A second-order solution of Saint-Venant's problem for a piezoelectric circular bar using Signorini's perturbation method

We study electromechanical deformations of a homogeneous transversely isotr opic piezoelectric prismatic circular bar loaded only at the end faces. The constitutive relations for the material of the bar are taken to be quadrat ic in the displacement gradients and the electric field. It is found that t he two end faces of the bar when twisted with no electric charge applied to them will exhibit a difference in the electric potential. Thus the piezoel ectric cylinder could be used to measure the torque or the angular twist.