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

Jacopo Quaglierini,Antonio Desimone,Alessandro Lucantonio

doi:10.1007/s10409-021-01068-0

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 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.

Highlights

Many biological structures can be modeled as tubular assemblies of helical rods, such as the tail sheaths of bacteriophage viruses [1,2], the cellulose filaments in the tendrils of climbing plants [3], the bundles of microtubules and motors in all eukaryotic flagella and cilia [4,5], the envelopes of shapeshifting unicellular organisms such as Lacrymaria Olor [6] and the pellicle of euglenids, a family of unicellular algae [7,8,9,10]
Understanding the mechanical behavior of these systems requires knowledge of how single helices deform under external loads, and how they interact with each other to produce the ensemble response. We address these questions by focusing on the response under compression and extension of a tubular assembly made of 8 helical rods
We report and discuss the main findings on the response under compression and extension of the assembly described in Sect. 2, as extracted from finite element method (FEM) simulations

Summary

Introduction

Tubular structures composed of helical fibers exhibit programmable shape-shifting capabilities This makes them adaptable to changing functional needs, by varying their conformation and properties. Exploiting these features, they have been employed in a broad range of domains, e.g., deployable antennas in aerospace engineering [11], tubular vascular stents in biomedical engineering, sheaths of McKibben artificial muscles and, more generally, helically-arranged fibers in soft robotics and biorobotics [12,13,14,15]. Understanding the mechanical behavior of these systems requires knowledge of how single helices deform under external loads, and how they interact with each other to produce the ensemble response

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Conclusion