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Lattice theory --- Homogenization (Differential equations)

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Microstructure. --- Composite materials --- Homogenization (Differential equations)

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Physically motivated dislocation density based models for the description of plastic deformation do need information about the underlying processes in a homogenized form. A rate formulation for the formation of the glissile junction for usage in continuum descriptions is developed by using three-dimensional Discrete Dislocation Dynamics. Furthermore, a contribution to the understanding of grain boundary modeling in Discrete Dislocation Dynamics as well as continuum descriptions is made.

homogenization --- Plastizität --- dislocations --- grain boundaries --- Homogenisierung --- plasticity --- Versetzungen --- Korngrenzen

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Engineering materials show a pronounced heterogeneity on a smaller scale that influences the macroscopic constitutive behavior. Algorithms for the periodic discretization of microstructures are presented. These are used within the Nonuniform Transformation Field Analysis (NTFA) which is an order reduction based nonlinear homogenization method with micro-mechanical background. Theoretical and numerical aspects of the method are discussed and its computational efficiency is validated.

microstructure --- order reduction method --- mesh generation --- computational homogenization --- composite materials

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Electromagnetic waves. --- Composite materials --- Homogenization (Differential equations) --- Testing.