Study of three-dimensional crack fronts under plane stress using a phase field model

The shape of a crack front propagating through a thin sample is studied using a phase field model. The model is shown to have a well defined sharp interface limit. The crack front is found to be an ellipse with large axis the width of the sample and small axis a function of the Poisson ratio and the width of the sample. Numerical results also indicate that the front shape is independent of the crack speed and of the sample extension perpendicular to its width.Comment: 6 pages, 5 figures. To appear in europhysics Letter

Crack front instabilities under mixed mode loading in three dimensions

The evolution of a crack front under mixed mode loading (I+III) is studied using a phase field model in 3 dimensions with no stress boundary conditions. As previously observed experimentally in gels, there is a relaxation toward a geometry where $K_{III}=0$ without any front fragmentation even for high values of the initial mode mixity $K_{III}/K_{I}$. The effects of the initial condition is studied and it is shown that irregularities in the initial slit can lead to front fragmentation for smaller values of the ratio $K_{III}/K_{I}$ as is observed in experiments.Comment: 6 pages, 7 figures, accepted for publication in EuroPhysics Letter

Spiral wave drift in an electric field and scroll wave instabilities

I present the numerical computation of speed and direction of the drift of a spiral wave in an excitable medium in the presence of an electric field. In contrast to earlier results, the drift speed presents a strong variation close to the parameter value where the drift speed component along the field changes direction. Using a simple phenomenological model and results from a numerical linear stability analysis of scroll waves, I show this behavior can be attributed to a resonance of the meander modes with the translation modes of the spiral wave. Extending this phenomenological model to scroll waves also clarifies the link between the drift and long wavelength instabilities of scroll waves.Comment: Phys Rev E accepte

The role of M cells and the long QT syndrome in cardiac arrhythmias: simulation studies of reentrant excitations using a detailed electrophysiological model

In this numerical study, we investigate the role of intrinsic heterogeneities of cardiac tissue due to M cells in the generation and maintenance of reentrant excitations using the detailed Luo-Rudy dynamic model. This model has been extended to include a description of the long QT 3 syndrome, and is studied in both one dimension, corresponding to a cable traversing the ventricular wall, and two dimensions, representing a transmural slice. We focus on two possible mechanisms for the generation of reentrant events. We first investigate if early-after-depolarizations occurring in M cells can initiate reentry. We find that, even for large values of the long QT strength, the electrotonic coupling between neighboring cells prevents early-after-depolarizations from creating a reentry. We then study whether M cell domains, with their slow repolarization, can function as wave blocks for premature stimuli. We find that the inclusion of an M cell domain can result in some cases in reentrant excitations and we determine the lifetime of the reentry as a function of the size and geometry of the domain and of the strength of the long QT syndrome

Dynamic instabilities of fracture under biaxial strain using a phase field model

We present a phase field model of the propagation of fracture under plane strain. This model, based on simple physical considerations, is able to accurately reproduce the different behavior of cracks (the principle of local symmetry, the Griffith and Irwin criteria, and mode-I branching). In addition, we test our model against recent experimental findings showing the presence of oscillating cracks under bi-axial load. Our model again reproduces well observed supercritical Hopf bifurcation, and is therefore the first simulation which does so

Etude de la fragmentation de fronts fissure par la méthode du champ de Phase

Soumis à un chargement mixte, un front de fissure présente en général une instabilité defragmentation qui aboutit à la formation de plusieurs fronts de fissureparallèles se propageant, donnant des structures en marche d'escalier. Néanmoins, des travaux récents dans des systèmes où la composante de mode III du chargement peut relaxer sans fragmentation indiquent que la fragmentation du front de fissure n'apparait qu'au delà d'un seuil et qu'en deça, une relaxation exponentielle est observée. Les travaux présentés ici reposent sur l'utilisation d'un modèle de champ de phase de la propagation de la fracture et indiquent que dans un milieu homogène, la relaxation exponentielle est effectivement observée. La valeur de la longueur de relaxation calculée est en bon accord avec les résultats expérimentaux. Par contre le seuil au delà duquel la fragmentation est observée est bien plus élevé lors des simulations que lors des expériences (inclinaison du front de $48^o$ au lieu de $20^o$.). Afin de comprendre ce désaccord, des simulations en présence de d'inhomogénéités dans l'énergie de fracture ainsi que dans des configurations où la relaxation est arrêtée ont été étudiées. Il montrent clairement que la présence d'inhomogénéités et leur nature (amplitude) jouent un role prépondérant dans la nucléation d'échelons dans le front de fragmentation

Phase-field simulations of viscous fingering in shear-thinning fluids

A phase-field model for the Hele-Shaw flow of non-Newtonian fluids is developed. It extends a previous model for Newtonian fluids to a wide range of shear-dependent fluids. The model is applied to perform simulations of viscous fingering in shear- thinning fluids, and it is found to be capable of describing the complete crossover from the Newtonian regime at low shear rate to the strongly shear-thinning regime at high shear rate. The width selection of a single steady-state finger is studied in detail for a 2-plateaux shear-thinning law (Carreau law) in both its weakly and strongly shear-thinning limits, and the results are related to previous analyses. In the strongly shear-thinning regime a rescaling is found for power-law (Ostwald-de-Waehle) fluids that allows for a direct comparison between simulations and experiments without any adjustable parameters, and good agreement is obtained

Dynamics of conduction blocks in a model of paced cardiac tissue

We study numerically the dynamics of conduction blocks using a detailed electrophysiological model. We find that this dynamics depends critically on the size of the paced region. Small pacing regions lead to stationary conduction blocks while larger pacing regions can lead to conduction blocks that travel periodically towards the pacing region. We show that this size-dependence dynamics can lead to a novel arrhythmogenic mechanism. Furthermore, we show that the essential phenomena can be captured in a much simpler coupled-map model.Comment: 8 pages 6 figure