NOTICE: this is the author’s version of a work that was accepted for publication in <Journal title>. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in PUBLICATION, [VOL#, ISSUE#, (DATE)] DOI
NOTICE: this is the author’s version of a work that was accepted for publication in International Journal of Plasticity. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Plasticity, 51, 2013. DOI: 10.1016/j.ijplas.2013.06.006
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[en] This paper presents an incremental secant mean-fi eld homogenization (MFH) procedure for composites made of elasto-plastic constituents. In this formulation, the residual stress and strain states reached in the elasto-plastic phases upon a fi ctitious elastic unloading are considered as starting point to apply the secant method. The mean stress fields in the phases are then computed using secant tensors, which are naturally isotropic and enable to de fine the
Linear-Comparison-Composite. The method, which remains simple in its formulation, is valid for general non-monotonic and non-proportional loading. It is applied on various problems involving elastic, elasto-plastic and perfectly-plastic phases, to demonstrate its accuracy compared to other existing MFH methods.
Research Center/Unit :
Computational & Multiscale Mechanics of Materials
Disciplines :
Materials science & engineering
Author, co-author :
Wu, Ling ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Noels, Ludovic ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Adam, Laurent; e-Xstream SA
Doghri, Issam; Université Catholique de Louvain - UCL
Language :
English
Title :
A combined incremental-secant mean-field homogenization scheme with per-phase residual strains for elasto-plastic composites
Publication date :
December 2013
Journal title :
International Journal of Plasticity
ISSN :
0749-6419
Publisher :
Pergamon Press - An Imprint of Elsevier Science, Oxford, United Kingdom
FP7 - 235303 - MATERA+ - ERA-NET Plus on Materials Research
Name of the research project :
SIMUCOMP The research has been funded by the Walloon Region under the agreement no 1017232 (CT-EUC 2010-10-12) in the context of the ERA-NET +, Matera + framework.
Funders :
Service public de Wallonie : Direction générale opérationnelle de l'économie, de l'emploi et de la recherche - DG06 CE - Commission Européenne
J. Aboudi, M.J. Pindera, and S. Arnold Higher-order theory for periodic multiphase materials with inelastic phases International Journal of Plasticity 19 2003 805 847
Y. Benveniste A new approach to the application of Mori-Tanaka's theory in composite materials Mechanics of Materials 6 1987 147 157
M. Berveiller, and A. Zaoui An extension of the self-consistent scheme to plastically-flowing polycrystals Journal of the Mechanics and Physics of Solids 26 1978 325 344
L. Brassart, I. Doghri, and L. Delannay Homogenization of elasto-plastic composites coupled with a nonlinear finite element analysis of the equivalent inclusion problem International Journal of Solids and Structures 47 2010 716 729
L. Brassart, L. Stainier, I. Doghri, and L. Delannay A variational formulation for the incremental homogenization of elasto-plastic composites Journal of the Mechanics and Physics of Solids 59 2011 2455 2475
L. Brassart, L. Stainier, I. Doghri, and L. Delannay Homogenization of elasto-(visco) plastic composites based on an incremental variational principle International Journal of Plasticity 36 2012 86 112
N. Carrere, R. Valle, T. Bretheau, and J.L. Chaboche Multiscale analysis of the transverse properties of ti-based matrix composites reinforced by sic fibres: from the grain scale to the macroscopic scale International Journal of Plasticity 20 2004 783 810
J. Chaboche, P. Kanouté, and A. Roos On the capabilities of mean-field approaches for the description of plasticity in metal matrix composites International Journal of Plasticity 21 2005 1409 1434
T. Christman, A. Needleman, S. Nutt, and S. Suresh On microstructural evolution and micromechanical modelling of deformation of a whisker-reinforced metal-matrix composite Materials Science and Engineering: A 107 1989 49 61 (Proceedings of the Symposium on Interfacial Phenomena in Composites: Processing Characterization and Mechanical Properties)
T. Christman, A. Needleman, and S. Suresh An experimental and numerical study of deformation in metal-ceramic composites Acta Metallurgica 37 1989 3029 3050
I. Doghri, L. Adam, and N. Bilger Mean-field homogenization of elasto-viscoplastic composites based on a general incrementally affine linearization method International Journal of Plasticity 26 2010 219 238
I. Doghri, L. Brassart, L. Adam, and J.S. Gérard A second-moment incremental formulation for the mean-field homogenization of elasto-plastic composites International Journal of Plasticity 27 2011 352 371
I. Doghri, and C. Friebel Effective elasto-plastic properties of inclusion-reinforced composites. Study of shape, orientation and cyclic response Mechanics of Materials 37 2005 45 68
I. Doghri, and A. Ouaar Homogenization of two-phase elasto-plastic composite materials and structures: study of tangent operators, cyclic plasticity and numerical algorithms International Journal of Solids and Structures 40 2003 1681 1712
I. Doghri, and L. Tinel Micromechanical modeling and computation of elasto-plastic materials reinforced with distributed-orientation fibers International Journal of Plasticity 21 2005 1919 1940
G.J. Dvorak Transformation field analysis of inelastic composite materials Proceedings: Mathematical and Physical Sciences 437 1992 311 327
G.J. Dvorak, Y.A. Bahei-El-Din, and A.M. Wafa Implementation of the transformation field analysis for inelastic composite materials Computational Mechanics 14 1994 201 228
R.A.B. Engelen, M. Geers, and F. Baaijens Nonlocal implicit gradient-enhanced elasto-plasticity for the modelling of softening behaviour International Journal of Plasticity 19 2003 403 433
J.D. Eshelby The determination of the elastic field of an ellipsoidal inclusion, and related problems Proceedings of the Royal Society of London Series A, Mathematical and Physical Sciences 241 1957 376 396
Geers, M.; 1997. Experimental Analysis and Computational Modelling of Damage and Fracture. Ph.D. Thesis. University of Technology, Eindhoven (The Netherlands).
