## 2 Tailoring Stiffness via Cellular Materials
Therefore, customization of the stiffness via Cellular Materials is possible as their apparent mechanical properties show dependence on the following: (i) the mechanical properties of the parent material, (ii) the topology and cell geometry, and (iii) the relative density. Properly planned selection or modification on any of these three can lead to a meta-material with tailored properties. In this regard, the stiffness of a compliant system can be modified through the implementation of specific cellular arrays in the flexible parts of the system. Tailoring stiffness has become more relevant with the emergence of modern manufacturing processes such as additive manufacturing techniques, capable of fabricating complex topologies and shapes [72; 73; 74; 75]. Some studies [76; 77; 78] showed how the stiffness in beams can be customized by using different types of cellular structures while obtaining minimum weight designs. Other works [79; 80; 81] focused on obtaining optimal designs of lattice structures to achieve the desired stiffness along with exceptional load-bearing efficiency and minimum weight. Later, [PERSON] et al. [82] investigated the effect of cell topology, orientation, and volume fraction to provide a specified stiffness in the lattice structures. Further, [PERSON] et al. [83] conducted research works where they proved that by modifying cell parameters, it is possible to control the stress-strain curve of a Cellular Material to assess specific load requirements and performance. A similar study was developed by [PERSON] et al. [84], where the authors optimized lattice structures to provide specific stiffness for given multi-loading scenarios in the low volume fraction limit. Most recently, [PERSON] et al. [85] synthesized a new type of Bezier-based metamaterial, characteristics of which enable the generation of structures with customized mechanical properties by adjusting the geometry of the unit cells. Some studies [86; 87; 88; 89; 90] demonstrated the possibility to tailor specific stiffness depending on the loading direction, allowing the design of customized anisotropic Cellular Materials. [PERSON] et al. [87] introduced the concept of multi-directional functionally graded Cellular Materials made by assembling porous unit cells of dissimilar densities and cell topologies to improve the performance of lightweight structural elements. In [88], the authors evidenced that tailoring the apparent anisotropy in Cellular Materials at the macroscopic level is possible by changing the ratio of bending-to-axial stiffness of the constituent beams, as, depending on the direction of loading, the nature of the mechanical response of cubic elementary trusses changes smoothly from bending-dominated to stretching-dominated. Figure 4: Schematic of (**a**) bending-dominated and (**b**) stretch-dominated structures. This concept was also studied in [86], where the authors performed customization of effective anisotropic material properties in micro-lattice structures by controlling the unit-cell topology. Recently, [PERSON] et al. [90] designed isotropic Cellular Materials created by superimposing complementary anisotropic lattices, enhancing the potential of high-stiff isotropic Cellular Materials. Variable stiffness is also achieved by including contacts during deformation of Cellular Materials. An example is found in [PERSON] et al. [91], where the authors synthesized a square-cell Cellular Material with the bi-stiffness property in response to compressive loading. The specific case of stiffness depends on the orientation of the unit cells leading to a specific deformation of cells and further overlapping of cell walls. [PERSON] et al. [89] synthesized a 3D variable stiffness and dual Poisson's ratio Cellular Material by including internal contacts between slit surfaces during both tensile and compressive loading achieving engineered stiffness. Applications of tailored Cellular Materials have been focused mainly on stiffness maximization.