Mixed Finite Element Analysis of Flexoelectric Response: Exploring Unit Cell Stacking and Strain Gradient Modulation

Flexoelectricity, a coupling between strain gradients and electric polarization, has attracted significant interest due to its critical role in enhanced effects at small scales and its applicability across a diverse range of materials. Modeling flexoelectricity is challenging, especially in 3D, due to the higher-order equations involved, which require continuity conditions that limit the use of standard finite element methods. This study employs a modified mixed finite element formulation, specifically designed to account for spurious oscillations that can hinder convergence, particularly in large-scale problems solved with iterative solvers. A numerical analysis has been conducted to evaluate the effectiveness of stacking individual flexoelectric unit cells to achieve an enhanced overall flexoelectric response. The study also seeks to determine the feasibility of locally modifying the strain gradient to induce localized enhancements in the flexoelectric effect.