A consistent nonlocal scheme based on filters for the homogenization of heterogeneous linear materials with non-separated scales - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue International Journal of Solids and Structures Année : 2014

A consistent nonlocal scheme based on filters for the homogenization of heterogeneous linear materials with non-separated scales

Résumé

In this work, the question of homogenizing linear elastic, heterogeneous materials with periodic microstructures in the case of non-separated scales is addressed. A framework if proposed, where the notion of mesoscopic strain and stress fields are defined by appropriate integral operators which act as low-pass filters on the fine scale fluctuations. The present theory extends the classical linear homogenization by substituting averaging operators by integral operators, and localization tensors by nonlocal operators involving appropriate Green functions. As a result, the obtained constitutive relationship at the mesoscale appears to be nonlocal. Compared to nonlocal elastic models introduced from a phenomenological point of view, the nonlocal behavior has been fully derived from the study of the microstructure. A discrete version of the theory is presented, where the mesoscopic strain field is approximated as a linear combination of basis functions. It allows computing the esoscopic nonlocal operator by means of a finite number of transformation tensors, which can be computed numerically on the unit cell.
Fichier principal
Vignette du fichier
_48_PP.pdf (1.1 Mo) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-00880393 , version 1 (07-09-2014)

Identifiants

Citer

Julien Yvonnet, Guy Bonnet. A consistent nonlocal scheme based on filters for the homogenization of heterogeneous linear materials with non-separated scales. International Journal of Solids and Structures, 2014, 51 (1), pp.196-209. ⟨10.1016/j.ijsolstr.2013.09.023⟩. ⟨hal-00880393⟩
195 Consultations
246 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More