An Introduction to the Theory of Three Dimensional Curved DislocationsMilan Cajić Plastic deformation of crystals is the result of dislocation motion. Owing to the long-range nature of dislocation interactions, the development of a continuum theory of plasticity, based on the averaged dynamics of dislocation systems, represents a difficult mathematical problem. Here, we summarize current advances in the field of size-dependent continuum plasticity of crystals, based on the dislocation density measure which is able to account for the evolution of systems of three-dimensional curved dislocations. In the first part of the current work we introduce a self-consistent theory and its dislocation density measure with a definition and an evolution equation which is a direct generalization of the definition and the kinematic evolution equation of the Kröner-Nye dislocation density tensor. In the second part of this paper we show a Finite Element Method application of a 3D continuum theory of curved dislocations, which is based on the definition of dislocation density in higher dimensional state space containing dislocation orientation information. Key words: crystallography, continuum mechanics, crystal deformation, plastic deformation, deformation tensor, density tensor, dislocation.
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