Nature and technology often adopt structures that can be described as tubular helical assemblies. However, the role and mechanisms of these structures remain elusive. In this paper, we study the mechanical response under compression and extension of a tubular assembly composed of 8 helical Kirchhoff rods, arranged in pairs with opposite chirality and connected by pin joints, both analytically and numerically. We first focus on compression and find that, whereas a single helical rod would buckle, the rods of the assembly deform coherently as stable helical shapes wound around a common axis. Moreover, we investigate the response of the assembly under different boundary conditions, highlighting the emergence of a central region where rods remain circular helices. Secondly, we study the effects of different hypotheses on the elastic properties of rods, i.e., stress-free rods when straight versus when circular helices, Kirchhoff’s rod model versus Sadowsky’s ribbon model. Summing up, our findings highlight the key role of mutual interactions in generating a stable ensemble response that preserves the helical shape of the individual rods, as well as some interesting features, and they shed some light on the reasons why helical shapes in tubular assemblies are so common and persistent in nature and technology. Graphic Abstract We study the mechanical response under compression/extension of an assembly composed of 8 helical rods, pin-jointed and arranged in pairs with opposite chirality. In compression we find that, whereas a single rod buckles (a), the rods of the assembly deform as stable helical shapes (b). We investigate the effect of different boundary conditions and elastic properties on the mechanical response, and find that the deformed geometries exhibit a common central region where rods remain circular helices. Our findings highlight the key role of mutual interactions in the ensemble response and shed some light on the reasons why tubular helical assemblies are so common and persistent.

McKibben artificial muscles are an important example of braided, tubular structures made of many interwoven helical fibers. Despite their high non-linearity, the elastic response of these soft pneumatic actuators is very robust and reproducible, making them particularly suitable for applications in Soft Robotics. The rich behavior of McKibben actuators has been studied either through minimal geometric models or through complex Finite Elements Methods (FEM).Here, we develop a simplified framework entirely based on the virtual envelope surface defined by the fibers of the mesh. In the axisymmetric cases studied, the problem boils down to solving for a single scalar field defined over 1D segments. We then validate our model against experimental and numerical results from the literature, achieving a good agreement at a significantly lower computational cost. Furthermore, simulations reveal that loads are sustained mostly by the braided mesh, whereas the inner chamber stores as elastic energy most of the external work. This phenomenon explains why simplified formulas for force-pressure relationship may be quite effective in predicting the behavior of McKibben actuators.