## 4 Mechanical Properties of Lattice Structures Built with Polygonal Hollow Shapes  
A growing number of engineering and manufacturing applications today take advantage of lattice structures built with polygonal hollow shapes because of their lightweight design [1; 2; 4; 7; 15; 17; 24; 25; 26; 27; 29; 30; 31; 32; 33; 34; 35; 36]. Multiple materials, such as composites, metals, and polymers, are available to build these lattice structures [15; 37; 38]. The shape of the polygons [17; 18], the material used [15; 37; 38], the manufacturing method adopted [12; 13; 14; 38], and the overall geometry of the lattice design [17] have a bearing on the mechanical properties of such lattice structures. The degree of porosity inherent in polygon structures is influenced by the density of the lattice structure, which is determined by the lattice design and the size of the polygonal hollow shape used [2; 13; 17]. Porosity in this case refers to the volume of the hollow space against the volume of the entire structure. A higher porosity lowers the overall weight of the structure but could potentially reduce its structural integrity [2; 8; 17]. To repair human bone defects, [PERSON] et al. [39] built four Ti6 Al4V scaffolds inspired by honeycomb designs. They observed that increasing the degree of porosity inherent in lattice designs lowered the stress shielding between the bone and lattice implant. This was because the elastic modulus of the implant was lowered to match that of the bone by increasing the volume of pores in honeycomb scaffolds. The load-bearing capacity of a polygon structure is influenced by the choice of materials, the geometry of the lattice structure, and the loading conditions. The strength-to-weight ratio can be optimised through the careful design of these factors. For modelling and predicting structural behaviour under different loading conditions, finite element analysis (FEA) is often adopted [40; 41; 42; 43]. For modelling the behaviour of lattice structures, FEA requires significant quantities of computational power. This is attributable to the high structural complexity of lattice structures. As a result, methods of simplification and advanced strategies for modelling are necessary to address this challenge. [PERSON] et al. [17] reviewed different geometrical designs of lattice structures and observed that they typically show great compressive strength. However, they also highlighted the fact that particular geometries of structures and chosen materials had significant effects on their compressive strength. [PERSON] et al. [16] reviewed the properties of tensile strength of lattice structures and observed that they presented a challenge, as tensile loads were often transferred by the struts, which were designated as thin members that were then liable to fail by buckling at low applied loads. The tensile strength of the lattice structures is often influenced by  
Figure 11: Other types of hollow structures adopted in engineering applications [13; 16; 17]. the polygonal shapes used to build them; therefore, different morphologies of polygon structures are likely to differ in terms of their mechanical properties [1; 7; 8; 13; 18]. In impact or crash conditions, the energy absorption capability of a lattice structure is critical. Numerous studies [17; 31; 44; 45] have highlighted the fact that the integration of the material properties and lattice design have a substantial impact on the structure's capacity to absorb and disperse energy. Additionally, lattice structures are typically used in applications that require cyclic loading [13; 16; 46; 47]. Their fatigue resistance is determined by the choice of materials, architecture, and manufacturing standards [13; 16]. It is clear from this that a substantial fatigue life requires an appropriate engineering design, manufacturing methods, and choice of materials. Under compressive loads, numerous studies [8; 13; 16; 17; 18] showed that lattice structures were prone to buckling.