## 2 Tailoring Stiffness via Cellular Materials
To this end, 2D cellular structures have been suggested for general morphing skin applications [113, 114, 115]. In [113], the authors presented a novel zero-Poisson's ratio honeycomb structure that can achieve deformations along two orthogonal directions and avoid the increase of effective stiffness in the morphing direction by restraining the Poisson's effect in the non-morphing direction. The same concept was explored by [PERSON] et al. [114, 115] in the development of zero-Poisson's ratio cellular structures with lightweight, low in-plane moduli and high strain capability. Results demonstrated the potential of the proposed structures for in-plane morphing. Moreover, the main application is in aircraft morphing, where efforts have been mainly focused in airfoil-core morphing [116, 117, 118, 119] and airfoil-skin morphing [120, 121, 122, 123, 124, 125, 126]. [PERSON] et al. [116] proposed the use of an auxetic hexagonal structure as the airfoil-core of wings as an attempt to take advantage of the high deformability of the structure thus providing the flexibility required for morphing, while preserving the structural integrity due to its high in-plane shear resistance. [PERSON] et al. [117] designed airfoil-cores with a re-entrant cellular structure due to their ability to undergo large in-plane displacements with limited deformation in span-wise direction. [PERSON] et al. [118] investigated the use of a cross-shaped honeycomb structure in airfoil-core morphing, resulting in great in-plane deformation capacity and adequate out-of-plane support. [PERSON] et al. [119] investigated the airfoil-core morphing capacity of three types of Cellular Materials through the in-plane flexible properties. Hexagonal chiral, regular honeycomb, and re-entrant honeycomb were chosen for this analysis. All structures showed high levels of in-plane flexibility. The re-entrant honeycomb showed the highest flexibility and causes a lower stress in cell walls than the other cellular cores, thus suggesting potential to be used in real morphing applications. On the other hand, [PERSON] et al. [120] studied the use of hexagonal honeycomb cellular structures in airfoil-skin morphing. Results showed that Cellular Materials could easily undergo global strains several times greater that the parent material while maintaining good out-of-plane stiffness; however, when honeycomb Cellular Materials are stretched along the principal axis they geometrically stiffen, thereby reducing the maximum global strain achievable. [PERSON] et al. [121] proposed two types of zero-Poisson's ratio cellular structures (hybrid and accordion) to be used in one-dimensional airfoil-skin morphing applications. Results showed that the axial stiffness in the motion direction of the zero-Poisson's ratio cellular structures remains low when the skins are restrained in the non-morphing direction, making these cellular structures ideal for use in airfoil-skin morphing. Other works [122, 123, 124] have studied similar zero-Poisson's ratio cellular structures to be used in airfoil-skin morphing, obtaining high levels of flexibility in the actuation direction while maintaining the desired shape and strength in the others. Most recently, in [125, 126] a new Cellular Material with zero-Poisson's ratio called Fish cell (Figure 5b) was introduced for applications in airfoil-skin morphing. The proposed cellular structures were parametrized to obtain desired stiffness values under specific conditions. Finally, 3D arrays have been reserved for complete wing morphing [127, 128]. 2D cellular structures used in airfoil-core and airfoil-skin morphing can be subdivided in three main categories according to the value of their Poisson's modulus (\(\
u\)): positive-Poisson (\(\
u>0\)), zero-Poisson (\(\
u\approx 0\)), and auxetic (\(\
u<0\)). A complete overview of airfoil morphing by 2D cellular structures is depicted in Figure 5a, graphically showing the main categories of 2D patterns: positive-Poisson, zero-Poisson, and auxetic.