Electromechanical Behavior of Interface Deformable Piezoelectric Bilayer Beams

Abstract

An interface deformable piezoelectric bilayer beam model is proposed to study the electromechanical responses and interface stress distributions in an intelligent layered structure. Like most of current approaches in the literature, the layerwise approximation of electric potential is employed. While in contrast to the linear approximation where the induced electric field is ignored, the present model takes a quadratic variation of the potentials across the thickness, thus warranting an efficient and accurate modeling of the electric field. Completely different from the widely used equivalent single layer model, in which the whole laminate is assumed to deform as a single layer and thus has a smooth variation of the displacement field over the thickness, the present model considers each sublayer as a single linearly elastic Timoshenko beam perfectly bonded together and therefore with individual deformations. To ensure the continuity of deformations of two adjacent sublayers along the interface, two interface compliance coefficients are introduced, by which both the longitudinal and vertical displacement components along the interface of two sublayers due to the interface shear and normal stresses are taken into account. To assess the performance of the present model, a number of benchmark tests are performed for a piezoelectric bimorph and a piezoelectric-elastic bilayer beam subjected to (1) a force density normal to the upper face and (2) an electric potential applied to the top and bottom faces. A remarkable agreement achieved between the present solution and the finite element computations illustrates the validity of the present study. The present model not only predicts well the global responses (displacement, electric charge, etc.), but also provides excellent estimates of the local responses (through-thickness variations of electromechanical state, interface stress distributions, etc.) of the piezoelectric layered structures. The novel mechanics model of electroelastic layered structures presented can be used to efficiently and effectively characterize hybrid smart devices and develop/optimize new multifunctional materials.