# Development of Everting Tubular Net Structures Using Simulation for Growing Structures
## 1 Introduction  
Depending on the situation, numerous technical structures need a certain geometry or additional volume to fulfill a specific task. Changes in system volume or stiffness are mostly accepted only for a previously specified duration. Exemplarily, medical applications in minimally invasive surgery benefit from endoscopes that are designed with necessary high volume-change rate between active and inactive state, when not in use. Flexible tubular structures that evert from inside to outside, and thus simultaneously elongate at the top, fulfill the demands in volume change rate. Several examples for the everting of tubular body parts exist in nature: caterpillars of myrmecophilous Lycaenidae hold tentacle organs, pulling out if needed to expel nutritious secretions, which decrease ant aggressiveness [1]. Nemerteans can evert their proboscis when catching and eating their prey [2]. Apple snails (Pomacea) possess both gills and lungs; while submerging under water they are additionally enabled to respire beneath due to the so-called siphon--a tube pushed by muscular activity from the mantle and connecting the pulmonary sac with air above the water surface [3]. A variety of studies deals with continuously growing telescope-like structures. Such applications temporarily provide an increase in volume to perform mechanical work and thus manipulate their environment. Further systems act locally in an entire structure. Their continuous movement can, for instance, cause a change in shape or movement direction of assembly. The intrinsic density of functionality facilitates very small system dimensions at low cost. For example, tubular working principles are known which are based on small prebent tubes made out of shape memory alloys(SMA) [4]. They incrementally adapt their shape in a limited space to the surrounding structure. Several patents were granted for tubular structures like endoscopes and insertion auxiliary devices that are covered by supportive encasements [5; 6; 7]. A flexible hose was used in [8] as a pneumatic artificial muscle (PAM) to generate a continuous growth of the structure by unfolding. The system is driven by air pressure to perform simple positioning tasks. The pressure supply provides an easy way to control the system, but additional components are necessary. The transferable loads are limited due to the thin foil-like skin. With the application of thicker foils, it is possible to increase stiffness, but this results on the other hand in a more difficult everting behavior. Another possibility to realize an everting process is to use net-like structures, which have been utilized for decades to protect contoured shafts while transport [9]. Several plane structural designs and in part tubular net shapes were studied in [10], everting of structures was not investigated. The deformation behavior via 3D buckling was investigated using nonperiodic nets. Additionally, further investigations used homogenization strategies to describe the effective material behavior of such anisotropic structures [11; 12]. Early studies like [13; 14] show the ability and necessity to develop extremely flexible structures in nature. They inspired authors to transfer the mechanisms into technical applications [15]. All of the aforementioned naturally or artificially driven basic mechanisms are characterized by a high amount of bearable deformation as well as the thin membrane structure principle to reduce bending loadings. With help from additive manufacturing, it is now possible to realize such compliant structures with free design flexibility. The first part of the paper deals with a preliminary study that ensures the printability of net structures, especially according to the highly loaded zones of crossing points while undergoing huge stresses in an everting process. Therefore, the additive manufacturing material was characterized and the Young's modulus was determined as input for calculation and structural design.