Mechanics of two filaments in tight orthogonal contact

Energetics of twisted elastic filament pairs

We investigate the elastic energy stored in a filament pair as a function of applied twist by measuring torque under prescribed end-to-end separation conditions. We show that the torque increases rapidly to a peak with applied twist when the filaments are initially separate, then decreases to a minimum as the filaments cross and come into contact. The torque then increases again while the filaments form a double helix with increasing twist. A nonlinear elasto-geometric model that combines the effect of geometrical nonlinearities with large stretching and self-twist is shown to capture the evolution of the helical geometry, torque profile, and stored energy with twist. We find that a large fraction of the total energy is stored in stretching the filaments, which increases with separation distance and applied tension. We find that only a small fraction of energy is stored in the form of bending energy, and that the contribution due to contact energy is negligible. Further, we provide analytical formulas for the torque observed as a function of the applied twist and the inverse relation of the observed angle for a given applied torque in the Hookean limit. Our study highlights the consequences of stretchablility on filament twisting, which is a fundamental topological transformation relevant to making ropes, tying shoelaces, actuating robots, and the physical properties of entangled polymers.

The strength of surgical knots involves a critical interplay between friction and elastoplasticity

Knots are the weakest link in surgical sutures, serving as mechanical ligatures between filaments. Exceeding their safe operational limits can cause fatal complications. The empirical nature of present guidelines calls for a predictive understanding of the mechanisms underlying knot strength. We identify the primary ingredients dictating the mechanics of surgical sliding knots, highlighting the previously overlooked but critical effect of plasticity and its interplay with friction. The characterization of surgeon-tied knots reveals the relevant ranges of tightness and geometric features. Using model experiments coupled with finite element simulations, we uncover a robust master curve for the target knot strength versus the tying pre-tension, number of throws, and frictional properties. These findings could find applications in the training of surgeons and robotic-assisted surgical devices.

Discrete-element-method model for frictional fibers

We present a discrete-element-method algorithm for the simulation of elastic fibers in frictional contacts. The fibers are modeled as chains of cylindrical segments connected to each other by springs taking into account elongation, bending, and torsion forces. The frictional contacts between the cylinders are modeled using a Cundall and Strack model routinely used in granular material simulations. The physical scales for simulations, the determination and the tracking of contacts, and the algorithm are discussed. Tests on different situations involving few or many contact points are presented and compared to experiments or to theoretical predictions.

Planar Equilibria of an Elastic Rod Wrapped Around a Circular Capstan

We present a study on planar equilibria of a terminally loaded elastic rod wrapped around a rigid circular capstan. Both frictionless and frictional contact between the rod and the capstan are considered. We identify three cases of frictionless contact - namely where the rod touches the capstan at one point, along a continuous arc, and at two points. We show that, in contrast to a fully flexible filament, an elastic rod of finite length wrapped around a capstan does not require friction to support unequal loads at its two ends. Furthermore, we classify rod equilibria corresponding to the three aforementioned cases in a limit where the length of the rod is much larger than the radius of the capstan. In the same limit, we incorporate frictional interaction between the rod and the capstan, and compute limiting equilibria of the rod. Our solution to the frictional case fully generalizes the classic capstan problem to include the effects of finite thickness and bending elasticity of a flexible filament wrapped around a circular capstan.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s10659-022-09939-8.

Aeroelastic characterisation of a bio-inspired flapping membrane wing

Natural fliers like bats exploit the complex fluid-structure interaction between their flexible membrane wings and the air with great ease. Yet, replicating and scaling the balance between the structural and fluid-dynamical parameters of unsteady membrane wings for engineering applications remains challenging. In this study, we introduce a novel bio-inspired membrane wing design and systematically investigate the fluid-structure interactions of flapping membrane wings. The membrane wing can passively camber, and its leading and trailing edges rotate with respect to the stroke plane. We find optimal combinations of the membrane properties and flapping kinematics that out-perform their rigid counterparts both in terms of increased stroke-average lift and efficiency, but the improvements are not persistent over the entire input parameter space. The lift and efficiency optima occur at different angles of attack and effective membrane stiffnesses which we characterise with the aeroelastic number. At optimal aeroelastic numbers, the membrane has a moderate camber between 15% and 20% and its leading and trailing edges align favourably with the flow. Higher camber at lower aeroelastic numbers leads to reduced aerodynamic performance due to negative angles of attack at the leading edge and an over-rotation of the trailing edge. Most of the performance gain of the membrane wings with respect to rigid wings is achieved in the second half of the stroke when the wing is decelerating. The stroke-maximum camber is reached around mid-stroke but is sustained during most of the remainder of the stroke which leads to an increase in lift and a reduction in power. Our results show that combining the effect of variable stiffness and angle of attack variation can significantly enhance the aerodynamic performance of membrane wings and has the potential to improve the control capabilities of micro air vehicles.