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FFT-based method for disclinations in heterogeneous materials

By Stephane Berbenni (LEM3/CNRS/Univ. Lorraine)
Co-authors: Komlan S. Djaka (LEM3/CNRS/Univ. Lorraine)
Vincent Taupin (LEM3/CNRS/Univ. Lorraine)

Spectral methods using Fast Fourier Transform (FFT) algorithms have recently seen a surge in interest in the mechanics of materials community. The present contribution addresses the critical question of determining accurate local mechanical fields near crystal defects (dislocations, disclinations) using the FFT method in comparison with the finite element (FE) method. Precisely, the present work introduces a numerical approach based on intrinsic discrete Fourier transforms for the simultaneous treatment of material discontinuities arising from the presence of disclinations, i.e. rotational discontinuities, together with inhomogeneities with various elastic stiffnesses. A centered finite difference scheme for differential rules is first used for numerically solving the Poisson equations in the Fourier space to get the incompatible elastic fields due to disclinations (incompatible elastic curvatures and strains). Second, a centered finite difference scheme on a rotated grid is chosen for the computation of the modified Fourier-Green’s operator in the Lippmann-Schwinger equation for heterogeneous media. Specific disclination dipole distributions in proximity of inclusions of varying stiffness or considered as grain boundaries in polycrystals are considered as illustrations of the present numerical method. Acknowledgments: This work was supported by the French State through the National Research Agency under the program Investment in the future (Labex DAMAS referenced as ANR-11-LABX-0008-01)

Ⓒ Photos:Toerisme Leuven