The role of network topology on the uniaxial tensile behaviour of low density random open cellular structures

Abstract

The effect of cellular structure on the mechanical properties of cellular solids is included in the prefactors of the relative density term in the Gibson and Ashby scaling laws. The effect of cell shape, cell size distribution, cell shape anisotropy, cell wall curvature and strut cross sectional variation have been known to affect these prefactors. This paper investigates the dependence of these prefactors on the network connectivity in random honeycombs and three-dimensional random open cellular structures. Beginning with intact structures, the network connectivity is reduced by randomly removing struts. A scaled genus density, that remains independent of sample volume, absolute cell size, and the relative density, has been defined and taken as a quantitative measure of the global connectivity. The variation in the overall stiffness and offset yield stress due to loss in connectivity was found to clearly depend on the scaled genus density when the relative density is kept constant, indicating that the geometric prefactors are functions of scaled genus density. The prefactors for intact perturbed cubic voronoi, perturbed BCC voronoi structures, and perturbed cubic body diagonal lattices with widely differing scaled genus density also confirm this strong correlation. We also show that the prefactors can be factored to quantitatively decouple the effects of anisotropy and scaled genus density.