Voronoi-based three-dimensional polygonal finite elements for electromechanical problems

We discuss the combination of a hybrid finite element approach and three-dimensional Voronoi-based mesh discretisations for electromechanically coupled problems. The fluxes, i.e. the stresses and electric displacements, are defined within the volume of the polygonal finite elements, whereas the displacements and electric potential are approximated on the boundaries of the elements. A Voronoi polygon with arbitrary, but admissible, number of surfaces and nodes thereby acts as a single finite element. Representative numerical examples for electromechanical problems, in particular piezoelectric materials, are presented and discussed.