A theory of flexoelectric membranes and effective properties of heterogeneous membranes

Recent developments in flexoelectricity, especially in nanostructures, have lead to several interesting notions such as piezoelectric materials without using piezoelectric materials and enhanced energy harvesting at the nanoscale, among others. In the biological context also, membrane flexoelectricity has been hypothesized to play an important role, e.g., biological mechanotransduction and hearing mechanisms, among others. In this paper, we consider a heterogeneous flexoelectric membrane and derive the homogenized or renormalized flexoelectric, dielectric, and elastic response, therefore, relating the corresponding effective electromechanical properties to its microstructural details. Our work allows design of a microstructure to tailor flexoelectric response, and an illustrative example is given for biological membranes.