Field Dislocation Mechanics for heterogeneous elastic materials: A numerical spectral approach

Abstract : 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 using FFT methods without artificial fluctuations arising from materials and defects induced discontinuities. 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 dislocations and from elastic stiffness heterogeneities. To this end, the elasto-static equations of the field dislocation mechanics theory for periodic heterogeneous materials are numerically solved with FFT in the case of dislocations in proximity of inclusions of varying stiffness. An optimal intrinsic discrete Fourier transform method is sought based on two distinct schemes. A centered finite difference scheme for differential rules are used for numerically solving the Poisson-type equation in the Fourier space, while centered finite differences on a rotated grid is chosen for the computation of the modified Fourier Green's operator associated with the Lippmann Schwinger-type equation. By comparing different methods with analytical solutions for an edge dislocation in a composite material, it is found that the present spectral method is accurate, devoid of any numerical oscillation, and efficient even for an infinite phase elastic contrast like a hole embedded in a matrix containing a dislocation. The present FFT method is then used to simulate physical cases such as the elastic fields of dislocation dipoles located near the matrix/inclusion interface in a 2D composite material and the ones due to dislocation loop distributions surrounding cubic inclusions in 3D composite material. In these configurations, the spectral method allows investigating accurately the elastic interactions and image stresses due to dislocation fields in the presence of elastic inhomogeneities. (C) 2016 Elsevier B.V. All rights reserved.
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Submitted on : Thursday, April 13, 2017 - 4:55:29 PM
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K. S. Djaka, Aurélien Villani, Vincent Toupin, Laurent Capolungo, Stephane Berbenni. Field Dislocation Mechanics for heterogeneous elastic materials: A numerical spectral approach. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2017, 315, pp.921-942. ⟨10.1016/j.cma.2016.11.036⟩. ⟨emse-01508070⟩



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