Mechanics of tubular helical assemblies:ensemble response to axial compression and extension

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 Kirchholf 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.