Multiphysics simulation of the aspherical deformation of piezo-glass membrane lenses including hysteresis, fabrication and non-linear effects

In this paper we present and verify the non-linear simulation of an aspherical adaptive lens based on a piezo-glass sandwich membrane with combined bending and buckling actuation. To predict the full non-linear piezoelectric behavior, we measured the non-linear charge coefficient, hysteresis and creep effects of the piezo material and inserted them into the FEM model using a virtual electric field. We further included and discussed the fabrication parameters -- glue layers and thermal stress -- and their variations. To verify our simulations, we fabricated and measured a set of lenses with different geometries, where we found good agreement and show that their qualitative behavior is also well described by a simple analytical model. We finally discuss the effects of the geometry on the electric response and find, e.g., an increased focal power range from $\pm 4.5$ to $\pm 9\, \mathrm{m}^{-1}$ when changing the aperture from $14$ to $10\, \mathrm{mm}$.