arXiv subjects

Julien Chopin

Publications and source records attributed to Julien Chopin.

11 recordsLinked to original sources

arXiv2026

Elasto-Hydrodynamic Propulsion of a Magnetically Actuated Filament

We investigate the low-Reynolds-number propulsion of a slender elastic filament with a dipolar magnetic head actuated by an oscillating field in a viscous fluid by studying its strokes and net forward motion. To capture these dynamics, we employ an elasto-hydrodynamic (EH) framework that couples Euler-Bernoulli beam mechanics with resistive force theory. Unlike prescribed-kinematics models, filament shapes here emerge self-consistently from the actuation and the force and torque boundary conditions (BCs). We demonstrate that viscous boundary contributions are crucial for quantitative agreement and show that the swimming dynamics are governed by the EH length and a magneto-viscous-elastic stroke amplitude introduced here. The swimming speed is non-monotonic with increasing ratio of the swimmer length to the EH length, and is shown to reach a maximum when the swimmer length is on the order of the EH length. We further discuss the analytical limit in which the tail BCs can be described as free, and the limitations that arise when viscous contributions to the BCs are ignored.

cond-mat.soft↗

arXiv2025

Bundling architecture in elastic filaments with applied twist

We investigate the formation of helical multifilament bundles and the torque required to achieve them as a function of applied twist. Hyperelastic filaments with circular cross sections are mounted parallel in a uniform circle onto end-clamps that can move along the twist axis depending on the applied axial load. With increasing twist, the filaments describe a hyperbolic hyperboloid surface before coming into contact in a circle, and then packing in a tight helical bundle in the center with increasing twist. While the bundle appears ordered for sufficiently small number of filaments, they are disordered for large enough number of filaments and applied twist. We reveal with x-ray tomography, that the packing of the filaments becomes disordered following a radial-instability which leads to a decrease in bundle radius, and migration of filaments relative to each other in the bundle. Nonetheless, the helical angle of the filaments in the bundle are found to be essentially constant, resulting in inclination angles which increase with distance from axis of rotation. We develop energy minimization analysis to capture the observed variations in bundle length and torque as a function of number of filaments considering the neo-Hookean nature of the filaments. We show that the bundle geometry and the applied load can be used to describe the non-linear torque profile measured as a function of twist angle.

cond-mat.soft↗

arXiv2023

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, the torque profile, and the 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. 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.

cond-mat.soft↗

arXiv2023

Tensional twist-folding of sheets into multilayered scrolled yarns

Twisting sheets as a strategy to form functional yarns relies on millennia of human practice in making catguts and fabric wearables, but still lacks overarching principles to guide their intricate architectures. We show that twisted hyperelastic sheets form multilayered self-scrolled yarns, through recursive folding and twist localization, that can be reconfigured and redeployed. We combine weakly nonlinear elasticity and origami to explain the observed ordered progression beyond the realm of perturbative models. Incorporating dominant stretching modes with folding kinematics, we explain the measured torque and energetics originating from geometric nonlinearities due to large displacements. Complementarily, we show that the resulting structures can be algorithmically generated using Schläfli symbols for star-shaped polygons. A geometric model is then introduced to explain the formation and structure of self-scrolled yarns. Our tensional twist-folding framework shows that origami can be harnessed to understand the transformation of stretchable sheets into self-assembled architectures with a simple twist.

cond-mat.soft↗

arXiv2020

Universal scaling of the velocity field in crack front propagation

The propagation of a crack front in disordered materials is jerky and characterized by bursts of activity, called avalanches. These phenomena are the manifestation of an out-of-equilibrium phase transition originated by the disorder. As a result avalanches display universal scalings which are however difficult to characterize in experiments at finite drive. Here we show that the correlation functions of the velocity field along the front allow to extract the critical exponents of the transition and to identify the universality class of the system. We employ these correlations to characterize the universal behavior of the transition in simulations and in an experiment of crack propagation. This analysis is robust, efficient and can be extended to all systems displaying avalanche dynamics.

cond-mat.stat-mech↗

arXiv2019

Birth and decay of tensional wrinkles in hyperelastic sheets

We demonstrate with experiments that wrinkling in stretched latex sheets occur over finite strains, and that their amplitudes grow and then decay to zero over a greater range of applied strains compared with linear elastic materials. The wrinkles occur provided the sheet is sufficiently thin compared to its width, and only over a finite range of length-to-width ratios. We show with simulations that the Mooney-Rivlin hyperelastic model describes the observed growth and decay of the wrinkles in our experiments. The decrease of wavelength with applied tension is found to be consistent with a far-from-threshold scenario proposed by Cerda and Mahadevan in 2003. However, the amplitude is observed to decrease with increasing tensile load, in contrast with the prediction of their original model. We address the crucial assumption of {\it collapse of compressive stress}, as opposed to collapse of compressive strain, underlying the far-from-threshold analysis, and test it by measuring the actual arc-length of the stretched sheet in the transverse direction and its difference from the width of a planar projection of the wrinkled shape. Our experiments and numerical simulations indicate a complete {\it collapse of the compressive stress}, and reveal that a proper implementation of the far-from-threshold analysis is consistent with the non-monotonic dependence of the amplitude on applied tensile load observed in experiments and simulations. Thus, our work support and extend far-from-threshold analysis to the stretching problem of rectangular hyperelastic sheets.

