[SY-C2] Symposium C-2

[SY-C2] Direct computation of the stress field due to geometrically necessary dislocation densities

^○Yichao Zhu¹, Yang Xiang² (1.Dalian University of Technology, China, 2.The Hong Kong University of Science and Technology, Hong Kong)

Computation of the stress field due to geometrically necessary dislocations (GNDs) is widely believed to be typical and straightforward, if compared to other challenging issues in modelling with continuum descriptions of dislocation microstrutures. A common treatment is to adopt the Kroener's formulation which relates the dislocation density field to plastic distortion (or the eigenstrain). Then the internal stress field can be computed by using the corresponding Green's formulae subject to particular loading conditions, e.g. periodic boundary conditions or in R³. For arbitrary loading conditions, complementary finite element (FE) analysis is needed in analogy with Van Der Giessen and Needleman's superposition method for discrete dislocation dynamics. In this talk, however, we will show that the stress field due to GNDs subject to arbitrary loading conditions can be resolved even more directly. With the introduction of a set of dislocation density potential functions (DDPFs), one simply needs to do one step of FE analysis, while the time for eigenstrain calculation is fully saved. Other advantages of adopting DDPFs, e.g., its capability of accommodating the anisotropic dislocation motion (e.g. glide v.s. climb) will also be addressed in the proposed presentation.