Fragmentation of brittle materials under high rates of loading is commonly encountered in materials processing and under impact loading conditions. Theoretical models intended to correlate the features of dynamic fragmentation have been suggested during the past few years with the goal of providing a rational basis for prediction of fragment sizes.; In this thesis, a new model based on the dynamics of the process is developed. In this model, the spatial distribution and strength variation representative of flaws in real brittle materials are taken into account. The model captures the competition between rising mean stress in a brittle material due to an imposed high strain rate and falling mean stress due to loss of compliance.; The model is studied computationally through an adaptation of a concept introduced by Xu and Needleman (1994). The deformable body is first divided into many small regions. Then, the mechanical behavior of the material is characterized by two constitutive relations, a volumetric constitutive relationship between stress and strain within the small continuous regions and a cohesive surface constitutive relationship between traction and displacement discontinuity across the cohesive surfaces between the small regions. These surfaces provide prospective fracture paths.; Numerical experiments were conducted for a system with initial and boundary conditions similar to those invoked in the simple energy balance models, in order to provide a basis for comparison. It is found that, these models lead to estimates of fragment size which are an order of magnitude larger than those obtained by a more detailed calculation. The differences indicate that the simple analytical models, which deal with the onset of fragmentation but not its evolution, are inadequate as a basis for a complete description of a dynamic fragmentation process.; The computational model is then adapted to interpret experimental observations on the increasing energy dissipation for increasing crack speed during dynamic crack growth in a brittle material. This higher energy consumption is due to a combination of a fixed amount of energy expended per unit area of created surface and a large increase in the surface area due to the formation of many unstable branches of the main crack. This interpretation has been proposed by Sharon et al. (1996) and it is supported by the computational results presented here.
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