Hybrid Micro-Macro Modeling of Evolving Microstructures in Finite Plasticity

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The modeling of developing anisotropies and size effects in materials undergoing finite elastic-plastic strains is an important challenge of current research with high importance for industrial applications, e.g. for simulations of forming processes. A crucial perspective towards the quantitative description of these effects is provided by multiscale approaches which account for the microstructure evolution of the material by modelinherent scale bridging techniques. The rootage of these techniques in recently developed energy-minimization-based incremental homogenization and relaxation methods provides an important new perspective for the analysis of plastic microstructures in single crystals and polycrystals. However, many of the scale bridging techniques developed so far are computationally extremely demanding and only of restricted applicability to largescale computations. There is a need for the construction of multiscale-based constitutive models which are predictive and handleable in large-scale computations. To this end, we investigate a class of hybrid micro-macro models, which ’mix’ ingredients of a purely macroscopic modeling with those of full two-scale models. These hybrid models are characterized by the coupling of a macroscopic plasticity model with a microscopic plasticity model, where the latter describes in a simplified manner a key microstructural mechanism such as grain reorientation. The coupling is provided by a linking hypothesis governed by specific homogenization assumptions, which define the evolution of effective structural anisotropy tensors of the macro model based on the micro-mechanism described by the micro model. The central goal of the research is the development of computationally efficient micro–macro scenarios for polycrystalline plasticity, which account for the evolution of texture– and dislocation–structure–based anisotropies as well as for size effects by length-scale-dependent balance equations for generalized internal variables.