Plane strain problem of flexoelectric cylindrical inhomogeneities

In nanotechnology, flexoelectric solids exhibit notable electrical polarization induced by internal strain gradients, rendering them promising for various applications. However, inherent material imperfections are inevitable. Particularly within flexoelectric solids, substantial strain gradients exist in proximity to internal defects, resulting in localized concentration of electrical polarization and potential structural failure. Among the various defect types, circular-shaped inhomogeneity is prevalent. This paper comprehensively investigates the plane strain problem on cylindrical inhomogeneities within flexoelectric solids. The full-field analytical solution is derived for this problem for the first time. Given that flexoelectric theory encompasses pure strain gradient elasticity theory, the strain gradient elasticity solution for plane strain cylindrical inhomogeneities is also established for the first time. This study reveals that the stiffness and size of the inhomogeneity, along with the loading ratio in two directions, exert a noteworthy influence on the local electromechanical coupling behavior near the inhomogeneity. Finally, the mixed finite element method is utilized to approximate the solution numerically, and the close agreement between the finite element results and the analytical solution demonstrates this study’s reliability and rigor. Therefore, this investigation imparts valuable insights into examining defects in flexoelectric solids and serves as a foundation for studying more intricate defect typologies. •The exact solution for flexoelectric cylindrical inhomogeneities is derived.•The inhomogeneity stiffness influences stress and polarization concentration.•Effects of loading conditions and inhomogeneity sizes are investigated.•A mixed finite element method is used for comparison with analytical results.