Dynamics of non-linear thin piezoelectric rods with domain switching

We obtain a model for the non-linear electromechanical motion of piezoelectric rod with domain switching. We assume the piezoelectric body as a continuum with a microstructure given by the effective number of switchable aligned dipoles. As in previous related works, by using suitable mechanical internal constraints and electrical semi-inverse hypotheses, we arrive at a one-dimensional functional. With standard variational techniques then we get one-dimensional equations of motion for the non-linear extension and bending of a piezoelectric rod with domain switching.