By designing an actuator composed of thin layers with different coefficients of thermal expansion (CTE) together with an electrically conductive layer, the CTE mismatch can be utilized to produce soft electrothermal actuators (ETAs). These actuators have been typically implemented using only two layers, commonly relying on Timoshenko's analytic model that correlates the temperature to the actuator's curvature. In this study, we extend the analytic model to include the thermoelectric relation present in ETAs, that is, the conductive layer's properties with respect to the operation temperature. By applying the thermoelectric relation, a minimal voltage optimization can be applied to the analytic model. Using dimensionless analysis, we optimize the ETAs performance for both bi- and tri-layer ETAs with and without the thermal modeling. The bi-layer optimization not only predicts the maximal value for the bi-layer performance but also provides the optimal thickness of each layer for any couple of materials. We validate the tri-layer analytic model experimentally by measuring the curvature for different third layer thicknesses. Finally, we optimize the tri-layer design based on the analytic model, which can achieve an improvement in curvature per voltage of >3000% over the optimal bi-layer ETA.
Keywords: electrothermal actuators; minimal voltage actuation; soft actuators; thermal expansion actuation.