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Multiscale Modeling of Anisotropies in Single Crystals and Polycrystals at Finite Strains

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Multifield Problems in Solid and Fluid Mechanics

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 28))

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Summary

The paper provides an overview about recent developments in the multiscale analysis of the anisotropic material behavior of single crystals and polycrystals. We outline a distinct incremental variational formulation for the local constitutive response of standard dissipative materials where an incremental stress potential is obtained from a local minimization problem with respect to the internal variables. This potential allows for the formulation of IBVPs for standard dissipative solids as a sequence of incremental minimization problems. Particular emphasis is put on crystal plasticity where we develop alternative stress update algorithms for Schmid-type single crystal plasticity with potential hardening. Furthermore the variational setting provides for the formulation of a canonical framework of nonlinear homogenization of standard dissipative microstructures where a quasi-hyperelastic incremental macro-stress potential is obtained from a global minimization problem with respect to the fine-scale displacement fluctuation field. Finally we extend the framework of standard local crystal plasticity to the setting of dislocation density based gradient plasticity for inhomogeneously deforming crystals. Here we equip the formulation with a sound micromechanical basis where an incompatibility induced storage of geometrically necessary dislocations results in a scale dependent material behavior. The performance of the formulations is demonstrated for benchmarks of single crystal and polycrystal plasticity as well as thin films.

Research Project A8 “Numerical Simulation of Thermo-Mechanical Deformation Processes of Heterogeneous Materials with the Concept of Micro-Macro- Transitions”

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Authors and Affiliations

  1. Institute of Applied Mechanics, Faculty of Civil and Environmental Engineering, University of Stuttgart, Pfaffenwaldring 7, 70569, Stuttgart, Germany

    Christian Miehe & Martin Becker

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  1. Christian Miehe
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  2. Martin Becker
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Editors and Affiliations

  1. Institut für Wasserbau, Hydromechanik und Hydrosystemmodellierung, Universität Stuttgart, Pfaffenwaldring 61, 70569, Stuttgart, Germany

    Rainer Helmig

  2. Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117, Berlin, Germany

    Alexander Mielke

  3. Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Barbara I. Wohlmuth

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Miehe, C., Becker, M. (2006). Multiscale Modeling of Anisotropies in Single Crystals and Polycrystals at Finite Strains. In: Helmig, R., Mielke, A., Wohlmuth, B.I. (eds) Multifield Problems in Solid and Fluid Mechanics. Lecture Notes in Applied and Computational Mechanics, vol 28. Springer, Berlin, Heidelberg . https://doi.org/10.1007/978-3-540-34961-7_5

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  • DOI: https://doi.org/10.1007/978-3-540-34961-7_5

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  • Print ISBN: 978-3-540-34959-4

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