Saint-Venant end effects in piezoceramic materials

The stress decay rate and characteristic decay length for anisotropic materials and ®ber composites have been intensively investigated. However, those for piezoelectric materials have not been studied. In this paper, we examine the Saint-Venant end e€ects of piezoceramic materials by considering the problem of a semi-in®nite piezoceramic strip polarized in the thickness direction and with applied voltages on the upper and lower surfaces. It is assumed that the gradient of electric potential in the axial direction is much smaller than that in the thickness direction. Thus, the governing equations in terms of the Airy stress function and electric potential function can be uncoupled. The governing equation in terms of the Airy stress function involves only two non-dimensional parameters after non-dimensionalization. Finally, the stress decay rates and characteristic decay lengths for a variety of piezoceramic materials are computed numerically, and their variation with the two non-dimensional parameters is presented.