Pre-stressed curved actuators consist of a piezoelectric ceramic (lead zirconate titanate or PZT) sandwiched between various substrates and other top layers. In one configuration, the substrates are stainless steel with a top layer made with aluminum (THUNDER). In another configuration, the substrates and top are based on fiberglass and carbon composite layers (Lipca-C2). Due to their enhanced strain capabilities, these pre-stressed piezoelectric devices are of interest in a variety of aerospace applications. Their performance as a function of electric field, temperature and frequency is needed in order to optimize their operation. During the processing steps, a mismatch between the properties of the various layers leads to pre-stressing of the PZT layer. These internal stresses, combined with restricted lateral motion, are shown to enhance the axial displacement. The goal is to gain an understanding of the resulting piezoelectric behavior over a range of voltages, and frequencies. A nonlinear model, which quantifies the displacements generated in THUNDER actuators in response to applied voltages for a variety of boundary conditions, is developed. The model utilizes a hysteretic electric field-polarization relationship and predicts displacements based on the geometry and physical characteristics of the actuator components. The accuracy of the model and associated numerical method is demonstrated through comparison with experimental data.