Fully coupled non-linear analysis of piezoelectric solids involving domain switching

Domain switching is the cause of signi cant non-linearity in the response of piezoelectric materials to mechanical and electrical e ects. In this paper, the response of piezoelectric solids is formulated by coupling thermal, electrical, and mechanical e ects. The constitutive equations are non-linear. Moreover, due to the domain switching phenomenon, the resulting governing equations become highly non-linear. The corresponding non-linear nite element equations are derived and solved by using an incremental technique. The developed formulation is rst veri ed against a number of benchmark problems for which a closed-form solution exists. Next, a cantilever beam made of PZT-4 is studied to evaluate the e ect of domain switching on the overall force–displacement response of the beam. A number of interesting observations are made with respect to the extent of non-linearity and its progressive spread as the load on the beam increases