cond-mat.soft↗

arXiv2018

Extreme Contractility and Torsional Compliance of Soft Ribbons under High Twist

We investigate experimentally and model the mechanical response of a soft Hookean ribbon submitted to large twist $η$ and longitudinal tension $T$, under clamped boundary conditions. We derive a formula for the torque $M$ using the \FvK equations up to third order in twist, incorporating a twist-tension coupling. In the stable helicoid regime, quantitative agreement with experimental data is obtained. When twisted above a critical twist $η_L(T)$, ribbons develop wrinkles and folds which modify qualitatively the mechanical behavior. We show a surprisingly large longitudinal contraction upon twist, reminiscent of a Poynting effect, and a much lower torsional stiffness. Far from threshold, we identify two regimes depending on the applied $T$. In a high-$T$ regime, we find that the torque scales as $η\cdot T$ and the contraction as $η^2$, in agreement with a far from threshold analysis where compression and bending stresses are neglected. In a low-$T$ regime, the contraction still scales as $η^2$ but the torque appears $T$-independent and linear with $η$. We argue that the large curvature of the folds now contribute significantly to the torque. This regime is discussed in the context of asymptotic isometry for very thin plates submitted to vanishing tension but large change of shape, as in crumpling.

cond-mat.soft↗

arXiv2018

Tension-dependent transverse buckles and wrinkles in twisted elastic sheets

We investigate with experiments the twist induced transverse buckling instabilities of an elastic sheet of length $L$, width $W$, and thickness $t$, that is clamped at two opposite ends while held under a tension $T$. Above a critical tension $T_λ$ and critical twist angle $η_{tr}$, we find that the sheet buckles with a mode number $n \geq 1$ transverse to the axis of twist. Three distinct buckling regimes characterized as clamp-dominated, bendable, and stiff are identified, by introducing a bendability length $L_B$ and a clamp length $L_{C}( L_B$), we find that mode $n=1$ develops above $η_{tr} \equiv η_S \sim (t/W) T^{-1/2}$, independent of $L$. In the bendable regime $L_{C} 1$ occur above $η_{tr} \equiv η_B \sim \sqrt{t/L}T^{-1/4}$. Here, we find the wavelength $λ_B \sim \sqrt{Lt}T^{-1/4}$, when $n > 1$. These scalings agree with those derived from a covariant form of the Föppl-von Kármán equations, however, we find that the $n=1$ mode also occurs over a surprisingly large range of $L$ in the bendable regime. Finally, in the clamp-dominated regime ($L < L_c$), we find that $η_{tr}$ is higher compared to $η_B$ due to additional stiffening induced by the clamped boundary conditions.

cond-mat.soft↗

arXiv2017

Dynamic wrinkling and strengthening of a filament in a viscous fluid

We investigate the wrinkling dynamics of an elastic filament immersed in a viscous fluid submitted to compression at a finite rate with experiments and by combining geometric nonlinearities, elasticity, and slender body theory. The drag induces a dynamic lateral reinforcement of the filament leading to growth of wrinkles that coarsen over time. We discover a new dynamical regime characterized by a timescale with a non-trivial dependence on the loading rate, where the growth of the instability is super-exponential and the wavenumber is an increasing function of the loading rate. We find that this timescale can be interpreted as the characteristic time over which the filament transitions from the extensible to the inextensible regime. In contrast with our analysis with moving boundary conditions, Biot's analysis in the limit of infinitely fast loading leads to rate independent exponential growth and wavelength.

cond-mat.soft↗

arXiv2016

Disclinations, e-cones, and their interactions in extensible sheets

We investigate the nucleation, growth, and spatial organization of topological defects with a ribbon shaped elastic sheet which is stretched and twisted. Singularities are found to spontaneously arrange in a triangular lattice in the form of vertices connected by stretched ridges that result in a self-rigidified structure. The vertices are shown to be negative disclinations or e-cones which occur in sheets with negative Gaussian curvature, in contrast with d-cones in sheets with zero-Gaussian curvature. We find the growth of the wrinkled width of the ribbon to be consistent with a far-from-threshold approach assuming a compression-free base state. The system is found to show a transition from a regime where the wavelength is given by the ribbon geometry, to where it is given by its elasticity as a function of the ratio of the applied tension to the elastic modulus and cross-sectional area of the ribbon.

cond-mat.soft↗

arXiv2014

Roadmap to the morphological instabilities of a stretched twisted ribbon

We address the mechanics of an elastic ribbon subjected to twist and tensile load. Motivated by the classical work of Green and a recent experiment that discovered a plethora of morphological instabilities, we introduce a comprehensive theoretical framework through which we construct a 4D phase diagram of this basic system, spanned by the exerted twist and tension, as well as the thickness and length of the ribbon. Different types of instabilities appear in various "corners" of this 4D parameter space, and are addressed through distinct types of asymptotic methods. Our theory employs three instruments, whose concerted implementation is necessary to provide an exhaustive study of the various parameter regimes: (i) a covariant form of the Föppl-von Kármán (cFvK) equations to the helicoidal state - necessary to account for the large deflection of the highly-symmetric helicoidal shape from planarity, and the buckling instability of the ribbon in the transverse direction; (ii) a far from threshold (FT) analysis - which describes a state in which a longitudinally-wrinkled zone expands throughout the ribbon and allows it to retain a helicoidal shape with negligible compression; (iii) finally, we introduce an asymptotic isometry equation that characterizes the energetic competition between various types of states through which a twisted ribbon becomes strainless in the singular limit of zero thickness and no tension.

cond-mat.soft↗