Bio-inspired functionally graded cellular materials (FGCM) have improved performance in energy absorption compared with a uniform cellular material (UCM). In this work, sheet-based and strut-based gyroid cellular structures with graded densities are designed and manufactured by stereo-lithography (SLA). For comparison, uniform structures are also designed and manufactured, and the graded structures are generated with different gradients. The mechanical behaviors of these structures under compressive loads are investigated. Furthermore, the anisotropy and effective elastic modulus of sheet-based and strut-based unit gyroid cellular structures are estimated by a numerical homogenization method. On the one hand, it is found from the numerical results that the sheet-based gyroid tends to be isotropic, and the elastic modulus of sheet-based gyroid is larger than the strut-based gyroid at the same volume fraction. On the other hand, the graded cellular structure has novel deformation and mechanical behavior. The uniform structure exhibits overall deformation and collapse behavior, whereas the graded cellular structure shows layer-by-layer deformation and collapse behavior. Furthermore, the uniform sheet-based gyroid is not only stiffer but also better in energy absorption capacity than the uniform strut-based gyroid structure. Moreover, the graded cellular structures have better energy absorption capacity than the uniform structures. These significant findings indicate that sheet-based gyroid cellular structure with graded densities have potential applications in various industrial applications, such as in crashworthiness.

Periodic cellular structures with excellent mechanical properties widely exist in nature. A generative design and optimization method for triply periodic level surface (TPLS)-based functionally graded cellular structures is developed in this work. In the proposed method, by controlling the density distribution, the designed TPLS-based cellular structures can achieve better structural or thermal performances without increasing its weight. The proposed technique can be divided into four steps. First, the modified 3D implicit functions of the triply periodic minimal surfaces are developed to design different types of cellular structures parametrically and generate spatially graded cellular structures. Second, the numerical homogenization method is employed to calculate the elastic tensor and the thermal conductivity tensor of the cellular structures with different densities. Third, the optimal relative density distribution of the object is computed by the scaling laws of the TPLS-based cellular structures added optimization algorithm. Finally, the relative density of the numerical results of structure optimization is mapped into the modified parametric 3D implicit functions, which generates an optimum lightweight cellular structure. The optimized results are validated subjected to different design specifications. The effectiveness and robustness of the obtained structures is analyzed through finite element analysis and experiments. The results show that the functional gradient cellular structure is much stiffer and has better heat conductivity than the uniform cellular structure.