## 2 Tailoring Stiffness via Cellular Materials
There are many works in the literature that prove the tailorability of Cellular Materials by manipulating their structural topology to enhance energy absorption capacity e.g., general energy absorption [129; 130] or impact absorption [131; 132; 133; 134]. Some studies generate negative stiffness materials [135; 136], increasing the amount of energy absorbed, and others include contacts during the deformation of Cellular Materials to ensure restorability [137; 138]. Many authors extensively studied the use of Cellular Materials in energy absorption applications, and a review of this application is out of the scope of this work. Therefore, interested readers are referred to specialized reviews in [139; 140; 141; 142]. In the process of tailoring stiffness via cellular materials approach, certain topologies are preferred depending on the stiffness objective (increase stiffness or reduce stiffness). When stiffness maximization is the objective, a stretch-dominated lattice and closed cell structures are preferred. On the other hand, if flexibility is the goal, a bending-dominated auxetic and zero-Poisson's ratio honeycombs are the most commonly used. The unit-cells of some of the most commonly used cellular structures for tailoring stiffness are shown in Figure 6. Increasing stiffness via cellular materials has been widely studied; therefore, unit cells for this objective, shown in Figure 6, are categorized in 2D-lattice structures, 3D-lattice structures, and Closed-cell structures. On the other hand, reducing stiffness via cellular materials has been limited to explore 2D-lattice structures; thus, unit cells for reduce stiffness, shown in Figure 6, are only in the category of 2D-lattice structures, nevertheless, they are separated according to their Poisson's ratio behavior in positive Poisson's ratio, auxetic, and zero-Poisson's ration. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Author**} & \multicolumn{2}{c}{**Cellular**} & \multicolumn{2}{c}{**Young’s Modulus Ratios**} \\ \cline{2-4}  & **Structure** & \(E_{cx}/E\) & \(G_{c}/E\) \\ \hline [PERSON] et al. [121] & Z—hybrid & 0.096–0.0047 & – \\  & Z—Accordion & 0.0047–0.10 & – \\ [PERSON] et al. [120] & P—Hexagonal & 0.39–2.88 \(\times\) 10\({}^{-5}\) & 0.022–1.07 \(\times\) 10\({}^{-5}\) \\ [PERSON] et al. [122] & Z—Chevron & 0.033–2.92 \(\times\) 10\({}^{-5}\) & 5.2 \(\times\) 10\({}^{-5}\)–6.74 \(\times\) 10\({}^{-4}\) \\ [PERSON] et al. [123] & Z—Chevron & 3.29 \(\times\) 10\({}^{-6}\) & 2.05 \(\times\) 10\({}^{-2}\) \\ [PERSON] et al. [124] & P—Hexagonal & 0.015 & 0.0025 \\  & Z—Accordion & 0.023 & 0.0026 \\ [PERSON] et al. [125; 126] & Z—Fish cell & 1.84 \(\times\) 10\({}^{-6}\)–5.75 \(\times\) 10\({}^{-7}\) & 1.30 \(\times\) 10\({}^{-7}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Stiffness reduction via Cellular Materials: Airfoil-skin morphing. Principal works found in literature by author and cellular structure used (P: positive Poisson, Z: zero-Poisson, A: auxetic). Main direction Young’s modulus ratio \(E_{cx}/E\), and shear stiffness ratio \(G_{c}/E\). “\(-\)” indicates that there is no sufficient information reported to obtain that parameter. Additionally, to address properly the problem of tailoring stiffness via cellular materials, it is convenient to follow the next guideline. First, define the stiffness objective (increase or reduce stiffness). Then, identify the appropriate cellular material, for which it is necessary to identify the desired deformation mechanism (bending-dominated or stretch-dominated) and select an adequate topology (honeycomb, closed-cell structure, or open-cell structure). After, adjust the unit-cell parameters (geometry and relative density) to modify the stiffness of the cellular material. Afterward, compare the obtainable stiffness with the stiffness objective and evaluate if the cellular material is adequate. Next, if the objective stiffness is achieved, then the final step is the implementation.