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A Model for an Anisotropic Flexoelectric Material with Cubic Symmetry

In this study, the responsive-behavior of an anisotropic, elastic, flexoelectric material with cubic internal structure to mechanical loads is formulated and examined. The elastic deformation and spontaneous polarization patterns of these materials, as well as the mechanical properties, are described. The first strain gradient theory is employed to describe flexoelectric phenomenon in dielectric materials. The equations governing the elastostatic equilibrium of flexoelectric materials under infinitesimal strain gradient regimes are derived depending on the elegant variational formulation introduced by Topuin [1956] and Mindlin [1972]. Explicit analytical expressions of the displacement and spontaneous polarization for the plane strain problem of the rectangular domain subjected to external forces are derived using the so-called semi-inverse method. The magnesium oxide MgO (magnesia) is used as an example of dielectric materials with cubic internal structure since it is widely used in thin-film substrate and fabrication of microwave devices. The results revealed that flexoelectric materials exhibit spontaneous polarization due to the elastic extensibility and elastic compressibility.