Comptes Rendus
A Mori–Tanaka homogenization scheme for non-linear elasto-viscoplastic heterogeneous materials based on translated fields: An affine extension
Comptes Rendus. Mécanique, Mechanics of granular and polycrystalline solids, Volume 343 (2015) no. 2, pp. 95-106.

A Mori–Tanaka homogenization scheme based on the “translated fields” approach is extended to elasto-viscoplastic composites with non-linear viscoplasticity described by a first-order “affine”-type linearization. This extension leads to a new theoretical interaction law between mechanical average phase fields and overall ones. This interaction law contains the coupling between elastic- and viscoplastic- mechanical interactions and phase stress histories. In order to study and discuss the validity of the present approach, the results are reported for two-phase composites and are compared to other approaches.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2014.12.003
Mots-clés : Homogenization, Translated fields, Non-linear composites, Elasto-viscoplastic materials, Mori–Tanaka, Affine formulation

Stéphane Berbenni 1 ; Laurent Capolungo 2

1 Laboratoire d'étude des microstructures et de mécanique des matériaux, UMR CNRS 7239, Université de Lorraine, île du Saulcy, 57045 Metz, France
2 George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, USA
@article{CRMECA_2015__343_2_95_0,
     author = {St\'ephane Berbenni and Laurent Capolungo},
     title = {A {Mori{\textendash}Tanaka} homogenization scheme for non-linear elasto-viscoplastic heterogeneous materials based on translated fields: {An} affine extension},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {95--106},
     publisher = {Elsevier},
     volume = {343},
     number = {2},
     year = {2015},
     doi = {10.1016/j.crme.2014.12.003},
     language = {en},
}
TY  - JOUR
AU  - Stéphane Berbenni
AU  - Laurent Capolungo
TI  - A Mori–Tanaka homogenization scheme for non-linear elasto-viscoplastic heterogeneous materials based on translated fields: An affine extension
JO  - Comptes Rendus. Mécanique
PY  - 2015
SP  - 95
EP  - 106
VL  - 343
IS  - 2
PB  - Elsevier
DO  - 10.1016/j.crme.2014.12.003
LA  - en
ID  - CRMECA_2015__343_2_95_0
ER  - 
%0 Journal Article
%A Stéphane Berbenni
%A Laurent Capolungo
%T A Mori–Tanaka homogenization scheme for non-linear elasto-viscoplastic heterogeneous materials based on translated fields: An affine extension
%J Comptes Rendus. Mécanique
%D 2015
%P 95-106
%V 343
%N 2
%I Elsevier
%R 10.1016/j.crme.2014.12.003
%G en
%F CRMECA_2015__343_2_95_0
Stéphane Berbenni; Laurent Capolungo. A Mori–Tanaka homogenization scheme for non-linear elasto-viscoplastic heterogeneous materials based on translated fields: An affine extension. Comptes Rendus. Mécanique, Mechanics of granular and polycrystalline solids, Volume 343 (2015) no. 2, pp. 95-106. doi : 10.1016/j.crme.2014.12.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.12.003/

[1] P. Suquet Elements of homogenization for inelastic solid mechanics (E. Sanchez-Palencia; A. Zaoui, eds.), Homogenization Techniques for Composite Media, Springer, Berlin, 1987, pp. 193-278

[2] Z. Hashin The inelastic inclusion problem, Int. J. Eng. Sci., Volume 7 (1969), pp. 11-36

[3] J. Li; G.J. Weng Strain-rate sensitivity, relaxation behavior and complex moduli of a class of isotropic viscoplastic composites, ASME J. Eng. Mater. Tech., Volume 116 (1994), pp. 495-504

[4] L.C. Brinson; W.S. Lin Comparison of micromechanics methods for effective properties of multiphase viscoelastic composites, Compos. Struct., Volume 41 (1998), pp. 353-367

[5] G. DeBotton; L. Tevet-Deree The response of a fiber-reinforced composite with a viscoelastic matrix phase, J. Compos. Mater., Volume 38 (2004), pp. 1255-1277

[6] N. Laws; R. McLaughlin Self-consistent estimates for the viscoelastic creep compliance of composite materials, Proc. R. Soc. Lond. Ser. A, Volume 359 (1978), pp. 251-273

[7] Y. Rougier; C. Stolz; A. Zaoui Self-consistent modelling of elastic–viscoplastic polycrystals, C. R. Acad. Sci. Paris Ser. IIb, Volume 318 (1994), pp. 145-151

[8] R. Masson; A. Zaoui Self-consistent estimates for the rate-dependent elastoplastic behaviour of polycrystalline materials, J. Mech. Phys. Solids, Volume 47 (1999), pp. 1543-1568

[9] O. Pierard; I. Doghri An enhanced affine formulation and the corresponding numerical algorithms for the mean-field homogenization of elasto-viscoplastic composites, Int. J. Plast., Volume 22 (2006), pp. 131-157

