The flexoelectric effect, which is sensitive to size, refers to the phenomenon of coupling between the strain gradient and electrical polarization and involves higher-order derivatives of physical quantities such as displacement, and the analytical process is complicated and difficult. Therefore, in this paper, a mixed finite element method is developed considering the effects of size effect and flexoelectric effect on the electromechanical coupling behavior of microscale flexoelectric materials. Based on the theoretical model of enthalpy density and the modified couple stress theory, the theoretical model and finite element model of microscale flexoelectric effect are established, and the Lagrange multiplier is used to coordinate the higher-order derivative relationship between the displacement field and its gradient, and the C1 continuous quadrilateral 8-node (displacement and potential) and 4-node (displacement gradient and Lagrange multipliers) flexoelectric mixed element. By comparing the numerical calculation results and analytical solutions of the electrical output characteristics of the microscale BST/PDMS laminated cantilever structure, it is proved that the mixed finite element method designed in this paper is an effective tool for studying the electromechanical coupling behavior of flexoelectric materials.
Keywords: C1 continuous mixed element; cross-scale laminated structure; flexoelectric effect; micro-scale electromechanical coupling characteristics.