Discrete Dislocation Dynamics (DDD) is an established mesoscopic numerical method for simulating dislocation motion to determine the plastic behaviour of metals. However, DDD’s reliance on analytical expressions for internal stress fields limits its application to infinite isotropic media. The Discrete-Continuous Model (DCM), which couples DDD with a finite element elastic solver, has been proposed to handle more complex boundary conditions by regularising plastic strain using the eigenstrain formalism. However, this model still relies on analytical solutions for short-range dislocation interactions, making it unsuitable for anisotropic media. In this work, we present an improved DCM framework that replaces the FE solver with a Fast Fourier transform (FFT) solver for improved computational efficiency and full numerical calculation of stress fields, eliminating the need for analytical corrections. The proposed FFT solver employs a discrete theory of Green’s operators and uses a sharp eigenstrain field to describe dislocations. The solver mesh is aligned with the face-centred cubic (fcc) lattice of the DDD, forming an octahedral cell to address symmetry artefacts around $\lbrace 111\rbrace $ slip planes. Our FFT-based approach successfully maintains numerical stability by representing fcc dislocations as sharp fields without generating oscillations. This coupling allows the study of plasticity in anisotropic materials and interactions between dislocations and diffuse inclusions, such as precipitates, without short-range stress corrections.
La dynamique des dislocations discrètes (DDD) est une méthode numérique mésoscopique bien établie pour simuler le mouvement des dislocations et déterminer le comportement plastique des métaux. Toutefois, elle repose généralement sur les expressions analytiques des champs de contraintes obtenues dans des milieux isotropes infinis, ce qui en limite l’application. Le modèle discret-continu (DCM), qui couple la DDD avec un solveur élastique par éléments finis (EF) grâce au formalisme des déformations libres, avait été proposé pour traiter des conditions aux limites plus complexes. Cependant, ce modèle utilise également des solutions analytiques pour les interactions à courte portée, ce qui le rend inadapté aux milieux anisotropes. Dans ce travail, nous présentons une version améliorée du DCM en remplaçant le solveur EF par un solveur utilisant les transformées de Fourier rapides (FFT), plus efficace et supprimant la nécessité des corrections analytiques à courte portée. Pour cela, ce solveur s’appuie sur trois ingrédients : (i) un champ de déformation propre abrupt (discontinu à l’échelle du maillage) pour décrire les dislocations ; (ii) un maillage CFC conforme à celui du code DDD sur lequel un “stencil” octaédrique est utilisé pour préserver les symétries des plans de glissement $\lbrace 111\rbrace $ ; (iii) enfin un opérateur de Green discret. Ce solveur parvient ainsi à gérer des dislocations décrites par des champs abrupts sans générer d’oscillations. Couplé à la DDD, il permet d’étudier la plasticité dans les matériaux anisotropes et les interactions entre dislocations et des inclusions diffuses, sans corriger les contraintes aux cœurs des dislocations comme ce qui est fait habituellement.
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Mots-clés : Dynamique des dislocations discrètes, transformée de Fourier rapide (FFT), déformation propre (eigenstrain), champ abrupt
Luis Eon 1; Benoît Appolaire 2; Riccardo Gatti 1
CC-BY 4.0
@article{CRMECA_2025__353_G1_1005_0,
author = {Luis Eon and Beno{\^\i}t Appolaire and Riccardo Gatti},
title = {Efficient {FFT} solver for discrete dislocation dynamics with sharp field description of plastic strain in {FCC} metals},
journal = {Comptes Rendus. M\'ecanique},
pages = {1005--1025},
year = {2025},
publisher = {Acad\'emie des sciences, Paris},
volume = {353},
doi = {10.5802/crmeca.306},
language = {en},
}
TY - JOUR AU - Luis Eon AU - Benoît Appolaire AU - Riccardo Gatti TI - Efficient FFT solver for discrete dislocation dynamics with sharp field description of plastic strain in FCC metals JO - Comptes Rendus. Mécanique PY - 2025 SP - 1005 EP - 1025 VL - 353 PB - Académie des sciences, Paris DO - 10.5802/crmeca.306 LA - en ID - CRMECA_2025__353_G1_1005_0 ER -
%0 Journal Article %A Luis Eon %A Benoît Appolaire %A Riccardo Gatti %T Efficient FFT solver for discrete dislocation dynamics with sharp field description of plastic strain in FCC metals %J Comptes Rendus. Mécanique %D 2025 %P 1005-1025 %V 353 %I Académie des sciences, Paris %R 10.5802/crmeca.306 %G en %F CRMECA_2025__353_G1_1005_0
Luis Eon; Benoît Appolaire; Riccardo Gatti. Efficient FFT solver for discrete dislocation dynamics with sharp field description of plastic strain in FCC metals. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 1005-1025. doi: 10.5802/crmeca.306
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