Continuum Mechanical Modelling of Coupled Ferroelectricity and Elastoplasticity

Abstract

The study of nonlinear electromechanical coupling has gained significant interest in recent years, driven by advancements in materials capable of large deformations in response to electric fields. These materials, often referred to smart materials, have a wide range of applications such as data storage, sensing, energy harvesting, and adaptive optics (Dorfmann and Ogden, 2014). Ferroelectrics are a subset of smart materials, distinguished by unique properties that make them highly useful in diverse applications. They are known for their irreversible polarisation and ability to switch polarisation states under an external electric field, exhibiting intricate nonlinear responses (Singh et al., 2022). By applying a large enough electric field to this material (higher than the coercive field), they attain an irreversible polarisation which can be removed by applying electric field in the opposite direction. Another specific property of these materials is their piezoelectric behaviour: they generate electrical charges when subjected to mechanical stress and undergo mechanical deformation in response to an external electric field. This thesis presents a comprehensive nonlinear frameworks for ferroelectricity and piezoelectricity behaviours by considering separate admissible domains for the electrical and the mechanical responses. First we introduce a framework for the ferroelectricity of a rigid body, i.e. without any deformation. Then we extend this framework to model the piezoelectric behaviour of a deformable ferroelectric body under finite deformations. To evaluate the capability of the proposed ferroelectricity model, two numerical methods are employed: the Finite Difference Method (FDM) and the Finite Element Method (FEM). For the piezoelectric model, FEM implementations are outlined as a foundation for the future simulation work.