Comptes Rendus
Fourier-based schemes for computing the mechanical response of composites with accurate local fields
Comptes Rendus. Mécanique, Volume 343 (2015) no. 3, pp. 232-245.

We modify the Green operator involved in Fourier-based computational schemes in elasticity, in 2D and 3D. The new operator is derived by expressing continuum mechanics in terms of centered differences on a rotated grid. Using the modified Green operator leads, in all systems investigated, to more accurate strain and stress fields than using the discretizations proposed by Moulinec and Suquet (1994) [1] or Willot and Pellegrini (2008) [2]. Moreover, we compared the convergence rates of the “direct” and “accelerated” FFT schemes with the different discretizations. The discretization method proposed in this work allows for much faster FFT schemes with respect to two criteria: stress equilibrium and effective elastic moduli.

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Accepted:
Published online:
DOI: 10.1016/j.crme.2014.12.005
Keywords: FFT methods, Homogenization, Heterogeneous media, Linear elasticity, Computational mechanics, Spectral methods

François Willot 1

1 Mines ParisTech, PSL Research University, Centre for mathematical morphology, 35, rue Saint-Honoré, 77300 Fontainebleau, France
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François Willot. Fourier-based schemes for computing the mechanical response of composites with accurate local fields. Comptes Rendus. Mécanique, Volume 343 (2015) no. 3, pp. 232-245. doi : 10.1016/j.crme.2014.12.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.12.005/

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