IF:
1.016
5-Year IF:
1.194
SJR:
0.554
SNIP:
0.68
CiteScore™:
1.18
ISSN Print: 1543-1649
ISSN Online: 1940-4352
Volumes:
Volume 17, 2019
Volume 16, 2018
Volume 15, 2017
Volume 14, 2016
Volume 13, 2015
Volume 12, 2014
Volume 11, 2013
Volume 10, 2012
Volume 9, 2011
Volume 8, 2010
Volume 7, 2009
Volume 6, 2008
Volume 5, 2007
Volume 4, 2006
Volume 3, 2005
Volume 2, 2004
Volume 1, 2003
|
International Journal for Multiscale Computational Engineering
DOI: 10.1615/IntJMultCompEng.2012003105
pages 527-549
EVALUATION OF GENERALIZED CONTINUUM SUBSTITUTION MODELS FOR HETEROGENEOUS MATERIALS
Duy Khanh Trinh
MINES ParisTech, Centre des materiaux, CNRS UMR 7633, BP 87, F−91003 Evry Cedex, France
Ralf Janicke
Ruhr-Universitat Bochum, Institut fur Mechanik-Kontinuumsmechanik, IA 3/28, Universitatsstr. 150, D−44780 Bochum, Germany
Nicolas Auffray
Laboratoire Modelisation et Simulation Multi-echelles (MSME), UMR 8208 CNRS, Universite Paris-Est Marne-la-Vallee, 5 Bd Descartes, D−77454 Marne-la-Vallee, France
Stefan Diebels
Universitat des Saarlandes, Lehrstuhl fuer Technische Mechanik, Postfach 1511 50, D−66041 Saarbrucken, Germany
Samuel Forest
ABSTRACT
Several extensions of standard homogenization methods for composite materials have been proposed in the literature that rely on the use of polynomial boundary conditions enhancing the classical affine conditions on the unit cell. Depending on the choice of the polynomial, overall Cosserat, second gradient, or micromorphic homogeneous substitution media are obtained. They can be used to compute the response of the composite when the characteristic length associated with the variation of the applied loading conditions becomes of the order of the size of the material inhomogeneities. A significant difference between the available methods is the nature of the fluctuation field added to the polynomial expansion of the displacement field in the unit cell, which results in different definitions of the overall stress and strain measures and higher order elastic moduli. The overall higher order elastic moduli obtained from some of these methods are compared in the present contribution in the case of a specific periodic two-phase composite material. The performance of the obtained overall substitution media is evaluated for a chosen boundary value problem at the macroscopic scale for which a reference finite element solution is available. Several unsatisfactory features of the available theories are pointed out, even though some model predictions turn out to be highly relevant. Improvement of the prediction can be obtained by a precise estimation of the fluctuation at the boundary of the unit cell.
REFERENCES
-
Auffray, N., Bouchet, R., and Brechet, Y.,
Derivation of anisotropic matrix for bi-dimensional strain-gradient elasticity behavior.
DOI: 10.1016/j.ijsolstr.2008.09.009
-
Auffray, N., Bouchet, R., and Brechet, Y.,
Strain gradient elastic homogenization of bidimensional cellular media.
DOI: 10.1016/j.ijsolstr.2010.03.011
-
Bacigalupo, A. and Gambarotta, L.,
Second-order computational homogenization of heterogeneous materials with periodic microstructure.
DOI: 10.1002/zamm.201000031
-
Bigoni, D. and Drugan, W. J.,
Analytical derivation of Cosserat moduli via homogenization of heterogeneous elastic materials.
DOI: 10.1115/1.2711225
-
Boutin, C.,
Microstructural effects in elastic composites.
DOI: 10.1016/0020-7683(95)00089-5
-
Bouyge, F., Jasiuk, I., and Ostoja-Starzewski, M.,
A micromechanically based couple-stress model of an elastic two-phase composite.
DOI: 10.1016/S0020-7683(00)00132-3
-
De Bellis, M. L. and Addessi, D.,
A Cosserat based multi-scale model for masonry structures.
DOI: 10.1615/IntJMultCompEng.2011002758
-
Dell'Isola, F., Rosa, L., and Wozniak, C.,
A micro-structured continuum modelling compacting fluid-saturated grounds: The effects of pore-size scale parameter.
DOI: 10.1007/BF01170371
-
Dillard, T., Forest, S., and Ienny, P.,
Micromorphic continuum modelling of the deformation and fracture behaviour of nickel foams.
DOI: 10.1016/j.euromechsol.2005.11.006
-
Ebinger, T., Steeb, H., and Diebels, S.,
Modeling macroscopic extended continua with the aid of numerical homogenization schemes.
DOI: 10.1016/j.commatsci.2004.09.034
-
Eringen, A. C. and Suhubi, E. S.,
Nonlinear theory of simple microelastic solids.
DOI: 10.1016/0020-7225(64)90004-7
-
Feyel, F.,
A multilevel finite element method (FE2) to describe the response of highly non-linear structures using generalized continua.
DOI: 10.1016/S0045-7825(03)00348-7
-
Fish, J. and Kuznetsov, S.,
Computational continua.
DOI: 10.1002/nme.2918
-
Forest, S.,
Mechanics of generalized continua: Construction by homogenization.
DOI: 10.1051/jp4:1998405
-
Forest, S.,
Aufbau und identifikation von stoffgleichungen für höhere kontinua mittels homogenisierungsmethoden.
