Exploring the Physics behind Dynamic Fragmentation through Parallel Simulations

The physical mechanisms underlying the dynamic fragmentation of heterogeneous brittle materials are explored through numerical simulations. The use of computational facilities, rather than experimental or fundamental sciences, ensures the accurate tracking of rapidly evolving fields (such as stress field, energies and damage). The numerical framework is based on Galerkin approximations coupled to the Cohesive Zone model, which addresses the failure response. Depending on the number of degrees of freedom, serial or parallel simulations are performed. The finite element method with dynamic insertion of cohesive elements constitutes the basis of the serial calculations. However, it is replaced by the scalable discontinuous Galerkin formulation for parallel computing. Both frameworks recover accurately the physical mechanisms behind dynamic fragmentation. The thesis is organized to handle gradually increasing complexity. First, the fragmentation of a quasi one-dimensional expanding ring, constituted of a heterogeneous material, is simulated. It involves two major mechanisms: crack initiation and crack interaction. Fragment sizes are highly dependent upon strain rate, material properties, and microstructural heterogeneity. Scaling laws of the average fragment size, as well as of the distribution of fragment masses, are proposed and lead to predictable laws. Then, crack propagation mechanisms are investigated through parallel simulations of the quasi three-dimensional breakage of a thin plate. By analyzing the energetic response, two regimes are defined: the strength controlled and the toughness controlled. At low strain rates, defects play a key role and govern energy levels. They correspond to the strength controlled regime and induce disordered responses. At high strain rates, fragmentation is more organized, fragment masses follow Weibull distributions, and crack interactions become secondary. This is the toughness controlled regime, governed by energetic arguments. The transition between the two regimes is derived as a function of material parameters. Finally, the transition between two- and three-dimensional fragmentation is analyzed. Massively parallel simulations of the fragmentation of a hollow sphere with variable thickness are conducted. The effect of dimensionality upon fragment shape and fragment mass distributions is analyzed. Interestingly, although these three tests involve distinct mechanisms due to the specimen geometry, they share common behaviors. Quasi-static loadings lead to highly dynamic fragmentation processes, involving extensive stress wave interactions. Defect distributions play a key role. By contrast, dynamic loadings are associated to smoother and more deterministic responses. They are primarily controlled by energy arguments. As suggested by Grady's energy balance theory, this results in a predictable dependence of the average fragment size and strain rate, characterized by a power law of exponent -2/3. However, we recover more fragments than Grady because of our ability to reproduce explicitly and accurately time-dependent mechanisms (dynamics of stress waves and energy transfers). Therefore, the interpretation of these numerical results sheds light on the complexity of the physics underlying fragmentation. The dynamics of stress waves, energetic arguments, the loading conditions, the dimensionality of the geometry, and the material itself (bulk and defects) must be all evoked to draw a global picture of the phenomenon. Reproducing such processes requires a high level of accuracy that novel parallel numerical frameworks are able to provide.