A convective instability mechanism for quasistatic crack branching in a hydrogel

Experiments on quasistatic crack propagation in gelatin hydrogels reveal a new branching instability triggered by wetting the tip opening with a drop of aqueous solvent less viscous than the bulk one. We show that the emergence of unstable branches results from a balance between the rate of secondary crack growth and the rate of advection away from a non-linear elastic region of size $\mathcal G/E$ where $\mathcal G$ is the fracture energy and $E$ the small strain Young modulus. We build a minimal, predictive model that combines mechanical characteristics of this mesoscopic region and physical features of the process zone. It accounts for the details of the stability diagram and lends support to the idea that non-linear elasticity plays a critical role in crack front instabilities

From thermally activated to viscosity controlled fracture of biopolymer hydrogels

We report on rate-dependent fracture energy measurements over three decades of steady crack velocities in alginate and gelatin hydrogels. We evidence that, irrespective of gel thermo-reversibility, thermally activated "unzipping" of the non-covalent cross-link zones results in slow crack propagation, prevaling against the toughening effect of viscous solvent drag during chain pull-out, which becomes efficient above a few mm.s$^{-1}$. We extend a previous model [Baumberger {\it et al.} Nature Materials, {\bf 5}, 552 (2006)] to account for both mechanisms, and estimate the microscopic unzipping rates

Travelling and Standing Waves in a Spatially Forced 2D Convection Experiment

International audienceRayleigh-Bénard convection is studied in a rectangular geometry with a spatial forcing induced in one direction by electric wires. When using fluids of relatively large Prandtl numbers, this forcing allows the existence of a perfect one-dimensional pattern until the onset of bimodal convection. The transition to bidimensional convection is studied for increasing Rayleigh number and reveals the existence of different spatio-temporal regimes depending on the value of the forcing. At the onset of the transition, a stationary pattern is observed for weak forcing, while travelling waves are evidenced for strong forcing. Both behaviours give place to collective oscillations at higher Rayleigh number

Interplay between shear loading and structural aging in a physical gel

We show that the aging of the mechanical relaxation of a gelatin gel exhibits the same scaling phenomenology as polymer and colloidal glasses. Besides, gelatin is known to exhibit logarithmic structural aging (stiffening). We find that stress accelerates this process. However, this effect is definitely irreducible to a mere age shift with respect to natural aging. We suggest that it is interpretable in terms of elastically-aided elementary (coil$\to$helix) local events whose dynamics gradually slows down as aging increases geometric frustration

Magic angles and cross-hatching instability in hydrogel fracture

The full 2D analysis of roughness profiles of fracture surfaces resulting from quasi-static crack propagation in gelatin gels reveals an original behavior characterized by (i) strong anisotropy with maximum roughness at $V$-independent symmetry-preserving angles, (ii) a sub-critical instability leading, below a critical velocity, to a cross-hatched regime due to straight macrosteps drifting at the same magic angles and nucleated on crack-pinning network inhomogeneities. Step height values are determined by the width of the strain-hardened zone, governed by the elastic crack blunting characteristic of soft solids with breaking stresses much larger that low strain moduli

Codage d'objets de type VOP par représentation en régions auto-extractibles

Le nouveau standard multimédia Mpeg-4 traite aussi bien des aspects compression que de fonctionnalités de haut niveau telles que la manipulation d'objets. Notre approche propose un cadre unique permettant une compression efficace tout en offrant une segmentation à coût « quasi-nul » à travers le principe de représentation en régions auto-extractibles. Aussi montrons-nous ici que notre méthode peut constituer une alternative au mode classique de codage intra de Mpeg-4. En particulier, l'approche réussi à unifier le codage de la forme et de la texture d'un VOP

Color LAR codec : a color image representation and compression scheme based on local resolution adjustment and on self-extracting region representation

This LAR (Locally Adaptive Resolution) color image coding scheme yields to an efficient progressive compression with a better subjective quality than Jpeg2000. Additionally, it offers region functionalities for low bit rate coding and decoding. From highly compressed luminance, a region description, without contours encoding, can be obtained through a segmentation process performed at both coder and decoder. Considering color results, controlled chrominance components segmentation provides a better data consistency simultaneously with a low bit rate compression. As regions and their encoding are based on a same representation grid, enhancement of image quality can be global, or only restricted to a Region Of Interest.Cet article présente un schéma original de codage progressif d'images couleur apportant à la fois une efficacité en termes de compression (meilleure qualité subjective que Jpeg2000) et des fonctionnalités au niveau région à bas débits pour le codeur et le décodeur. À partir de l'image des luminances codée à bas débit par le codec LAR (Locally Adaptive Resolution), une description en régions, sans codage des contours, est obtenue à travers un procédé de segmentation effectué au codeur et au décodeur. Cette segmentation peut être contrôlée par les composantes chromatiques pour une meilleure cohérence du résultat d'un point de vue couleur. Un codage basé régions appliqué sur les images de chrominance produit alors une compression de ces composantes à très bas débit. Comme les régions et le codage de leur contenu partagent une même grille de représentation, l'amélioration de la qualité de l'image peut être globale, ou limitée à une zone d'intérêt

Rifts in Spreading Wax Layers

We report experimental results on the rift formation between two freezing wax plates. The plates were pulled apart with constant velocity, while floating on the melt, in a way akin to the tectonic plates of the earth's crust. At slow spreading rates, a rift, initially perpendicular to the spreading direction, was found to be stable, while above a critical spreading rate a "spiky" rift with fracture zones almost parallel to the spreading direction developed. At yet higher spreading rates a second transition from the spiky rift to a zig-zag pattern occurred. In this regime the rift can be characterized by a single angle which was found to be dependent on the spreading rate. We show that the oblique spreading angles agree with a simple geometrical model. The coarsening of the zig-zag pattern over time and the three-dimensional structure of the solidified crust are also discussed.Comment: 4 pages, Postscript fil

Stable propagation of an ordered array of cracks during directional drying

We study the appearance and evolution of an array of parallel cracks in a thin slab of material that is directionally dried, and show that the cracks penetrate the material uniformly if the drying front is sufficiently sharp. We also show that cracks have a tendency to become evenly spaced during the penetration. The typical distance between cracks is mainly governed by the typical distance of the pattern at the surface, and it is not modified during the penetration. Our results agree with recent experimental work, and can be extended to three dimensions to describe the properties of columnar polygonal patterns observed in some geological formations.Comment: 8 pages, 4 figures, to appear in PR

Theory of dynamic crack branching in brittle materials

The problem of dynamic symmetric branching of an initial single brittle crack propagating at a given speed under plane loading conditions is studied within a continuum mechanics approach. Griffith's energy criterion and the principle of local symmetry are used to determine the cracks paths. The bifurcation is predicted at a given critical speed and at a specific branching angle: both correlated very well with experiments. The curvature of the subsequent branches is also studied: the sign of $T$, with $T$ being the non singular stress at the initial crack tip, separates branches paths that diverge from or converge to the initial path, a feature that may be tested in future experiments. The model rests on a scenario of crack branching with some reasonable assumptions based on general considerations and in exact dynamic results for anti-plane branching. It is argued that it is possible to use a static analysis of the crack bifurcation for plane loading as a good approximation to the dynamical case. The results are interesting since they explain within a continuum mechanics approach the main features of the branching instabilities of fast cracks in brittle materials, i.e. critical speeds, branching angle and the geometry of subsequent branches paths.Comment: 41 pages, 15 figures. Accepted to International Journal of Fractur