A nonlinear mathematical model for large deflection of incompressible saturated poroelastic plates with in-plane diffusion

In this paper, a nonlinear mathematical model for large defection analysis of microscopic incompressible saturated poroelastic plates with in-plane diffusion was established. First, based on the theory of porous media (mixture theory with concept of volume fraction), the dynamical coupled equations for nonlinear deformations of the fluid-solid mixture were presented in the Lagrangian reference system. Secondly, with the Kirchhoff hypothesis and neglecting the in-plane inertia effect, a system of nonlinear governing equations for the large defections of incompressible saturated poroelastic plates with in-plane diffusion was derived. Finally, a cylindrical nonlinear bending problem of a rectangular poroelastic plate was investigated and discussed.