Mathematical Modeling of Dislocation Behavior and Its Application to Crystal Plasticity Analysis

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There are several textbooks and monographs on dislocations and the mechanical and physical properties of metals, but most of them discuss the topics in terms of more or less one-dimensional or scalar quantities. However, actual metallic materials are often three-dimensionally heterogeneous in their microstructure, and this heterogeneity has a significant impact on the macroscopic mechanical properties. With advances in computational technology, the complexity introduced by spatial heterogeneity in the microstructure of metals can now be explored using numerical methods. This book explains in simple terms the idea of extending the continuum mechanics theory of plastic deformation of crystals to three-dimensional analysis and applying it to the analysis of more realistic models of metal microstructures. This book links solid mechanics and materials science by providing clear physical pictures and mathematical models of plastic slip deformation and the accumulation of dislocations and atomic vacancies in metallic materials. Both monotonic and cyclic loading cases are considered.