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Nonlocal/coarse graining homogenization of linear elastic media with non-separated scales using least-square polynomial filters

Abstract : In this paper, a nonlocal computational method is proposed to construct a mesoscopic (coars-grained) model of linear elastic heterogeneous materials in the case of nonseparated scales. The framework, introduced in our previous paper (Yvonnet and Bonnet, 2014) extends the classical homogenization framework by using low-pass filters operators instead of averaging operators, and Green's nonlocal functions instead of localization operators. In the present work, we introduce a filtering procedure based on least-square polynomial approximation to avoid the numerical drawbacks of Gaussian filters in finite domains. The complete associated homogenization scheme is described, as well aa a numerical procedure based on finite elements to compute the different homogenized operators from a unit cell. The methodology is validated by analyzing both local and mesoscopic mechanical fields in structures where heterogeneities are of comparable size with respect to the loading characteristic fluctuation wavelength.
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https://hal-upec-upem.archives-ouvertes.fr/hal-01056157
Contributor : J. Yvonnet <>
Submitted on : Thursday, June 11, 2020 - 10:55:42 AM
Last modification on : Tuesday, September 29, 2020 - 2:38:44 PM

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Julien Yvonnet, Guy Bonnet. Nonlocal/coarse graining homogenization of linear elastic media with non-separated scales using least-square polynomial filters. International Journal for Multiscale Computational Engineering, Begell House, 2014, 12 (5), pp.375-395. ⟨10.1615/IntJMultCompEng.2014010414⟩. ⟨hal-01056157⟩

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