Couple stress-based flexoelectricity of frictionless contact in dielectrics

The presence of flexoelectricity in dielectric materials can affect the mechanics of contact between solid bodies, especially when viewed at the micro/nano-scale. Such an effect can also contribute significantly to contact electrification a charge transfer event that takes place at the contact interface. In particular, the state of deformation and stresses in the vicinity of the contacting area can differ markedly from that anticipated from classical elastic Hertzian contact theory. In the present work, we investigate the flexoelectric effect near the contacting area of an isotropic dielectric material pressed by a frictionless rigid insulator probe, serving as a model problem to reveal the potential role of flexoelectricity in contact mechanics and electrification. The investigation is based on consistent couple stress flexoelectric theory, in which electric polarization may appear due to two-way coupling between the electric field and mean curvature vectors, even for centrosymmetric dielectric materials. To this end, we develop a new boundary element formulation to calculate the displacement, stress, electric potential, and electric displacement for two-dimensional isotropic flexoelectric contact problems. The subsequent computational mechanics investigation highlights several important characteristics of triboelectric phenomena and shows that the state of stress and polarization in contacting isotropic dielectrics is dependent on the effective length scale parameter l of couple stress elasticity and the coupling flexoelectric coefficient f.