M. Geers, V. Kouznetsova, and A. Brekelmans Multi-scale computational homogenization: trends and challenges Journal of Computational and Applied Mathematics 234 2010 2175 2182
R. Hill Continuum micro-mechanics of elastoplastic polycrystals Journal of the Mechanics and Physics of Solids 13 1965 89 101
R. Hill A self-consistent mechanics of composite materials Journal of the Mechanics and Physics of Solids 13 1965 213 222
S. Jansson Homogenized nonlinear constitutive properties and local stress concentrations for composites with periodic internal structure International Journal of Solids and Structures 29 1992 2181 2200
B. Ji, and T. Wang Plastic constitutive behavior of short-fiber/particle reinforced composites International Journal of Plasticity 19 2003 565 581
P. Kanouté, D. Boso, J. Chaboche, and B. Schrefler Multiscale methods for composites: a review Archives of Computational Methods in Engineering 16 2009 31 75 10.1007/s11831-008-9028-8
V. Kouznetsova, M. Geers, and W. Brekelmans Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy Computer Methods in Applied Mechanics and Engineering 193 2004 5525 5550 (Advances in Computational Plasticity)
V. Kouznetsova, M.G.D. Geers, and W.A.M. Brekelmans Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme International Journal for Numerical Methods in Engineering 54 2002 1235 1260
E. Kröner Berechnung der elastischen konstanten des vielkristalls aus den konstanten des einkristalls Zeitschrift für Physik A Hadrons and Nuclei 151 1958 504 518 10.1007/BF01337948
N. Lahellec, P. Ponte Castañeda, and P. Suquet Variational estimates for the effective response and field statistics in thermoelastic composites with intra-phase property fluctuations Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 467 2011 2224 2246
N. Lahellec, and P. Suquet On the effective behavior of nonlinear inelastic composites: I. Incremental variational principles Journal of the Mechanics and Physics of Solids 55 2007 1932 1963
N. Lahellec, and P. Suquet On the effective behavior of nonlinear inelastic composites: II. A second-order procedure Journal of the Mechanics and Physics of Solids 55 2007 1964 1992
N. Lahellec, and P. Suquet Effective response and field statistics in elasto-plastic and elasto-viscoplastic composites under radial and non-radial loadings 2013 International Journal of Plasticity
G. Li, and P. Ponte Castañeda Variational estimates for the elastoplastic response of particle-reinforced metal-matrix composites Applied Mechanics Reviews 47 1994 77
C. Lissenden, and S. Arnold Theoretical and experimental considerations in representing macroscale flow/damage surfaces for metal matrix composites International Journal of Plasticity 13 1997 327 358
R. Masson, M. Bornert, P. Suquet, and A. Zaoui An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals Journal of the Mechanics and Physics of Solids 48 2000 1203 1227
S. Mercier, and A. Molinari Homogenization of elasticviscoplastic heterogeneous materials: self-consistent and Mori-Tanaka schemes International Journal of Plasticity 25 2009 1024 1048
A. Molinari, G. Canova, and S. Ahzi A self consistent approach of the large deformation polycrystal viscoplasticity Acta Metallurgica 35 1987 2983 2994
A. Molinari, F. El Houdaigui, and L. Tóth Validation of the tangent formulation for the solution of the non-linear Eshelby inclusion problem International Journal of Plasticity 20 2004 291 307
T. Mori, and K. Tanaka Average stress in matrix and average elastic energy of materials with misfitting inclusions Acta Metallurgica 21 1973 571 574 (Cited by (since 1996) 1814)
H. Moulinec, and P. Suquet Intraphase strain heterogeneity in nonlinear composites: a computational approach European Journal of Mechanics -A/Solids 22 2003 751 770
R. Peerlings, R. de Borst, W. Brekelmans, and S. Ayyapureddi Gradient-enhanced damage for quasi-brittle materials International Journal for Numerical Methods in Engineering 39 1996 3391 3403
