A FFT method for continuum dislocation mechanics with heterogeneous elasticity (INVITED)

Abstract eng:
A Fast Fourier Transform (FFT) method is developed to solve the elasto-static equations of the field dislocation mechanics for periodic media with heterogeneous linear elasticity. After prescribing a Nye's dislocation density tensor, the incompatible and compatible parts of the elastic distortion are obtained, respectively, from the resolution of a Poisson-type equation and a Lippmann-Schwinger integral equation with incompatibilities. Both equations are solved through an iterative basic scheme based on intrinsic discrete Fourier transforms with centered and rotated finite difference schemes, respectively. For a single pixel regularization of the dislocation density within the dislocation core, the elastic fields due to dislocations with elastic heterogeneities are accurately obtained by the present method without Gibbs oscillations.

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