The Emergence of Surface Boundary Layers and Surface Effects in Flexoelectric Dielectrics

  • Codony, David (Universitat Politècnica de Catalunya)
  • Greco, Francesco (Universitat Politècnica de Catalunya)
  • Dingle, Mònica (Universitat Politècnica de Catalunya)
  • Mohammadi, Hossein (Universitat Politècnica de Catalunya)
  • Fernández-Méndez, Sonia (Universitat Politècnica de Catalunya)
  • Arias, Irene (Universitat Politècnica de Catalunya)

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Flexoelectricity is a universal property of all dielectric materials. While traditionally viewed as a bulk phenomenon only, in finite samples the symmetry-breaking nature of free surfaces induces electromechanical responses that are absent in infinite media. Just as the surface of a liquid behaves differently than the bulk fluid by surface tension due to the molecules at the edge missing neighbors, the surfaces of a flexoelectric material behave as a piezoelectric skin that dominates the material's behavior at small enough scales. This talk discusses how bulk flexoelectricity naturally causes boundary layers in strain and electric field components in finite samples [1]. These boundary layers grow exponentially near the surfaces, with widths dictated by the material's internal length scales. As a result, additional electromechanical couplings emerge at the surface, reminiscent of surface-elasticity and surface-piezoelectricity. Such surface effects can play a critical role in electromechanical devices with high surface-to-volume ratios [2], such as lattice metamaterials, where surface-driven responses can compete with, or even overtake, bulk effects at the nanoscale. These findings are taken into account in a newly developed formulation for 1D Euler-Bernoulli beams [3], which accounts for transversal strains, longitudinal electric field, and the bulk flexoelectricity-induced longitudinal and transversal boundary layers. While transversal boundary layers may tune the effective bending stiffness and other relevant properties of the beam, the role of longitudinal boundary layers is found to be essential to explain non-vanishing longitudinal electric fields, as those present in flexoelectric truss structures. REFERENCES [1] Mohammadi, H., Greco, F., Codony, D., Arias, I., Flexoelectricity causes surface piezoelectric-like effects in dielectrics, International Journal of Mechanical Sciences, 293, 110162, 2025. [2] Dingle, M., Arias, I., Codony, D., Continuum and computational modeling of surface effects in flexoelectric materials, Computer Methods in Applied Mechanics and Engineering, 441, 117971, 2025. [3] Greco, F., Codony, D., Arias, I., High-order flexoelectric beam and bar elements, To be submitted, 2026.