Design of compliant meanders for applications in MEMS, actuators, and flexible electronics

Meandering beams, crenellated surfaces, and zigzag-shaped electrodes are employed as compliant elements in microscale applications ranging from springs attached to proof masses in microelectromechanical systems (MEMS) to stretchable electrodes in flexible electronics and dielectric elastomer actuators. An understanding of how the meander shape affects the stiffness of these structures would permit preliminary design without the necessity of fabricating or running simulations on each case. In this paper, we present general guidelines for designing meandering cantilevers, showing how the amplitude, angle, length, and thickness affect both the axial and bending stiffnesses. Simple analytical expressions are derived, and the results are compared with those from numerical simulations and experimental measurements. The more complex case of a stiff thin film overlying a crenellated elastomer is also simulated.