# Design and Optimization of Lattice Structures: A Review
## 1 Introduction  
Lattice structure is an attractive material for many design applications (aerospace, biological engineering, mechanical engineering, etc.) because of the excellent properties including the light-weighting, high specific strength and stiffness, dissipate heat, and so on. As porous materials, before the lattice structure appeared, the name of cellular structure was more widely spread. The concept of \"cellular structure\" was originally proposed by [PERSON] and [PERSON], [PERSON], et al. [1; 2; 3]. [PERSON] and [PERSON] deemed that cellular structure included foams (open-cell and closed-cell foams), honeycombs [1; 2]. However, lattice structure as another type of cellular material is different from foams and honeycombs, and the difference of structure mainly lies in unit cell topology and scale, and properties [4; 5]. In order to classify more clearly the types of cellular structures, [PERSON] [6], [PERSON] and [PERSON] [7] classified cellular structures into three categories, i.e., foams (open-cell and closed-cell foams), honeycombs, and lattice structures. The shape of unit cells in the foam structures are randomly generated (as shown in Figure 1a), and the cell walls have random orientations in space [2]. In the book of Metal Foams: A Design Guide, [PERSON], [PERSON] and [PERSON], et al. had introduced in detail the properties, applications, and manufacturing methods of metallic foam structures [8]. [PERSON] and [PERSON] indicated clearly that metallic foam structures had high porosity ranging from 40% to 98% [9]. Foams are the common cellular structures. Like cork, cancellous bone and wood show various foams. Honeycomb structures have regular shape, and unit cells have the same shape and size (Figure 1b) [2,10]. There are many cell shapes in honeycombs such as tetrahedron, triangular prism, square prism, hexagonal prism, and so on [2,11]. At present, re-entrant honeycomb auxetic structures [12, 13, 14, 15, 16] and chiral honeycomb structures [17, 18, 19] are attractive, which improve the performance and extend the application of honeycombs. Lattice structures are the kind of architecture that are formed by the array of spatial unit cells with edges and faces (as shown in Figure 1c) [7,20]. Cellular shape and size can be uniform or non-uniform. In some academic studies, cellular structures are often equivalent to lattice structures because of neglecting the differences between lattices and foams and honeycombs [21,22]. In their research literatures, the foam structures are actually the lattice structures. In fact, compared with foams and honeycombs, lattice structures have better mechanical properties [3,23]. [PERSON], et al. [24,25] and [PERSON] et al. [26] demonstrated that lattice structures have the potential to improve compressive and shear strength over foams and honeycomb structures when designed to suppress buckling. Otherwise, lattice structures have many superior properties that foams and honeycombs do not get because of the unique property of tailoring. In other words, each unit cell, and even each strut in the lattice structure can be set as the design variable and be optimized to satisfy specific customized requirements functionally, which means mechanical properties of lattices are more flexible to be controlled than foams and honeycombs [23,27]. Therefore, it can be concluded that lattice structures have better performance than foam structures and honeycomb structures. Figure 1: _Cont._  
In fact, in early industrial structure design, the solid material structure is mainly used because of its sufficient and other material properties. Although the solid material structure to a large extent meets the design requirements, there are still many defects, such as waste of materials, inflexible design, huge structure volume, and manufacturing difficulties. Besides, with the development of science and technology, the requirements for structural properties are higher than before. At present, structure design in industrial field pays more attention to lightweight and high performance.