At the fundamental level, fragmentation occurs as a result of the initiation and growth of multiple, mutually interacting dynamic fractures. The statistical distributions of fragment sizes, shapes, and velocities are determined by the density of cracks and the competition between crack growth and other modes of material deformation. In this paper, we describe a three-dimensional computational model that allows spontaneous crack initiation and multiple cracks to coalesce to form fragments.The model is based on a relatively new theory of continuum mechanics called peridynamic theory. This theory is formulated in terms of integral equations that remain valid in the presence of discontinuities in the displacement field. This feature of the theory overcomes a major obstacle in the modeling of fragmentation using the classical theory, which is based on partial differential equations that cannot be applied directly to a body containing cracks. An added benefit of the peridynamic approach is that crack growth is self-guided: there is no need for supplemental equations that govern crack initiation, velocity, growth direction, branching, and arrest. All of these features emerge directly from the equation of motion and constitutive model. This paper outlines the basics of peridynamic theory and its implementation in a three-dimensional meshless computer code called EMU. It discusses detonation modeling and provides an application to fragmentation of an explosively loaded shell. We conclude that peridynamic theory is a physically reasonable and viable approach to modeling fragmentation phenomena and envision its use in addressing problems of design and performance of warheads.
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