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

Abstract

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.

Mechanics of tubular meshes made of helical fibers and application to modeling McKibben artificial muscles

“…As shown in Section III, the results obtained using this simplifying assumption are still in good agreement with experiments in Hassan et al. A more thorough discussion of merits and limitations of this assumption is in [5].…”

“…On one hand, if we approximate the mesh as a cylinder [1], we can derive a simple formula for the axial force necessary to balance a given pressurization by applying the Principle of Virtual Work (PVW); while some key features are captured, this modeling approach is too simplistic to reproduce the behavior of braided meshes in a broad range of operating conditions. On the other hand, Finite Elements Methods (FEM) have been employed, describing each fiber as an individual beam linked together through boundary conditions [2,3,4]. These simulations are indeed accurate, yet computationally expensive, and do not reveal the inner working principles of these structures.…”

“…As a consequence, the behavior of the mesh depends only on the angle θ(v) that the fibers form with the parallels of the envelope surface along its axis. A more general theory in which both θ(v) and φ(v) are retained as degrees of freedom is discussed in [5].…”

Shape Control, Morphing and Mechanobiology

“…This approach has been pioneered by E. Sharon and collaborators [53] and has seen applications to a wide variety of material systems such as biological tissues experiencing growth, swimming micro-organisms, hydrogels, LCEs, inflatables, martensitic films etc., see [18,10,67,43,82,62,4,49,60]. Morphing of tubular structures is discussed, in particular, in [66,70,71].…”

Biomechanics in “Sino-Italian Joint”

“…This enables them to adapt to changing functional requirements by altering conformations and specific properties. To understand the underlying mechanism, Quaglierini et al [1] analyzed the mechanical response of tubular assemblies composed of 8 helical Kirchhoff rods under compression and tension, and revealed the relation between individual rod interactions and favored stable configurations of tubular assemblies.…”