-
Forest, S.,
Homogenization methods and the mechanics of generalized continua—Part 2.
DOI: 10.2298/TAM0229113F
-
Forest, S.,
The micromorphic approach for gradient elasticity, viscoplasticity and damage.
DOI: 10.1061/(ASCE)0733-9399(2009)135:3(117)
-
Forest, S. and Sab, K.,
Cosserat overall modeling of heterogeneous materials.
DOI: 10.1016/S0093-6413(98)00059-7
-
Forest, S. and Trinh, D. K.,
Generalized continua and non-homogeneous boundary conditions in homogenization methods.
DOI: 10.1002/zamm.201000109
-
Geers, M. G. D., Kouznetsova, V. G., and Brekelmans, W. A. M.,
Gradient-enhanced computational homogenization for the micro-macro scale transition.
DOI: 10.1051/jp4:2001518
-
Gologanu, M., Leblond, J. B., and Devaux, J.,
Continuum micromechanics, Recent extensions of Gurson's model for porous ductile metals.
-
Janicke, R.,
Micromorphic media: Interpretation by homogenisation.
-
Janicke, R. and Diebels, S.,
A numerical homogenisation strategy for micromorphic continua.
DOI: 10.1393/ncc/i2009-10348-1
-
Janicke, R., Diebels, S., Sehlhorst, H.-G., and Duster, A.,
Two-scale modelling of micromorphic continua.
DOI: 10.1007/s00161-009-0114-4
-
Kaczmarczyk, L., Pearce, C. J., and Bicanic, N.,
Scale transition and enforcement of RVE boundary conditions in second-order computational homogenization.
DOI: 10.1002/nme.2188
-
Kanit, T., Forest, S., Galliet, I., Mounoury, V., and Jeulin, D.,
Determination of the size of the representative volume element for random composites: Statistical and numerical approach.
DOI: 10.1016/S0020-7683(03)00143-4
-
Kouznetsova, V., Geers, M. G. C., and Brekelmans, W. A. M.,
Size of a RVE in a second order computational homozenization framework.
-
Kouznetsova, V. G., Geers, M. G. D., and Brekelmans, W. A. M.,
Multi-scale second-order computational homogenization of multi-phase materials: A nested finite element solution strategy.
DOI: 10.1016/j.cma.2003.12.073
-
Larsson, R. and Diebels, S.,
A second-order homogenization procedure for multi-scale analysis based on micropolar kinematics.
DOI: 10.1002/nme.1854
-
Masiani, R. and Trovalusci, P.,
Cosserat and Cauchy materials as continuum models of brick masonry.
DOI: 10.1007/BF00429930
-
Mindlin, R. D.,
Micro-structure in linear elasticity.
DOI: 10.1007/BF00248490
-
Mindlin, R. D. and Eshel, N. N.,
On first strain gradient theories in linear elasticity.
DOI: 10.1016/0020-7683(68)90036-X
-
Muhlich, U., Zybell, L., and Kuna, M.,
Micromechanical modelling of size effects in failure of porous elastic solids using first oder plane strain gradient eslaticity.
-
Ostoja-Starzewski, M., Boccara, S. D., and Jasiuk, I.,
Couple-stress moduli and characteristic length of two-phase composite.
DOI: 10.1016/S0093-6413(99)00039-7
-
Pham, T. T. T.,
Un modèle d'endommagement à gradient de déformation à partir de la méthode d'homogénéisation pour les matériaux fragiles.
-
Sansalone, V., Trovalusci, P., and Cleri, F.,
Multiscale modeling of composite materials by a multifield finite element approach.
DOI: 10.1615/IntJMultCompEng.v3.i4.50
-
Tekoglu, C. and Onck, P. R.,
Size effects in two-dimensional Voronoi foams: A comparison between generalized continua and discrete models.
DOI: 10.1016/j.jmps.2008.06.007
-
Triantafyllidis, N. and Bardenhagen, S.,
The influence of scale size on the stability of periodic solids and the role of associated higher order gradient continuum models.
DOI: 10.1016/0022-5096(96)00047-6
-
Trovalusci, P. and Masiani, R.,
Non-linear micropolar and classical continua for anisotropic discontinuous materials.
DOI: 10.1016/S0020-7683(02)00584-X
-
Yuan, X., Tomita, Y., and Andou, T.,
A micromechanical approach of nonlocal modeling for media with periodic microstructures.
DOI: 10.1016/j.mechrescom.2007.07.004
Articles with similar content:
NON-LOCAL COMPUTATIONAL HOMOGENIZATION OF PERIODIC MASONRY
International Journal for Multiscale Computational Engineering, Vol.9, 2011, issue 5
Andrea Bacigalupo , Luigi Gambarotta
Homogenization Method Based on Eigenvector Expansions
International Journal for Multiscale Computational Engineering, Vol.4, 2006, issue 1
Dechao Zhu, Wenjian Xie, Jinmei Tian
A Stochastic Nonlocal Model for Materials with Multiscale Behavior
International Journal for Multiscale Computational Engineering, Vol.4, 2006, issue 4
Jianxu Shi, Roger Ghanem
KNUDSEN'S PERMEABILITY CORRECTION FOR GAS FLOW IN TIGHT POROUS MEDIA USING THE R26 MOMENT METHOD
Journal of Porous Media, Vol.20, 2017, issue 9
Q. Sheng, Gui-Hua Tang, Y. H. Zhang, David R. Emerson, Yin-Bin Lu , Xiao-Jun Gu
|