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Interaction and Multiscale Mechanics
  Volume 2, Number 1, March 2009, pages 15-30
open access

Interaction fields based on incompatibility tensor in field theory of plasticity-Part II: Application-
Tadashi Hasebe

    The theoretical framework of the interaction fields for multiple scales based on field theory is applied to one-dimensional problem mimicking dislocation substructure sensitive intra-granular inhomogeneity evolution under fatigue of Cu-added steels. Three distinct scale levels corresponding respectively to the orders of (A)dislocation substructures, (B)grain size and (C)grain aggregates are set-up based on FE-RKPM (reproducing kernel particle method) based interpolated strain distribution to obtain the incompatibility term in the interaction field. Comparisons between analytical conditions with and without the interaction, and that among different cell size in the scale A are simulated. The effect of interaction field on the B-scale field evolution is extensively examined. Finer and larger fluctuation is demonstrated to be obtained by taking account of the field interactions. Finer cell size exhibits larger field fluctuation whereas the coarse cell size yields negligible interaction effects.
Key Words
    multiscale modeling; crystal plasticity; field theory; differential geometry; non-Riemannian plasticity.
Tadashi Hasebe; Kobe University, Rokkodai, Nada, Kobe 657-8501, Japan

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