Browsing by Author "Becker, Martin"

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    Incompatibility and instability based size effects in crystals and composites at finite elastoplastic strains
    (2006) Becker, Martin; Miehe, Christian (Prof. Dr.-Ing.)
    The purpose of this work is the description of length scale dependencies in nonhomogeneously deforming crystals and the elimination of size dependencies in classical homogenization approaches for instable elastoplastically deforming composites. Key aspects, on the side of the investigation of size effects in crystals, are a comprehensive discussion of the underlying micromechanical interpretation, the deformation geometry and related experimental observations. These include a detailed incompatibility analysis and an extensive discussion of the dislocation density tensor and the storage of geometrically necessary dislocations. A dislocation density based strain gradient crystal plasticity model is developed as a main outcome of these investigations. This model is subsequently treated in the context of a mixed finite element formulation or alternatively in a more efficient manner through an extended standard local formulation. The developments are validated through various numerical examples which cover also a comparison with experimental observations or predictions obtained through alternative approaches such as discrete dislocation simulations. In view of an investigation of size dependencies in the homogenization analysis of instable inelastic composites, first criteria for an instability analysis on the micro- as well as the macro-scale are developed. The underlying basis is an incremental variational formulation of the homogenization problem. This allows for an investigation of the interaction between micro- and macro-instabilities and the development of a non-convex homogenization approach for inelastic composites at finite strains. The implications of the non-convex homogenization approach which, as a key point additionally determines the relevant microstructure size, are finally demonstrated for several examples.