Axisymmetric Contact Mechanics of Flexoelectric Solids

 Axisymmetric couple stress–based contact mechanics brings a refined lens to how flexoelectric solids behave when they are pressed, indented, or otherwise mechanically contacted. Unlike classical elasticity, couple stress theory captures size-dependent effects by accounting for material microstructure and rotational interactions at small scales. This becomes especially important for flexoelectric solids, where mechanical strain gradients can directly induce electric polarization, even in centrosymmetric materials that would otherwise be non-piezoelectric.

When an axisymmetric contact problem—such as spherical or cylindrical indentation—is analyzed under a couple stress framework, the stress field no longer depends solely on conventional force stresses. Higher-order stresses and characteristic length scales enter the formulation, leading to modified pressure distributions and displacement fields. These microstructural effects become pronounced as the contact radius approaches the internal material length scale, making classical Hertzian contact predictions insufficient for micro- and nano-scale applications.

Flexoelectric coupling further enriches this behavior by linking the strain gradient near the contact zone to an induced electric field. In axisymmetric contact, large strain gradients naturally develop beneath the indenter, resulting in localized electric polarization and measurable electric potentials. This electromechanical interaction can alter the effective stiffness of the contact region, influencing both load–displacement relations and energy transfer at the interface.

The couple stress formulation also improves the understanding of boundary conditions at the contact surface. Traditional theories often underestimate surface effects, while couple stress–based models capture additional resistance to deformation due to material curvature and rotation. In flexoelectric solids, these surface and gradient effects can amplify or suppress the generated electric response, depending on material properties and contact geometry.

Overall, axisymmetric couple stress–based contact mechanics provides a powerful framework for designing and interpreting experiments on flexoelectric materials at small scales. It supports the development of advanced sensors, energy harvesters, and nanoelectromechanical systems, where contact-induced electromechanical coupling is not a side effect but a functional advantage driven by material microstructure and strain-gradient physics.