constitutive model that takes into account the electro‐viscoelastic behavior of the isotropic matrix and the influence of unidirectional fibers on both the hyperelastic response and the viscous behavior of the whole composite. Two distinct existing models that describe the electro‐mechanical coupling, are demonstrated and implemented, moreover, a numerical link between both models for three‐dimensional continua in terms of tensor calculus, is identified. We propose the extended‐tube model for the elastic response with some of its parameters evolving in response to the electric field, in order to fit electro‐viscoelastic experiments. Regarding the finite element implementation, in addition to the deformation field and the electric potential, two pairs of field variables are introduced on the element level, to enforce quasi‐incompressibility and quasi‐inextensibility. It is shown that using the mixed finite element improves the convergence behavior for the simulation of soft EAP with relatively stiff fibers. Moreover, the choice of the model that expresses the nature of the underlying coupling is shown to noticeably affect the degree of simulated actuation in fiber reinforced actuators.

中文翻译：

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纤维增强电活性聚合物中电粘弹性的有限元建模

在这项工作中，考虑了考虑纤维增强电活性聚合物（EAP）中机电耦合材料建模的方面以及相应的有限元实现方式。我们提出了一个本构模型，该模型考虑了各向同性基体的电粘弹性行为以及单向纤维对整个复合材料的超弹性响应和粘性行为的影响。演示并实现了两个描述机电耦合的现有模型，此外，还确定了两个用于张量微积分的三维连续性模型之间的数值联系。为了适应电粘弹性实验，我们提出了弹性响应的扩展管模型，其中一些参数随电场的变化而变化。关于有限元的实现，除了形变场和电势外，在单元层还引入了两对场变量，以增强准不可压缩性和准不可拉伸性。结果表明，使用混合有限元可以改善具有相对刚性纤维的软EAP仿真的收敛性。而且，表明基本耦合特性的模型的选择显示出显着影响纤维增强执行器中模拟执行器的程度。结果表明，使用混合有限元可以改善具有相对刚性纤维的软EAP仿真的收敛性。而且，表明基本耦合特性的模型的选择显示出显着影响纤维增强执行器中模拟执行器的程度。结果表明，使用混合有限元可以改善具有相对刚性纤维的软EAP仿真的收敛性。而且，表明基本耦合特性的模型的选择显示出显着影响纤维增强执行器中模拟执行器的程度。