# Design and Optimization of Lattice Structures: A Review
## 2 Lattice Structures
### Properties and Applications of Lattice Structures  
#### 2.2.1 Properties  
Lattice structure is usually used in lightweight structure design to minimize material loss and energy consumption in the manufacturing process. Energy, material, and time of manufacturing process can be saved effectively by designing and optimizing the lattice structure [71]. It is common knowledge that lattice structure has good mechanical properties. In Section 2.2, the properties of lattice structure are described in detail. (1) High stiffness and strength [82; 83; 84; 85; 86; 87; 25; 88]. [PERSON] et al. [82] fabricated and characterized micro-truss and -shell structures made form cellular ceramic composites. They observed a size dependent strengthening of the alumina shell, especially when the characteristic thickness was less than 100 nm. The compressive strength of the artificial porous material was 280 MPa and the density was less than 1000 kg/m\({}^{3}\). [PERSON] et al. [88] fabricated structure samples including solid, hollow, and lattice structure, and compared the strength of structures by compression test. The deformation of samples after compression test is shown in Figure 4. The result indicated that though the strength of lattice structure was lower than that of solid structure, it can still meet the application requirements, and reduced the use of materials, and achieve lightweight design. (2) High energy absorption [40; 41; 42; 89; 90; 91]. [PERSON] et al. [42] carried out quasi-static test analysis on lattice structures with cubic cells, diamond cells, and re-entrant cells respectively. They studied the dynamic load deformation behavior of lattice structures, including failure process and stress-strain  
Figure 4: Deformation of samples in compression test [88]: (**a**) solid; (**b**) hollow; (**c**) lattice. Figure 3: Gradient lattice structures [76]. response. Under the condition of low-speed and high-speed collision, the lattice structures showed obvious difference in deformation behavior and energy absorption effect. [PERSON] et al. [90] investigated that the energy absorption capability of graded and uniform lattice structures (as shown in Figure 5). The result indicated that the total cumulative energy absorbed by the graded lattice structure was \(3.2\pm 0.1\) MJ/m\({}^{3}\), and by the uniform lattice structure was \(2.6\pm 0.2\) MJ/m\({}^{3}\). The total cumulative energy absorption per unit volume was higher in functionally graded lattice than in uniform lattice (as shown in Figure 6). (3) High damping [58; 59; 60; 61]. [PERSON] et al. [60] studied the damping performance of Hollow composite pyramidal lattice (CPL) through vibration test. The experimental results showed that the CPL structure increased the damping property of the material and had a tremendous damping effect. [PERSON] pointed put that the damping ratios of space-filled CPL structures increased about two times that of hollow CPL structures for first three orders and four times for the fourth order. Bandgap is the most promising feature for lattice structure when it comes to vibration isolation and damping. [PERSON], [PERSON], and [PERSON] et al. [92; 93; 94; 95; 96], carried out many studies on bandgaps. [PERSON] et al. designed six different lattice structures to investigate the vibration damping and isolation [92]. They used finite element simulation to analyze the displacement of six lattice structures under the same load condition. The results showed that the lattice structures of model 2, model 3, and model 5  
Figure 5: Lattice structures [90]: (**a**) grade; (**b**) uniform. Figure 6: Cumulative energy absorption per unit volume vs. compressive strain curves of uniform and graded structures [90]. had strong damping and vibration isolation effect (as shown Figure 7). As for vibration amplitude, model 3 can reduce vibration more than model 2 and model 5 for all damping factors. But model 1, 4, and 6 were too weak to sustain the predefined load.