Fast Fourier transform based algorithms, relying on the initial idea proposed by Moulinec and Suquet in 1998, are very efficient in the context of periodic homogenization in solid mechanics. The purpose of this short note is to propose a simple modification of these algorithms to extend their application domain from periodic boundary conditions (BC) to Dirichlet BC. The method is validated by a direct comparison with standard finite element simulations with prescribed displacements at the boundary. The convergence properties of the iterative algorithm are then analyzed using a simple example (2D matrix–inclusion) as a function of various parameters (material and algorithm parameters).
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@article{CRMECA_2020__348_8-9_693_0,
author = {Lionel G\'el\'ebart},
title = {A modified {FFT-based} solver for the mechanical simulation of heterogeneous materials with {Dirichlet} boundary conditions},
journal = {Comptes Rendus. M\'ecanique},
pages = {693--704},
publisher = {Acad\'emie des sciences, Paris},
volume = {348},
number = {8-9},
year = {2020},
doi = {10.5802/crmeca.54},
language = {en},
}
TY - JOUR AU - Lionel Gélébart TI - A modified FFT-based solver for the mechanical simulation of heterogeneous materials with Dirichlet boundary conditions JO - Comptes Rendus. Mécanique PY - 2020 SP - 693 EP - 704 VL - 348 IS - 8-9 PB - Académie des sciences, Paris DO - 10.5802/crmeca.54 LA - en ID - CRMECA_2020__348_8-9_693_0 ER -
%0 Journal Article %A Lionel Gélébart %T A modified FFT-based solver for the mechanical simulation of heterogeneous materials with Dirichlet boundary conditions %J Comptes Rendus. Mécanique %D 2020 %P 693-704 %V 348 %N 8-9 %I Académie des sciences, Paris %R 10.5802/crmeca.54 %G en %F CRMECA_2020__348_8-9_693_0
Lionel Gélébart. A modified FFT-based solver for the mechanical simulation of heterogeneous materials with Dirichlet boundary conditions. Comptes Rendus. Mécanique, Volume 348 (2020) no. 8-9, pp. 693-704. doi : 10.5802/crmeca.54. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.54/
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