R. Peerlings, R. de Borst, W. Brekelmans, and M. Geers Gradient-enhanced damage modelling of concrete fracture Mechanics of Cohesive-Frictional Materials 3 1998 323 342
R. Peerlings, M. Geers, R. de Borst, and W. Brekelmans A critical comparison of nonlocal and gradient-enhanced softening continua International Journal of Solids and Structures 38 2001 7723 7746
H.E. Pettermann, A.F. Plankensteiner, H.J. Böhm, and F.G. Rammerstorfer A thermo-elasto-plastic constitutive law for inhomogeneous materials based on an incremental Mori-anaka approach Computers & Structures 71 1999 197 214
O. Pierard, and I. Doghri An enhanced affine formulation and the corresponding numerical algorithms for the mean-field homogenization of elasto-viscoplastic composites International Journal of Plasticity 22 2006 131 157
O. Pierard, and I. Doghri Study of various estimates of the macroscopic tangent operator in the incremental homogenization of elastoplastic composites International Journal for Multiscale Computational Engineering 4 2006 521 543
O. Pierard, C. Gonzlez, J. Segurado, J. LLorca, and I. Doghri Micromechanics of elasto-plastic materials reinforced with ellipsoidal inclusions International Journal of Solids and Structures 44 2007 6945 6962
O. Pierard, J. LLorca, J. Segurado, and I. Doghri Micromechanics of particle-reinforced elasto-viscoplastic composites: finite element simulations versus affine homogenization International Journal of Plasticity 23 2007 1041 1060
P. Ponte Castañeda The effective mechanical properties of nonlinear isotropic composites Journal of the Mechanics and Physics of Solids 39 1991 45 71
P. Ponte Castañeda A new variational principle and its application to nonlinear heterogeneous systems SIAM Journal on Applied Mathematics 52 1992 1321 1341
P. Ponte Castañeda Exact second-order estimates for the effective mechanical properties of nonlinear composite materials Journal of the Mechanics and Physics of Solids 44 1996 827 862
P. Ponte Castañeda Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I - Theory Journal of the Mechanics and Physics of Solids 50 2002 737 757
P. Ponte Castañeda Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: II - Applications Journal of the Mechanics and Physics of Solids 50 2002 759 782
J. Segurado, and J. Llorca A numerical approximation to the elastic properties of sphere-reinforced composites Journal of the Mechanics and Physics of Solids 50 2002 2107 2121
J. Segurado, J. Llorca, and C. González On the accuracy of mean-field approaches to simulate the plastic deformation of composites Scripta Materialia 46 2002 525 529
P. Suquet Overall properties of nonlinear composites: a modified secant moduli theory and its link with Ponte Castañeda's nonlinear variational procedure Comptes Rendus de l Académie des Sciences 320 1995 563 571
D. Talbot, and J. Willis Some simple explicit bounds for the overall behaviour of nonlinear composites International Journal of Solids and Structures 29 1992 1981 1987
D.R.S. Talbot, and J.R. Willis Variational principles for inhomogeneous non-linear media IMA Journal of Applied Mathematics 35 1985 39 54
D.R.S. Talbot, and J.R. Willis Bounds and self-consistent estimates for the overall properties of nonlinear composites IMA Journal of Applied Mathematics 39 1987 215 240
Z. Wieckowski Dual finite element methods in homogenization for elasticplastic fibrous composite material International Journal of Plasticity 16 2000 199 221
L. Wu, L. Noels, L. Adam, and I. Doghri Multiscale mean-field homogenization method for fiber-reinforced composites with gradient-enhanced damage model Computer Methods in Applied Mechanics and Engineering 233-236 2012 164 179
A. Zaoui, and R. Masson Modelling stress-dependent transformation strains of heterogeneous materials Y.A. Bahei-El-Din, G.J. Dvorak, G.M.L. Gladwell, IUTAM Symposium on Transformation Problems in Composite and Active Materials Solid Mechanics and Its Applications vol. 60 2002 3 15
