7th International Eurasian Conference On Mathematical Sciences And Applications (IECMSA-2018), Kiev, Ukraine, 28 August 2018, vol.1, pp.1
In this study, the effect of various boundary conditions on the critical parameters in the 3D buckling delamination problem around the interface band crack contained in PZT/Metal/PZT sandwich rectangular thick plate is examined. Investigations of these problems are carried out within the scope of the piecewise homogeneous body model by utilizing the so-called 3D linearized theory of stability loss for piezoelectric materials .
It is assumed that band cracks lay on the interface surfaces between the face (PZT layers) and core (Metal) layers of the plate along the axis and the lateral edges of the plate are mechanically simply supported. Two type’s boundary conditions are considered with respect to the electrical quantities. For the first one it is assumed that electrical potentials are equal to zero on all face planes of the PZT layers. However, in the second one it is assumed that on the upper and lower face planes of the PZT layers the normal component of the electric displacement vector is equal to zero but on the all lateral edges of that the electric potential is equal to zero.
Moreover, it is assumed that on the opposite two ends of the plate which are parallel to the band crack’s fronts, uniformly distributed normal compressive mechanical forces act. Also, it is assumed that neither mechanically nor electrically any forces act on the cracks surfaces.
It is supposed that in the natural state the cracks’ edge surfaces have infinitesimal initial imperfections and due to aforementioned external compressive forces the magnitude of these imperfections grow and becomes indefinitely great under in the certain value of these forces. Namely, as in , this "certain" value of the external forces is taken as critical forces related to the buckling delamination of the plate under consideration.
The mathematical formulation of the problem under consideration is made as in  and corresponding boundary value problems are solved numerically by employing 3D FEM. Numerical results illustrated the influence of the difference of the boundary conditions with respect to the electrical quantities on the values of the critical forces are presented and discussed.
Keyword: Piezoelectric material, electrical potential, band crack, critical force, buckling delamination, sandwich rectangular thick plate.