Analytical study of electromechanical buckling of a micro spherical elastic film on a compliant substrate part II: Postbuckling analysis

This work presents an analytical study of the electromechanical postbuckling of a spherical elastic thin film electrode that is bonded to a spherical dielectric compliant substrate. The compliant substrate is bonded to an inner rigid, fixed and electrically grounded spherical electrode. As will be shown, when the applied voltage reaches a critical value, the film buckles into a well ordered periodic surface patterns. The electromechanical postbuckling problem will analytically be solved for the one-dimensional, square checkerboard, hexagonal and herringbone periodic patterns. This work studies the effect of different geometry and material parameters on the selection and wavelength of the preferred/stable surface pattern of the buckled film. As will be deduced, the preferred buckling pattern can be determined to be either hexagonal or herringbone pattern depending on the geometry and material parameters of the film/substrate system. Furthermore, we study the effect of nonlinear stiffness of the compliant substrate on the electromechanical behavior of the film. The simplicity of generating and removing elastic surface wrinklings by On/Off voltage switching sufficiently increases the potential of the electromechanical buckling response to be employed in different MEMS application, such as, micro sensors, micro optical switches and deformable micro mirrors.