A numerical approach to study the post-yield softening in cellular solids: role of microstructural ordering and cell size distribution

Abstract

Designing meta-materials and cellular solids with biomimetic structures has received increasing attention in the past few years partially due to advances in additive manufacturing techniques that have enabled the fabrication of advanced materials with arbitrarily complex microarchitectures and novel functionalities. To impact on this trend, it is essential to develop our understanding about the role of microstructure on mechanical responses of these structures. Although a large literature exists on the general subject, the role of microstructure on the post-yield instability is not yet adequately documented. This research introduces a numerical approach to study the post-yield instability in 2D infinite honeycombs as a bottleneck for understanding the instability in more complex 3D systems. Two distinct algorithms are used to systematically vary the ordering in the microstructure of regular hexagonal honeycombs and the mean cell size in the microstructure of Voronoi honeycombs. Finite elements together with a nonlinear homogenization technique are incorporated to quantify the instability responses. Finally, the contribution of microstructure on initial post-yield instability—the slope and magnitude of stress drop after yielding—is statistically investigated. It is found that changing the degree of ordering in the microstructure with respect to a parent symmetry can systematically vary the post-yield instability properties. However, systematic variation of the cell size distribution in absence of ordering in the microstructure cannot remarkably change the post-yield instability in the meta-material. Instead, a tailored cell size distribution can systematically influence its yield strength and plateau stress.