A primal/dual approach for the accurate evaluation of the electromechanical coupling in MEMS

This paper presents a primal/dual approach to solve the coupled electromechanical problem arising in the modelling of electrostatically actuated micro-electromechanical systems (MEMS). After a derivation of complementary energy functionals for both the mechanical and the electrical problems, an original coupling strategy using a displacement-based (primal) mechanical formulation and an electric vector potential-based (dual) electrostatic formulation are elaborated. A derivation of the electric force and the tangent stiffness matrix of the coupled problem is obtained, based on the virtual work principle. The new formulation has interesting properties with respect to error estimation and pull-in voltage calculation, which is highlighted on the finite element solution of a micro-resonator structure.

► We develop a new variational approach for electromechanical problems in MEMS.
► A mechanical primal approach is strongly coupled to an electrostatic dual approach.
► Combination with primal approach provides good error estimation on pull-in curves.
► The maximum of the pull-in curve is computed with standard nonlinear algorithms.
► The primal/dual formulation greatly simplifies accurate pull-in computations.