Analysis and Computation of Microstructure in Finite Plasticity

1. Front Matter

   Pages 1-11

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2. Numerical Algorithms for the Simulation of Finite Plasticity with Microstructures

   • Carsten Carstensen, Dietmar Gallistl, Boris Krämer

   Pages 1-30

3. Variational Modeling of Slip: From Crystal Plasticity to Geological Strata

   • Sergio Conti, Georg Dolzmann, Carolin Kreisbeck

   Pages 31-62

4. Rate-Independent versus Viscous Evolution of Laminate Microstructures in Finite Crystal Plasticity

   • Christina Günther, Dennis M. Kochmann, Klaus Hackl

   Pages 63-88

5. Variational Gradient Plasticity: Local-Global Updates, Regularization and Laminate Microstructures in Single Crystals

   • Steffen Mauthe, Christian Miehe

   Pages 89-123

6. Variational Approaches and Methods for Dissipative Material Models with Multiple Scales

   • Alexander Mielke

   Pages 125-155

7. Energy Estimates, Relaxation, and Existence for Strain-Gradient Plasticity with Cross-Hardening

   • Keith Anguige, Patrick W. Dondl

   Pages 157-173

8. Gradient Theory for Geometrically Nonlinear Plasticity via the Homogenization of Dislocations

   • Stefan Müller, Lucia Scardia, Caterina Ida Zeppieri

   Pages 175-204

9. Microstructure in Plasticity, a Comparison between Theory and Experiment

   • Olga Dmitrieva, Dierk Raabe, Stefan Müller, Patrick W. Dondl

   Pages 205-218

10. Construction of Statistically Similar RVEs

    • Lisa Scheunemann, Daniel Balzani, Dominik Brands, Jörg Schröder

    Pages 219-256

11. Back Matter

    Pages 257-257

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This book addresses the need for a fundamental understanding of the physical origin, the mathematical behavior and the numerical treatment of models which include microstructure. Leading scientists present their efforts involving mathematical analysis, numerical analysis, computational mechanics, material modelling and experiment. The mathematical analyses are based on methods from the calculus of variations, while in the numerical implementation global optimization algorithms play a central role. The modeling covers all length scales, from the atomic structure up to macroscopic samples. The development of the models ware guided by experiments on single and polycrystals and results will be checked against experimental data.

• Crystal Plasticity
• Deformation Laminates
• Finite Plasticity
• Hybrid Micro-macro Modeling
• Microplast

• Inst. für Angewandte Mathematik, Universität Bonn, Bonn, Germany

  Sergio Conti

• Lehrstuhl für Mechanik - Materialtheorie, Ruhr-Universität Bochum, Bochum, Germany

  Klaus Hackl

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