Smart materials respond to external stimuli, e.g., electric fields, which enables their use as sensors and actuators. The electromechanical coupling of the direct and converse piezoelectric effects, for instance, is used for both actuation and sensing in diverse engineering applications. The response of ferroelectric materials depends on their state of remanent polarization and the presence of an external electric field. To extend the operational range of sensors and actuators, an accurate understanding of the evolution of the material’s state of polarization is imperative, which requires both physical and geometric nonlinearities to be taken into account. Moreover, polymeric smart materials like PVDF allow significantly larger deformation as compared to conventional piezoelectric ceramics. The electromechanical coupling in piezoelectric materials manifests in ferroelectric and ferroelastic hystereses, which are related to both reversible and irreversible processes. Focusing on the latter, we transfer phenomenological models for domain switching in ferroelectric materials to the geometrically nonlinear regime. For this purpose, we follow related concepts of geometrically nonlinear elastoplasticity, where the concept of a multiplicative decomposition of the deformation gradient plays a key role. Accordingly, an additional deformation path that describes the evolution of the poled state from the unpoled referential configuration is introduced. The constitutive response of the material to mechanical and electrical loads is discussed, and dissipative internal forces that drive the evolution of the remanent polarization are derived within a thermodynamical framework and the principle of maximum dissipation.

中文翻译：

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铁电材料中的非线性机电耦合：大变形和滞后

智能材料会对外部刺激做出反应，例如电场，这使得它们能够用作传感器和执行器。例如，正反压电效应的机电耦合可用于各种工程应用中的驱动和传感。铁电材料的响应取决于它们的剩余极化状态和外部电场的存在。为了扩展传感器和执行器的操作范围，必须准确了解材料极化状态的演变，这需要同时考虑物理和几何非线性。此外，与传统压电陶瓷相比，像 PVDF 这样的聚合物智能材料允许显着更大的变形。压电材料中的机电耦合表现为铁电和铁弹性滞后，这与可逆和不可逆过程有关。关注后者，我们将铁电材料中域切换的现象学模型转移到几何非线性区域。为此，我们遵循几何非线性弹塑性的相关概念，其中变形梯度乘法分解的概念起着关键作用。因此，引入了一个额外的变形路径，该路径描述了从非极化参考配置极化状态的演变。讨论了材料对机械和电气负载的本构响应，