A three-dimensional collocation finite element method for higher-order electromechanical coupling

Flexoelectricity is a fundamental property found in all nano/micro-scale dielectric materials, even those with centrosymmetry. It describes coupling between electric field and nonuniform mechanical strains, as well as between electric field gradient and mechanical strains. This work presents a three-dimensional second-order collocation finite element method, which can model higher-order electromechanical coupling and is computationally efficient. The formulations for the 27-noded mixed finite element based on the collocation principle are derived and translated into Fortran code. Additionally, a 27-noded element mesh generating script is developed. The new finite element is validated by simulating various boundary value problems and comparing the outcomes with known 2D and 3D results, showing a good agreement. The developed finite element can be used for computationally efficient simulations of the complex electromechanical structures including flexoelectricity.