Phase Field Modeling of Fast Crack Propagation

We present a continuum theory which predicts the steady state propagation of cracks. The theory overcomes the usual problem of a finite time cusp singularity of the Grinfeld instability by the inclusion of elastodynamic effects which restore selection of the steady state tip radius and velocity. We developed a phase field model for elastically induced phase transitions; in the limit of small or vanishing elastic coefficients in the new phase, fracture can be studied. The simulations confirm analytical predictions for fast crack propagation.Comment: 5 pages, 11 figure

Phasenfeld-Untersuchungen zur Hydrodynamik partieller Benetzung

This work presents a new technique to simulate hydrodynamic systems with free surfaces in complex geometries. It is based on a new type of projective phasefield model coupled to a conventional type of Navier-Stokes equation. The decoupling of the phasefield-parameters hereby allows a free choice of the surface tension. The model is applied to simulate dynamical pattern formation of a partial wetted surface. These simulations show that in the case of small Reynolds numbers hydrodynamic dewetting can be accurately described by a purely diffusive growth. Higher Reynolds numbers lead to surface ripples of gravitytype, whereby the interaction with the substrate acts as an effective gravitational field. Extensions to three-dimensional simulations reveal an intrinsic dewetting front instability of Mullins-Sekerka-type. Laterally stabilized perturbances typically show an oscillatory damping of capillary type. An analytic treatment of the instability, considering diffusive as well as convective transport, shows that in some cases the instability can be damped out by stabilizing terms of hydrodynamic origin. Additional simulations addressing dewetting inside a channel show that dewetting-patterns and selection-criteria correspond to the equivalent concepts in a two-dimensional purely diffusive description of the front growth