Electric field–curvature relationships for small and large deformation of piezoelectric bi-layers

A simple analytical framework is developed to capture the characteristic features of the electric field–curvature response of piezoelectric bi-layers. For small deformations, the curvatures developed depend on the mismatch in the piezoelectric strengths and the mechanical stiffnesses in both the layers, and the relative thicknesses and the electric potentials applied across each of the layers. For large deformations, a bifurcation in curvature is generally observed at characteristic electric fields which depend strongly on the geometric asymmetry of the bi-layers.