Second-Order Collocation-Based Mixed FEM for Flexoelectric Solids

Flexoelectricity is an electromechanical coupling between the electric field and mechanical strain gradient, as well strains observed in all dielectric materials, including those with centrosymmetry. demands C1-continuity for straightforward numerical implementation governing equations gradient theory are fourth-order partial differential equations. In this work, alternative collocation-based mixed finite element method direct flexoelectricity used, which a newly developed quadratic high capability of capturing gradients introduced. collocation method, through independently assumed polynomials collocated derived from displacements potential at points inside element. The obtained by taking directional derivative independent gradients. However, earlier proposed linear unable to capture components and, thus, simulate correctly. This problem solved present work using shape functions fewer degrees freedom than traditional method. A Fortran user-element code authors: first, after that, After verifying results literature, both elements’ behaviors tested different problems. It shown that second-order FEM can flexoelectric behavior better compared existing formulations.