Christian B. Silbermann - Introduction to Geometrically Nonlinear Continuum Dislocation Theory: FE Implementation and Application on Subgrain Formation in Cubic Single Crystals ... in Applied Sciences and Technology)

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This book deals with solid continuum mechanics applied to crystal plasticity on a mesoscopic length scale. The formation of dislocation structures and subgrain boundaries is decisive for the macroscopic properties of metallic materials. To simulate and predict this, Gurtins established geometrically nonlinear mesoscopic theory of crystal plasticity with continuously distributed, geometrically necessary dislocations is adopted and specified. Here, the degrees of freedom essential for subgrain formation are available, while the number of phenomenological approaches and associated material parameters are kept as small as possible. With this continuum dislocation theory (CDT), it is proven that subgrain formation can be simulated. To this end, a minimalistic model of elastically and plastically anisotropic single crystal viscoplasticity is derived. Subsequently employing the finite element method (FEM), it is possible to follow the formation of subgrain boundaries during large plastic deformations of a crystallite. In addition, preparation and synthesis of algorithms for the numerical solution of the associated multi-field problem using the FEM are provided and aspects of thermodynamic consistency are discussed. Finally, proper experiments are suggested for the validation of the numerical results, and open problems are discussed for future research.

The intention of this book is threefold: Firstly, it presents a comprehensive introduction to single crystal plasticity with continuously distributed dislocations. Secondly, it provides a straightforward, extensive preparation for the implementation into FEM codes including solution algorithms in the context of a higher gradient theory. Thirdly, a simple simulation example introduces the characteristics of pattern forming systems and points out the numerical challenges involved in dealing with localization phenomena. Thus, the book may serve as a starting point for entering and contributing to the research in this interesting field of computational materials science.

This book is based on results previously published within Christian B. Silbermanns doctoral thesis (English title On the modeling of dislocation- and deformation-induced plastic localization phenomena of metallic materials, https://nbn-resolving.org/urn:nbn:de:bsz:ch1-qucosa2-359730 ).