A mixed finite element method for large deformation of flexoelectric materials

Flexoelectricity is a universal and size-dependent electromechanical phenomenon coupling the electric field with strain gradient in dielectric materials. we establishe a mixed variational principle and develop a mixed finite element method (FEM). This allows us to use C⁰-continuous interpolation functions in FEM instead of C¹ that is difficult to construct but has to be used in conventional FEM to investigate flexoelectricity. A good agreement between the analytical solutions and our numerical results of an infinite cylinder problem validates the present developed mixed FEM. We further investigate the effects of geometrically nonlinearity on flexoelectricity in soft dielectrics under large deformation. It is found that the flexoelectricity can be greatly enhanced due to the large deformation of soft dielectrics even with much smaller flexoelectric coefficients than popular ceramics. We also demonstrate the necessarity of adopting finite strain model or considering geometrical nonlinearity to precisely describing flexoelectric response in soft dielectrics. The findings in this work also suggest tremendous potential application of soft materials in the field of electromechanical sensors via flexoelectricity.