Bending behavior of optimally graded 3D printed cellular beams

• DOI: 10.1016/j.addma.2020.101327
• Publication Date: 2020-05-23T15:46:54Z
• Authors: A. Seyedkanani; H. Niknam; A.H. Akbarzadeh
• Keywords: Relative density

Abstract Periodic cellular materials can substantially improve the stiffness-to-weight ratio of structures. This improvement depends on the geometry of periodic cells. This article presents the idea of enhancing the bending stiffness of an architected cellular beam by an optimum distribution of relative density through its length and/or across its thickness. We employ a hybrid-homogenized model to expedite the computational evaluation of the bending performance of the graded cellular beams. Detailed finite element analysis (FEA) and experimental bending tests on specimens 3D printed by stereolithography validate the hybrid-homogenized modeling approach. The hybrid-homogenized model facilitates transforming the general optimization problem into a shape optimization process with the relative density of unit cells as design variables. The teaching-learning-based optimization (TLBO) algorithm is used to obtain the optimum relative density distribution, which maximizes the bending stiffness. The optimization results show a substantial increase in bending stiffness; as high as 43%, 155%, and 182% for a cellular beam graded through the length, across the thickness, and in both directions, respectively. It is found that varying the relative density of cells across the beam thickness is more effective than variation through the length. Detailed FEA and experimental bending tests corroborate the optimization findings and confirm the practicality of such graded designs for developing advanced lightweight structures. Investigating the effect of cell architecture also reveals that optimally graded cellular beams have a potential to outperform uniform cellular beams made out of ideal unit cells (Voigt bound for elastic properties) by reaching bending stiffness-to-density ratios greater than one. The relatively simple graded cellular designs are beneficial in applications where high bending stiffness and low density are essential. Recent advances in additive manufacturing promise extending the presented grading strategy for polymeric, composite, and metallic 3D printed cellular materials to fabricate high performance lightweight structural elements at a relatively low cost.