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Abstract : 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. Use of 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) or Willot and Pellegrini (2008). 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.
https://hal-mines-paristech.archives-ouvertes.fr/hal-01096757 Contributor : François WillotConnect in order to contact the contributor Submitted on : Friday, July 13, 2018 - 12:19:52 AM Last modification on : Friday, November 26, 2021 - 6:22:07 PM Long-term archiving on: : Monday, October 15, 2018 - 9:28:04 PM
François Willot. Fourier-based schemes for computing the mechanical response of composites with accurate local fields. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 2015, 343 (3), pp.232-245. ⟨10.1016/j.crme.2014.12.005⟩. ⟨hal-01096757v2⟩