Extended finite element for electromechanical coupling

In MEMS modelling the electro-mechanical coupling takes an important place. Indeed many devices use electrostatic forces as actuator. The numerical modelling of this type of problem needs a strong coupling between the mechanics and the electrostatic field. In fact when the structure is moving, the electrostatic field around it has to be modified in consequence. The first solution is to use finite element method to model the electrostatic field. In this case the mesh has to be updated depending on the displacement of the structure. Many researches have been performed to deform properly the electrostatic mesh, but when large displacement are takeninto account, the elements become distorted. Furthermore, when the pull-in is achieved, the electrodes are in contact and the layer of electrostatic elements is totally squeezed. The second usual solution is to use the boundary element method to model the electrostatic field. In this case, there are no more remeshing problem, but the computational time is larger and singularity problems appears when the electrodes become in contact. One solution for this remeshing problem is to use extended finite elements (X-FEM) which are a new type of elements tailored to simulate problems involving discontinuities and moving boundaries. Initially this methodology was created for crack propagation problems [1, 3, 5], but its application has been extended to several other problems such as elastic problem involving inclusions, flow-structure interaction and solidification problems. In this paper the concept of extended finite elements is applied to develop modelling approaches for the electro-mechanical coupling. The method will be illustrated here for a one-dimensional problem and implementation issues relative to the two-dimensional case are discussed.