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Article Dans Une Revue European Journal of Mechanics - A/Solids Année : 2024

FFT-based simulations of heterogeneous conducting materials with combined non-uniform Neumann, Periodic and Dirichlet boundary conditions

Résumé

Because of their simplicity, efficiency and ability for parallelism, FFT-based methods are very attractive in the context of numerical periodic homogenization, especially when compared to standard FE codes used in the same context. The purpose of the paper is to go beyond the use of periodic Boundary Conditions (BC), but keeping the advantages of FFT-based implementations. The present paper focuses on conductivity problems, considered as a first step towards mechanical problems. The proposed implementation is highly flexible, allowing to apply non-uniform loadings, to choose between periodic, Neumann and Dirichlet BC for each face of the unit-cell (of couple of faces for periodic BC), and to choose between different types of Finite Differences schemes (two types are considered here). The implementation relies on the use of Discrete Trigonometric Transforms and their relation with the Discrete Fourier Transform on 4 times extended signals. The implementation has been precisely validated for various types of loading (uniform or non-uniform, full or combined, Dirichlet, Neumann and periodic BC) from a direct comparison with the same FE simulations.
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Dates et versions

cea-04475967 , version 1 (23-02-2024)

Identifiants

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Lionel Gelebart. FFT-based simulations of heterogeneous conducting materials with combined non-uniform Neumann, Periodic and Dirichlet boundary conditions. European Journal of Mechanics - A/Solids, 2024, 105, pp.105248. ⟨10.1016/j.euromechsol.2024.105248⟩. ⟨cea-04475967⟩
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