Thin piezoelectric rods with quasi-static domain switching

We obtain a simple model for the electromechanical motion of a linear piezoelectric rod with quasi-static domain switching. We start from the three-dimensional linear piezoelasticity an by using suitable mechanical internal constraints and electrical semi-inverse hypotheses, we arrive at a one-dimensional enthalpy functional. By using standard variational tecniques then we get one-dimensional equations of motion for extension and bending which show the coupling between the mechanical and electrical properties of the material.