The level set method provides a novel approach to describing dislocation structures and dynamics. We will first describe the level set method and its application to describing linear (co-dimension 2) objects. Next, the level set method is specialized to the case of the elastic properties and dynamics of dislocations in crystalline materials (including definition of the Burgers vector, line direction, elastic field, core, glide and climb mobility). A brief discussion of the relevant numerical methods is followed by two series of applications: dislocations interacting with second phase particles and the dislocation structure of low angle grain boundaries. In the first application, we will show videos of dislocations bypassing rigid and misfitting second phase particles. Several of the bypass mechanisms have been previously been observed and some are altogether new. Finally, we will discuss the dislocation reactions that occur in low angle grain boundaries to produce stable dislocation networks. Comparisons with experiments will be presented.
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