Mechanics of two filaments in tight orthogonal contact

Abstract

Networks of flexible filaments often involve regions of tight contact. Predictively understanding the equilibrium configurations of these systems is challenging due to intricate couplings between topology, geometry, large nonlinear deformations, and friction. Here, we perform an in-depth study of a simple, yet canonical, problem that captures the essence of contact between filaments. In the orthogonal clasp, two filaments are brought into contact, with each centerline lying in one of a pair of orthogonal planes. Our data from X-ray tomography (μCT) and mechanical testing experiments are in excellent agreement with finite element method (FEM) simulations. Despite the apparent simplicity of the physical system, the data exhibit strikingly unintuitive behavior, even when the contact is frictionless. Specifically, we observe a curvilinear diamond-shaped ridge in the contact-pressure field between the two filaments, sometimes with an inner gap. When a relative displacement is imposed between the filaments, friction is activated, and a highly asymmetric pressure field develops. These findings contrast to the classic capstan analysis of a single filament wrapped around a rigid body. Both the μCT and FEM data indicate that the cross-sections of the filaments can deform significantly. Nonetheless, an idealized geometrical theory assuming undeformable tube cross-sections and neglecting elasticity rationalizes our observations qualitatively and highlights the central role of the small, but nonzero, tube radius of the filaments. We believe that our orthogonal clasp analysis provides a building block for future modeling efforts in frictional contact mechanics of more complex filamentary structures.

A Fully Implicit Method for Robust Frictional Contact Handling in Elastic Rods

“…Moving forwards, we denote the following vector concatenation describing an edge-to-edge contact pair: 12 , where | j − i| > 1 to exclude consecutive edges from consideration when enforcing contact. We describe the set of all valid edge combinations as X.…”

“…This in turn has resulted in the need to study and better understand the complicated mechanics of filaments. Thus, several previous works have sought out to understand the various mechanics of rod-like structures including the deployment of rods [1,2,3], elastic gridshells [4,5,6], plant growth [7], knots [8,9,10,11,12], and propulsion of bacterial flagella [13,14,15].…”

Aeroelastic characterisation of a bio-inspired flapping membrane wing

“…The mixture is poured into a flat cast to create different silicon sheets of h = 0.3 mm to 1.4 mm thickness. The membrane sheets have a density of ρ = 1160 kg/m 3 and a Young's modulus of E = 1.22 ± 0.05 kPa [53]. Rectangular wings are cut from the silicon sheets and fixed between two thin carbon fibre plates without pre-stretching the membranes (figure 1a).…”

A Discrete Element Method model for frictional fibers

“…Cyclic mechanical stresses can form very compact natural structures [11], and birds also assemble fibers to build their nests [12,13]. The contacts between fibers play a fundamental role in describing the physics of knots, which is a subtle competition between tension and friction [14,15], as well as eventual bending of the fibers [16][17][18][19].…”

“…One approach is to use finite element algorithms to discretize the fibers [20]. This approach allows a complete solution of the elasticity equations in complex geometries such as nodes [18], but is only possible for systems with small numbers of contacts. Another approach is to model the fibers as connected spheres [21] or sphero-cylinders [22] and to use the discrete element method algorithm widely used for the study of granular materials.…”