Finite Element Investigation of Mechanical Properties of Highly Porous Nanoscale Materials Composed of Regular Lattices from Gibson-Ashby Cells of Variable Geometry

In this research, a finite element model of regular highly porous foam structure based on the macro or nano sized Gibson-Ashby cell is proposed. To account for the dimensional effect, the Gurtin-Murdoch model was used, which considers the surface stresses arising on the boundaries of the cell. The computer model construction, finite element meshing, and the numerical solution of the homogenization problem were carried out in the ANSYS software package. Here, the influence of the cell geometry at a fixed porosity was initially investigated. The obtained results confirm that the effective moduli of highly porous structures composed of Gibson-Ashby cells depend not only on porosity, but also on the geometric configuration. For example, at the same porosity, cells with thicker edges have greater rigidity. Numerical experiments were also carried out at the nanoscale, that is, model considered surface stresses. The relative stiffness moduli of nanoscale structures are significantly higher than similar values of regular size structures. Moreover, the dimensional effect has a greater influence on the effective properties of a highly porous material than the cell configuration. For example, the relative effective Young’s modulus of a regular size structure with thick edges is smaller than that of a nanoscale structure with thin edges. In this paper, cells with a complex geometric structure are considered, so a representative volume loses the isotropic properties of the material. Therefore, a study of the anisotropic effective properties based on the Zener coefficient was also carried out.