Plane strain couple stress based contact mechanics of flexoelectric solids

Flexoelectric solids have the ability to convert strain gradients into electrical polarization, offering broad application prospects in micro- and nanoelectromechanical systems. In particular, when an indenter acts on a flexoelectric solid, a strong electromechanical coupling effect occurs near the contact area. However, to date, research on the contact mechanics of flexoelectric solids remains incomplete. This paper conducts the first thorough investigation into a family of contact problems in flexoelectric solids and uncovers novel multiphysics contact mechanisms rooted in generalized continuum mechanics. These multiple contact problems include half-plane contact, tilted contact, adhesive contact, contact of a finite-thickness layer, sliding frictional contact, and normal fretting contact. On the one hand, we employ Fourier transforms to convert these contact problems into singular integral equations, solve them to obtain the multiphysics fields on the contact surface, and investigate the effects of various indenter types. On the other hand, we establish mixed finite element formulations for couple stress based flexoelectricity. Combining contact surface stress distributions derived from solving singular integral equations, we perform finite element simulations of flexoelectric plane strain contact problems and obtain the internal field variable distributions. The theoretical solutions from the singular integral equations and the corresponding mixed finite element numerical solutions are mutually corroborative and complementary. This study helps to understand the mechanics and physics of flexoelectric contact problems and offers guidance for flexoelectric nanoindentation experiments and device design.