Nonlinear bending of a sandwich beam with metal foam and GPLRC face-sheets using Chebyshev–Ritz method : Effects of agglomeration and internal pore

In this study, a sandwich structure composed of functionally graded graphene platelet (GPL)-reinforced composite (FG-GPLRC) face-sheets and a metal foam core considering GPL agglomeration is proposed. The face-sheets are multilayered, and the GPL volume fraction is constant in each layer. However, this volume varies according to a layer-wise rule in the thickness direction. A two-parameter model supported by the Mori–Tanaka approach is developed to provide solutions that quantifiably consider the negative influence of GPL agglomeration on the elastic properties of nanocomposites. The core is made of a metal foam with closed cells whose effective elastic properties are determined using the Gibson–Ashby model. Two types of porosity distributions, uniform and non-uniform variations in thickness, are considered. The nonlinear bending behaviors of this sandwich beam are investigated. Within the framework of an equivalent single-layer theory, the formulations governing the nonlinear bending problems are derived from a third-order shear deformation theory supported by the von Kármán nonlinearity. The Chebyshev–Ritz method, a numerically stable method, is applied to describe the beam under various classical boundary conditions. An extensive numerical study is implemented to examine the effects of the agglomerations and volume fraction of GPLs in the face-sheets, internal pores, and core-to-face ratio on the nonlinear bending response of sandwich beams.