Title: 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 work addresses the critical question of determining accurate local mechanical fields using FFT methods without artificial fluctuations arising from materials and defects induced discontinuities. Precisely, this 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 efficientmore » 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.« less

Authors:

Djaka, Komlan Senam ^[1]; Villani, Aurelien ^[2]; Taupin, Vincent ^[1]; Capolungo, Laurent  ^[3];

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Berbenni, Stephane ^[1]

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+ Show Author Affiliations

1. Univ. of Lorraine, CNRS UMR, (France). Lab. of Microstructures and Materials Mechanics
2. Saint-Etienne School of Mines, CNRS UMR, (France)
3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:

Wed Mar 01 00:00:00 EST 2017

Research Org.:

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:

USDOE; French National Research Agency (ANR)

OSTI Identifier:

1441326

Report Number(s):

LA-UR-18-20017
Journal ID: ISSN 0045-7825

Grant/Contract Number:  

AC52-06NA25396; ANR-11-LABX-0008-01

Resource Type:

Accepted Manuscript

Journal Name:

Computer Methods in Applied Mechanics and Engineering

Additional Journal Information:

Journal Volume: 315; Journal Issue: C; Journal ID: ISSN 0045-7825

Publisher:

Elsevier

Country of Publication:

United States

Language:

English

Subject:

36 MATERIALS SCIENCE; 42 ENGINEERING; Dislocation mechanics; Heterogeneous media; Elastic fields; Spectral method; FFT; Numerical algorithms