Three-dimensional modeling of static deformation of arbitrary functionally graded multilayered multiferroic composites plates with weakly and highly conducting imperfect interfaces

Abstract

In this paper, a three-dimensional static deformation of arbitrary functionally graded multilayered multiferroic composites plates with weakly and highly conducting imperfect interfaces is derived. The magnetoelectroelastic properties of each layer of the composite plates have been assumed varying throughout the thickness direction. The imperfect interfaces between the layers are assumed to be mechanically compliant, dielectrically and magnetically weakly or highly conducting. In each layer, the state-space approach is firstly applied leading to space variable. Cauchy’s problem and adapted Runge-Kutta numerical procedure is used to solve the established state-space equation. The elaborated semi-analytical solution has been propagated throughout the multilayered multiferroic composites plates using the propagator matrix method and accounting the transfers matrices at each imperfect interface. The developed formulas have been programmed and the numerical obtained results have been well compared with available ones. For the computation process, the piezoelectric material $\mathrm{BaTi}{O}_3$ and piezomagnetic material $\mathrm{CoF}{e}_2{O}_4$ are used. In addition, these numerical tests showed that the proposed solution is in good agreement with the available 3D asymptotic approach, the modified Pagano method, the pseudo-Stroh formalism, the finite elements method and the Peano series solution. Furthermore, the effects of mechanically compliant, dielectrically and magnetically weakly or highly conducting imperfect interface on the static response and the magnetoelectric coupling coefficient of the functionally graded multilayered multiferroic composites plates for various configurations have been also analyzed. It has been carried out that, the bending response and the magnetoelectric coupling coefficient of the multiferroic composites plates remarkably depend on the kind of imperfect interface, the used sequences as well as on the loadings conditions namely mechanical, electric or magnetic, respectively.