Yield surface of multi-directional gradient lattices with octet architectures

Abstract

In this paper, a theoretical method is developed to delineate the effective elastic properties and yield surface of the gradient cellular structure. Additionally, a technique is presented for the construction of multi-directional gradient lattices, and two novel tri-directional gradient lattices (TD-GLs) by assembling octet unit cells with side lengths following specified gradient topological parameters serve as an illustrative example. Their effective elastic properties and yield surfaces are systematically investigated with the aid of theoretical, experimental, and finite element methods. It is found that the effective elastic modulus of the proposed TD-GLs exceeds by 48.80% as compared to that of conventional uniform octet lattices. Moreover, the normalized yield surfaces are proposed to emphasize the predominant role of structural topological features by eliminating the influence of the relative density on the yield behavior of TD-GLs, and this method that also can be extrapolated to other tension-dominated lattices. Subsequently, a theoretical model is developed to establish closed-form yield functions for characterizing the yield behavior of TD-GLs. The predicted yield surfaces from the proposed theoretical model demonstrate good agreement with the simulated results. Finally, the proposed TD-GLs demonstrate outstanding yield performance in various directions deviating from their orthogonal principal axes or planes, compared to lattices with uni- or dual-directional gradient topological configurations. In summary, the proposed multi-directional gradient lattices in this study exhibit the exceptional stiffness and outstanding yield performance in various directions, offering valuable insights for the structural design and engineering applications of lattice structures.