## 2 Tailoring Stiffness via Cellular Materials
Examples of Cellular Materials customized to offer maximum possible stiffness using different cellular structures such as 2D honeycombs [92; 93], 3D lattices [94; 95], and 3D closed-cell foams [96] are found in the literature. Tailored Cellular Materials have been also used to maximize transverse shear stiffness in honeycomb cores [97; 98]. Studies of applications including the use of Cellular Materials to enhance buckling behavior [99], tune stress localization, minimize stress levels [100], and engineer failure location for specific load conditions [101] are limited. Optimization via Cellular Materials can also be used for match specific stiffness. This aspect is particularly attractive for the manufacturing of bone implants, where the elastic modulus of the implant should match that of the bone in order to avoid stress shielding effects, bone atrophy, and implant loosening. Additionally, offering advantages such as improving stability by promoting tissue ingrowth and high energy absorption to withstand impacts. Three-dimensional topologies are the most frequently encountered in this application. A variety of works for this application can be found in the literature. [PERSON] et al. [102] presented a thorough review where they expose the capacity of additive manufacturing techniques to fabricate biomedical devices with mechanical properties of surrounding bone tissue with replacements parts. Most recently, tailoring stiffness through Cellular Materials to enhance flexibility or compliance behavior has been studied. Some of the first examples can be found in the works of [PERSON] et al. [103; 104], where the authors proposed Cellular Materials with customized anisotropic stiffness. The proposed materials consisted of flexible mesostructures designed from the deformation of re-entrant auxetic (negative Poisson's ratio) honeycomb and compliant amplifiers mechanisms. They could tailor in-plane properties of the said mesostructures, obtaining low stiffness and high strain in one direction and high stiffness and low strain in the other direction. A complete review of auxetic cellular materials is found in [105]. After, [PERSON] et al. [106] demonstrated the possibility to independently tailor compression and shear response in 3D printed Cellular Materials offering the extremal property of negative shear stiffness in designed structures. Then, [PERSON] et al. [107] used modified diamond lattice structures to create Cellular Materials with reduced stiffness, advantageous for energy absorption, vibration isolation, and reduction of stress. Later, [PERSON] et al. [108] modified the topology of hexagonal chiral lattices and demonstrated that purposely choosing the parameters permits to tailor the behavior of the chiral lattice, enabling extreme variations in stiffness, including the possibility to attain negative and zero-stiffness regimes over large compressive strains which exemplifies the potential to tune deformation of compliant systems. Additionally, [PERSON] et al. [109] introduced the metamaterial mechanisms concept, which considers cellular materials as machines instead of materials and allows the creation of macroscopic movement through the well-defined interaction of cells in a single block of cellular material. Similarly, [PERSON] et al. [110] presented a group of auxetic-inspired material structures that can transform into various shapes upon compressive loading. Most recently, in [111] a 2D kagome honeycomb was optimized for delivering high amplitude actuation. In the same year, [PERSON] et al. [112] demonstrate that changing the cell size in lattice materials might involve maximizing stiffness in one mode while minimizing it in another. Regarding this, some applications have taken advantage of the compliance behavior offered by Cellular Materials. One of the most extensively studied applications is in shape morphing as the material used should not only be in-plane flexible enough to morph with actuation, but stiff enough not to deform excessively under out-of-plane loads.