Nonlinear bending of FG metal/graphene sandwich microplates with metal foam core resting on nonlinear elastic foundations via a new plate theory

Nonlinear bending of functionally graded metal/graphene (FGMG) sandwich rectangular plate with metal foam core resting on nonlinear elastic foundations is elucidated in this article. A new shear deformation plate theory is presented to formulate the displacement field. The nonlinear partial differential equations considering the small size effect are established via the principle of virtual work. The nonlinearity is considered by using Von Karman's strain-displacement relations. While, the size effect is captured by employing the modified couple stress theory. The upper and lower layers are made of aluminum as a matrix that reinforced with graphene platelets (GPLs). The GPLs are functionally graded through the thickness of the face layers according to a new cosine rule. Moreover, the metal foam core is also made of aluminum containing porosities that uniformly distributed or functionally graded through the core thickness. The governing equations are solved based on the Galerkin and Newton's methods. The obtained results are examined by introducing some comparison examples. In addition, several parametric examples are discussed including the effects of the porosity type, GPLs distribution type, core-to-face thickness, elastic foundation stiffness, side-to-thickness ratio, plate aspect ratio and material length scale parameter on the nonlinear deflection and stresses of FGMG sandwich plate with metal foam core.