# An Innovative Adaptive-Dimension Accordion Honeycomb for Circumferential Deformation
## 1 Introduction  
Cellular materials have garnered significant attention from researchers due to their remarkable mechanical properties, including lightweight, stiffness anisotropy, and exceptional energy absorption [1; 2; 3; 4; 5]. These materials also exhibit a unique ability to demonstrate syncastic or dome-shaped out-of-plane curvature, a characteristic distinct from regular materials that typically display anti-clastic or saddle-shaped curvature [6; 7]. This curvature is advantageous in the fabrication of doubly curved sandwich panels. In the aerospace industry, honeycoms with positive, negative, and zero Poisson ratios have been designed for various morphing applications owing to their robust in-plane deformation capability [8; 9; 10; 11]. In the field of biomedical engineering, studies have explored the use of tubular-shaped 2D auxetic patterns to enhance the effectiveness of stents. These configurations enhance the openness of the lumen and reduce migration. They also provide structures with high circumferential strength when expanded and low flexural rigidity upon delivery in a crimped configuration. Furthermore, these tubular structures have found application in tissue engineering due to their resemblance to various biological tissues [12; 13; 14; 15]. The hexagonal honeycomb structure represents one of the earliest configurations extensively studied in structural design. [PERSON] et al. [16] investigated its auxiliary behavior and suggested its application in structural design. [PERSON] [17] proposed a three-dimensional configuration based on the 2D honeycomb structure, achieving Poisson's ratio of \(-1\) in all three dimensions. Various honeycombs with different Poisson ratios [18; 19; 20; 21] and configurations, such as chiral [22; 23; 24], double-arrow shape [25; 26], and star-shaped [6; 27; 28], have been proposed and applied in structural design. However, most of these studies indicate that honeycombs with non-zero Poisson ratios generate strain and stress in directions otherthan the loading direction, thereby limiting their application in one-dimensional deformations. Therefore, there is a demand for the development of honeycombs with Poisson ratios close to zero or zero for one-dimensional morphing applications. [PERSON] and [PERSON] [29] proposed and investigated an accordion cellular honeycomb with vertical beams oriented parallel to each other and V-type beams filling the spaces between them. [PERSON] et al. [30] manufactured a flexible skin supported by a reinforced accordion cellular honeycomb with V-type beams and analyzed the in-plane equivalent moduli in two directions. [PERSON] et al. [31] introduced a cellular structure with a close-to-zero Poisson ratio using in-plane corrugated cosine beams and examined its elastic and shear moduli. [PERSON] [32] developed a mathematical model to describe the elastic behavior of the accordion cellular honeycomb core, taking into account the effects of in-plane curved beams on the overall mechanical properties of the structure. These studies demonstrate the suitability of accordion honeycombs with close-to-zero in-plane Poisson ratios for one-dimensional morphing. However, their morphing typically involves tension, compression, or shear, which are predominantly confined to the orthogonal directions of the Cartesian coordinate system. Consequently, circumferential morphing applications, such as the sweep-angle variations of an aircraft wing, require considerable effort to implement. On the other hand, traditional honeycomb structure design methods typically initiate with a single-cell structure, employing uniform cell size combinations to create the honeycomb structure. This approach inherently imposes design constraints, limiting the flexibility and adaptability of the honeycomb structure. Despite these limitations, there is currently limited research exploring honeycombs with variable-dimension cells.