Electromechanical FEM models and electrostatic forces near sharp corners

Accounting for multiphysical coupling in models of Micro Electro Mechanical Systems (MEMS) is
essential for accurate simulations. One essential multiphysical effect in MEMS is the electromechanical
coupling since electrostatic forces are often used for actuation or sensing in those devices. Often
MEMS are designed such that their shape exhibits many corners. In this paper two different numerical
approaches are used to model this coupling using the Finite Element Method: the electrostatic forces
are either derived from the variational approach or a local approach based on the Maxwell stress tensor
such as implemented in commercial Finite Element codes. The evaluation of electrostatic forces near
corners is investigated in detail and in this paper the two approaches are compared around corners.
Although the issue of numerical models around singularities is not new, the question addressed here is
related to the computation of electric forces in the vicinity of corners. Since those forces are quadratic
functions of the electric field, namely the gradient of the electric potential, here the primal unknown,
computing those forces accurately is a challenge in itself. Elements which use special shape functions
are used to discretize the field near this corner singularity as well. In the work presented here, it is shown that a significant discrepancy appears in the electrostatic force computed around a corner
depending on the discretization approach considered, and we conclude that the variational approach
or equivalently the full Maxwell tensor should be used to properly evaluate electrostatic forces around
corners.