Nonlinear electromechanical behaviour of piezoelectric thin sheet actuators under large deformation

Piezoelectric thin sheet actuators have diverse potential applications in designing advanced structures, such as programmable systems, tunable active metamaterials and buckling-based energy harvesting systems. In this paper, the nonlinear electromechanical behaviour of piezoelectric thin sheet actuators under large deformation is studied based on a generalized elastica model. The presented model is distinct from the classical elastica, notably by considering the extensibility of the actuator and the coupled electromechanical loads. The thin-sheet actuator is treated as an extensible electroelastic Euler–Bernoulli beam, incorporating piezoelectric effects, axial deformation and large deflection. The problem is formulated as a generalized elastica problem and the analytical solution is provided. The general nonlinear behaviour of the actuator is then evaluated and the existence of different deformation modes is discussed. Typical examples are provided to show the effect of the electromechanical loading condition upon the nonlinear response of the actuator. The results from the new model are also compared with those from a simplified nonlinear model of elastic thin sheets to evaluate the effect of large deformation. The comparison shows a very good agreement for small deformation but predicts a significant discrepancy between the two modes when the deformation is large, indicating the necessity of considering the elastica effect when large deformation is to be considered in design. The current work offers fundamental insights into the electromechanical behaviour of thin-sheet piezoelectric actuators with large deformation, thereby advancing their performance for applications in advanced structures.