Dynamic crack propagation with phase-field approach

This project aims at studying the non-unicity of crack paths in materials using the phase-field approach. The energy functional to be minimized in the variational phase-field modelling of brittle fracture is not convex. Hence, multiple local minima can coexist and could be interpreted as multiple solutions associated with various crack patterns. Recent work on the subject revealed and illustrated this fact. By introducing perturbations in the model, it is possible to trigger some variability in the crack patterns. It is applied here by small variations of the geometry, leading to distinct crack paths with associated probabilities computed using the Monte Carlo method. Moreover, in this context, the Monte Carlo method allows drawing expectation maps of the damage. Thus, starting from a previous publication on stochastic phase-field modelling of brittle fracture, this piece of work explores the variability of mode 1 crack in static. It is observed here that slight changes in geometry yields considerable variations in the expectation maps. The physical properties of the material seem also to influence significantly the variability of the damage field. Finally, the same experiment is made once more, but this time with dynamic resolution. Varying the velocity at which the load is applied to the model allows observing changes in variability of fissure patterns according to the loading speed. Even for low velocities, the experiments in this project show differences between results in static and in dynamic. One notable difference is that the variability disappears with very low or very high speeds. At high velocities, some branching can also be witnessed, but no variability associated with it is observed. Globally, in all the experiment, the variability of the crack patterns seems to be highly sensitive to slight changes in the geometry, modification of the physical properties of the material or, in the dynamic case, to the loading velocity. And, considering that even low velocities in dynamic resolution have shown to lead to results distinct from the experiment in static, studying only the static case in not sufficient to have a global insight of the plausible crack paths.