Crushing behavior and optimization of sheet-based 3D periodic cellular structures

Sheet-based 3D periodic cellular structures attract great attentions due to their lightweight and excellent mechanical properties. Unlike other traditional honeycombs and lattice structures, sheet-based cellular structures consist of triply periodic minimal surface (TPMS) cores, which are continuous through space with a porous cavity surrounded by continuous surfaces. In this study, the crashworthiness of four types of TPMS sheet structures (i.e., Primitive, FRD, IWP, and Gyroid) under axial loading was investigated. According to the results obtained by the nonlinear finite element analysis, the level-constant in the implicit form of TPMS and the shell thickness of TPMS sheet structures were found to affect the crashworthiness significantly. To achieve an optimal design, a metamodel-based multi-objective optimization method was developed to optimize the four types of TPMS sheet structures. Three different metamodels, i.e., Kriging (KRG), polynomial response surface (PRS) and radial basis function (RBF), were compared to identify the most accurate model, which was then utilized for the optimization. Followed by the multiobjective optimization, four Pareto fronts of these TPMS sheet structures were plotted and compared, of which the FRD-sheet structure was found to have the best energy absorption capacity. Moreover, the crashworthiness of the TPMS sheet structures was compared with that of the other materials or structures in nature and engineering, and an Ashby plot was given. Overall, TPMS sheet structures possess excellent specific energy absorption and specific strength and show great potential for engineering applications.