Geometry Independent Direct and Converse Flexoelectric Effects in Functionally Graded Dielectrics: An Isogeometric Analysis

In the present study, a functionally graded material (FGM) based dielectric composite is investigated for direct and converse flexoelectric effects induced due to material inhomogeneity. An Isogeometric analysis based formulation is employed to effectively capture the gradient terms appearing in the electro-elastic coupling constitutive laws of flexoelectricity. Non-uniform stresses and strains generated due to non-uniform elastic properties in the domain induce flexoelectricity inherently without any special geometric and/or boundary conditions. A two-dimensional (2D) FGM structure made by the combination of polyvinylidene fluoride (PVDF) and barium titanate (BaTiO₃) is studied under mechanical and thermal loading conditions for its flexoelectric response. The induced polarization and voltage along with its dependence on grading index (n) is analyzed. Further, to extend the study to converse flexoelectricity, the mechanical response of the FG flexoelectric material under an applied electric potential is studied. Finally, the actuation of the structure by an applied electric field is studied. As high as 10% actuation of original displacement is observed for higher values of n. Effectiveness of the grading concept to induce flexoelectric response is established through numerical studies. Longitudinal and transverse modes of flexoelectricity are scrutinized and the concept of grading is proved to inherently induce the flexoelectricity in dielectrics without special geometric modifications.