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2 results

  • 6 - Differential Geometrical Field Theory of Dislocations and Defects

  • from Part II - Theoretical Backgrounds
  • Tadashi Hasebe, Kobe University, Japan
  • Book:
    Field Theory of Multiscale Plasticity
    Published online:
    14 December 2023
    Print publication:
    04 January 2024, pp 304-370

  • Summary

    Descriptions of the inhomogeneity including dislocations and defects based on the differential geometry forms the basic core of FTMP. This chapter first provides the basic notions of differential geometry necessary for understanding “non-Riemannian plasticity.” The fundamental concepts and quantities are presented second, which is followed by some new features peculiar to the present field theory of multiscale plasticity.

Field Theory of Multiscale Plasticity
  • Tadashi Hasebe
  • Published online:
    14 December 2023
    Print publication:
    04 January 2024
  • This unique book provides a concise and systematic treatment of foundational material on dislocations and metallurgy and an up-to-date discussion of multiscale modeling of materials, which ultimately leads to the field theory of multiscale plasticity (FTMP). Unlike conventional continuum models, this approach addresses the evolving inhomogeneities induced by deformation, typically as dislocation substructures like dislocation cells, as well as their interplay at more than one scale. This is an impressively visual text with many and varied examples and viewgraphs. In particular, the book presents a feasible constitutive model applicable to crystal plasticity-based finite element method (FEM) simulations. It will be an invaluable resource, accessible to undergraduate and graduate students as well as researchers in mechanical engineering, solid mechanics, applied physics, mathematics, materials science, and technology.