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.

Accepted:

Published online:

François Willot ^{1}

@article{CRMECA_2015__343_3_232_0, author = {Fran\c{c}ois Willot}, title = {Fourier-based schemes for computing the mechanical response of composites with accurate local fields}, journal = {Comptes Rendus. M\'ecanique}, pages = {232--245}, publisher = {Elsevier}, volume = {343}, number = {3}, year = {2015}, doi = {10.1016/j.crme.2014.12.005}, language = {en}, }

TY - JOUR AU - François Willot TI - Fourier-based schemes for computing the mechanical response of composites with accurate local fields JO - Comptes Rendus. Mécanique PY - 2015 SP - 232 EP - 245 VL - 343 IS - 3 PB - Elsevier DO - 10.1016/j.crme.2014.12.005 LA - en ID - CRMECA_2015__343_3_232_0 ER -

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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