Comptes Rendus
no. 3
Nonlocal modeling of a randomly distributed and aligned long-fiber composite material
Azdine Nait-ali1
1 ISAE-ENSMA, Institut Pprime, UPR CNRS 3346, Département “Physique et mécanique des matériaux”, ENSMA, Téléport 2, 1, avenue Clément-Ader, BP 40109, 86961 Futuroscope – Chasseneuil-du-Poitou cedex, France
Comptes Rendus. Mécanique, Volume 345 (2017) no. 3, pp. 192-207.

The work under study is about the variational and stochastic modeling of randomly distributed and aligned long-fiber composites. Its objective is to derive a homogenized behavior that exhibits the nonlocal phenomenon of this type of material at the macroscopic scale. Several methods of applied mathematics are used in order to keep the maximum information about the nonlocal behavior after homogenization.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2016.11.004
Mots-clés : Asymptotic analysis, Non-local energy, Deterministic model

Azdine Nait-ali 1

1 ISAE-ENSMA, Institut Pprime, UPR CNRS 3346, Département “Physique et mécanique des matériaux”, ENSMA, Téléport 2, 1, avenue Clément-Ader, BP 40109, 86961 Futuroscope – Chasseneuil-du-Poitou cedex, France 
@article{CRMECA_2017__345_3_192_0,
     author = {Azdine Nait-ali},
     title = {Nonlocal modeling of a randomly distributed and aligned long-fiber composite material},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {192--207},
     publisher = {Elsevier},
     volume = {345},
     number = {3},
     year = {2017},
     doi = {10.1016/j.crme.2016.11.004},
     language = {en},
}
TY  - JOUR
AU  - Azdine Nait-ali
TI  - Nonlocal modeling of a randomly distributed and aligned long-fiber composite material
JO  - Comptes Rendus. Mécanique
PY  - 2017
SP  - 192
EP  - 207
VL  - 345
IS  - 3
PB  - Elsevier
DO  - 10.1016/j.crme.2016.11.004
LA  - en
ID  - CRMECA_2017__345_3_192_0
ER  - 
%0 Journal Article
%A Azdine Nait-ali
%T Nonlocal modeling of a randomly distributed and aligned long-fiber composite material
%J Comptes Rendus. Mécanique
%D 2017
%P 192-207
%V 345
%N 3
%I Elsevier
%R 10.1016/j.crme.2016.11.004
%G en
%F CRMECA_2017__345_3_192_0
Azdine Nait-ali. Nonlocal modeling of a randomly distributed and aligned long-fiber composite material. Comptes Rendus. Mécanique, Volume 345 (2017) no. 3, pp. 192-207. doi : 10.1016/j.crme.2016.11.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.11.004/

[1] M. Frémond Non-Smooth Thermo-Mechanics, Springer-Verlag, Berlin, Heidelberg, New York, 2002

[2] R. Laniel; P. Alart; S. Pagano Consistent thermodynamic modelling of wire-reinforced geomaterials, Eur. J. Mech. A, Solids, Volume 26 (2007) no. 5, pp. 854-871

[3] R. Laniel; P. Alart; S. Pagano Discrete element investigations of wire-reinforced geomaterial in a three-dimensional modeling, Comput. Mech., Volume 42 (2008) no. 1, pp. 67-76

[4] G. Michaille; A. Nait Ali; S. Pagano Macroscopic behavior of a randomly fibered medium, J. Math. Pures Appl., Volume 42 (2011) no. 3, pp. 230-252

[5] C. Castaing; M. Valadier Convex Analysis and Measurable Multifunctions, Lect. Notes Math., vol. 590, Springer-Verlag, Berlin, 1977

[6] M.A. Ackoglu; U. Krengel Ergodic theorem for superadditive processes, J. Reine Angew. Math., Volume 323 (1981), pp. 53-67

[7] G. Michaille; A. Nait Ali; S. Pagano Two-dimensional deterministic model of a thin body with randomly distributed high-conductivity fibers, Appl. Math. Res. Express (2013) (abt007v1-35)

[8] C. Licht; G. Michaille Global-local subadditive ergodic theorems and application to homogenization in elasticity, Ann. Math. Blaise Pascal, Volume 9 (2002), pp. 21-62

[9] H. Attouch; G. Buttazzo; G. Michaille Variational Analysis in Sobolev and BV Space: Application to PDEs and Optimization, MPS-SIAM Book Series on Optimization, vol. 6, December 2005

[10] M. Valadier Intégration de convexes fermés notamment d'épigraphes inf-convolution continue, Volume 1 (1970), pp. 67-76 (28A99, Classical Measure Theory)

[11] A. Gloria; F. Otto An optimal variance estimate in stochastic homogenization of discrete elliptic equations, Ann. Probab., Volume 39 (2011), pp. 779-856

[12] A. Gloria; F. Otto An optimal error estimate in stochastic homogenization of discrete elliptic equations, Ann. Probab., Volume 22 (2012) no. 1, pp. 1-28

[13] G. Michaille; J. Michel; L. Piccinini Large Deviations Estimates for Epigraphical Superadditive Processes in Stochastic Homogenization, ENS, Lyon, 1998 (Préprint N. 220)

[14] E. Chabi; G. Michaille Ergodic theory and application to nonconvex homogenization, Set-Valued Anal., Volume 2 (1994), pp. 117-134

[15] A. Nait-Ali; O. Kane-diallo; S. Castagnet Catching the time evolution of microstructure morphology from dynamic covariograms, C. R. Mecanique, Volume 343 (2015) no. 4, pp. 301-306

Cited by Sources:

Comments - Policy