The lattice structure is a type of cellular material with trusslike frames which can be optimized for specific loading conditions. The fabrication of its intricate architecture is restricted by traditional manufacturing technologies. However, additive manufacturing (AM) enables the fabrication of complex structures by aggregation of materials in a layer-by-layer fashion, which has unlocked the potential of lattice structures. In the last decade, lattice structures have received considerable research attention focusing on the design, simulation, and fabrication for AM techniques. And different modeling approaches have been proposed to predict the mechanical performance of lattice structures. This review introduces the aspects of modeling of lattice structures and the correlation between them, summarizes the existing modeling approaches for simulation, and discusses the strength and weakness in different simulation methods. This review also summarizes the characteristics of AM in manufacturing cellular materials and discusses their influence on the modeling of lattice structures.

Cellular architectures are promising in a variety of engineering applications due to attractive material properties. Additive manufacturing has reduced the difficulty in the fabrication of three-dimensional (3D) cellular materials. In this paper, the numerical homogenization method for 3D cellular materials is provided based on a short, self-contained matlab code. It is an educational description that shows how the homogenized constitutive matrix is computed by a voxel model with one material to be void and another material to be solid. A voxel generation algorithm is proposed to generate the voxel model easily by the wireframe scripts of unit cell topologies. The format of the wireframe script is defined so that the topology can be customized. The homogenization code is then extended to multimaterial cellular structures and thermal conductivity problems. The result of the numerical homogenization shows that different topologies exhibit anisotropic elastic properties to a different extent. It is also found that the anisotropy of cellular materials can be controlled by adjusting the combination of materials.

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.

Lattice structures with different desired physical properties are promising for a broad spectrum of applications. The availability of additive manufacturing (AM) technology has relaxed the fabricating limitation of lattice structures. However, manufacturing constraints still exist for AM-fabricated lattice structures, which have a significant influence on the printing quality and mechanical properties of lattice struts. In this paper, a design and optimization strategy is proposed for lattice structures with the consideration of manufacturability to ensure desired printing quality. The concept of manufacturable element is used to link the design and manufacturing process. A meta-model is constructed by experiments and the artificial neural network to obtain the manufacturing constraints. Sizes of struts are optimized by a bidirectional evolutionary structural optimization-based algorithm with these manufacturing constraints. An arm of quadcopter is redesigned and optimized to validate the proposed method. Its result shows that optimized heterogeneous lattice structures can improve the stiffness of the model compared to the homogeneous lattice structure and the original design. Both the Von-Mises stress and the maximum displacement are reduced without increasing the weight of designed part. And by considering the manufacturability constraints, the optimized design has been successfully fabricated by the selected additive manufacturing process. Note to Practitioners-Lattice structures might fail to be fabricated by the additive manufacturing technique if the designed model exceeds the processability of the machine. Our approach has the capability of considering the manufacturing constraints in the design and optimization process. We conducted experiments to investigate the manufacturability and proposed a method that can give the domain of the design variables for a selected manufacturing process. And we also designed an algorithm that can optimize the lattice structure inside the domain of design variables. It ensures that the lattice model can be successfully fabricated by the selected process and the performance is dramatically increased compared to the original design. Engineers can use our approach to optimize the lattice structure automatically without knowing the knowledge of optimization and manufacturability.