Electrical coupling analysis of 2D time-multiplexing memory actuators exhibiting asymmetric butterfly hysteresis

We present the modeling and analysis of electrical coupling in a hysteretic deformable mirror with 2D memory piezoac- tuators, which are made of a purposely-designed piezomaterial sandwiched between electrodes arranged crosswise and actuated by a multiplexing approach. Using a modified Miller model to describe the memory effect which is based on the ferroelectric domain switching processes, the proposed framework is used to simulate the electric field dependence of the strain in the piezoelectric material that exhibits asymmetric butterfly loops with remnant deformation through the finite element method. The desired butterfly memory effect in the material is obtained by modifying the saturated dipole polarization curve in the Miller model. The proposed method allows us to numerically investigate the electrical coupling between actuators in more detail and correspondingly understand their influence to the mirror facesheet.