[10] A. Molinari; S. Ahzi; R. Kouddane On the self-consistent modelling of elastic–plastic behavior of polycrystals, Mech. Mater., Volume 26 (1997), pp. 43-62

[11] A. Paquin; H. Sabar; M. Berveiller Integral formulation and self-consistent modelling of elasto-viscoplastic behavior of heterogeneous materials, Arch. Appl. Mech., Volume 69 (1999), pp. 14-35

[12] A. Molinari Averaging models for heterogeneous viscoplastic and elastic–viscoplastic materials, ASME J. Eng. Mater. Tech., Volume 124 (2002), pp. 62-70

[13] H. Sabar; M. Berveiller; V. Favier; S. Berbenni A new class of micro–macro models for elastic–viscoplastic heterogeneous materials, Int. J. Solids Struct., Volume 39 (2002), pp. 3257-3276

[14] S. Berbenni; V. Favier; X. Lemoine; M. Berveiller Micromechanical modeling of the elastic–viscoplastic behavior of polycrystalline steels having different microstructures, Mater. Sci. Eng. A, Volume 372 (2004), pp. 128-136

[15] N. Lahellec; P. Suquet Effective behavior of linear viscoelastic composites: a time-integration approach, Int. J. Solids Struct., Volume 44 (2007), pp. 507-529

[16] N. Lahellec; P. Suquet On the effective behavior of non-linear inelastic composites: I. Incremental variational principles, J. Mech. Phys. Solids, Volume 55 (2007), pp. 1932-1963

[17] J.M. Ricaud; R. Masson Effective properties of linear viscoelastic heterogeneous media: internal variables formulation and extension to ageing behaviours, Int. J. Solids Struct., Volume 46 (2009), pp. 1599-1606

[18] R. Masson; R. Brenner; O. Castelnau Incremental homogenization approach for ageing viscoelastic polycrystals, C. R., Méc., Volume 340 (2012), pp. 378-386

[19] N. Lahellec; P. Suquet On the effective behavior of non-linear inelastic composites: II. A second-order procedure, J. Mech. Phys. Solids, Volume 55 (2007), pp. 1964-1992

[20] P. Ponte Castañeda Exact second-order estimates for the effective mechanical properties of nonlinear composite materials, J. Mech. Phys. Solids, Volume 44 (1996), pp. 827-862

[21] L. Brassard; L. Stainier; I. Doghri; L. Delannay Homogenization of elasto-(visco)plastic composites based on an incremental variational principle, Int. J. Plast., Volume 36 (2012), pp. 86-112

[22] M. Coulibaly; H. Sabar New integral formulation and self-consistent modeling of elastic–viscoplastic heterogeneous materials, Int. J. Solids Struct., Volume 48 (2011), pp. 753-763

[23] K. Kowalczyk-Gajewska; H. Petryk Sequential linearization method for viscous/elastic heterogeneous materials, Eur. J. Mech. A, Solids, Volume 30 (2011), pp. 650-664

[24] S. Mercier; N. Jacques; A. Molinari Validation of an interaction law for the Eshelby inclusion in elasto-viscoplasticity, Int. J. Solids Struct., Volume 42 (2005), pp. 1923-1941

[25] S. Mercier; A. Molinari; S. Berbenni; M. Berveiller Comparison of different homogenization approaches for elastic–viscoplastic materials, Model. Simul. Mater. Sci. Eng., Volume 20 (2012), p. 024004

[26] R. Masson; M. Bornert; P. Suquet; A. Zaoui An affine formulation for the prediction of the effective properties of non-linear composites and poly-crystals, J. Mech. Phys. Solids, Volume 48 (2000) no. 6–7, pp. 1203-1227

[27] A. Molinari; G.R. Canova; S. Ahzi A self-consistent approach of the large deformation polycrystal viscoplasticity, Acta Metall., Volume 35 (1987), pp. 2983-2994

[28] T. Mori; K. Tanaka Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metall., Volume 21 (1973), pp. 571-574

  • K. Kowalczyk-Gajewska; S. Berbenni; S. Mercier An additive Mori–Tanaka scheme for elastic–viscoplastic composites based on a modified tangent linearization, Mechanics of Materials, Volume 200 (2025), p. 105191 | DOI:10.1016/j.mechmat.2024.105191
  • Stéphane BERBENNI; Samuel FOREST Analytical Micromechanical Methods for Elasto‐Viscoplastic Composites and Polycrystals, Digital Materials (2024), p. 113 | DOI:10.1002/9781394332489.ch3
  • Bo Zhang; Nathan Deisman; Rick Chalaturnyk; Jeff Boisvert Numerical upscaling of anisotropic failure criteria in heterogeneous reservoirs, Engineering Geology, Volume 331 (2024), p. 107455 | DOI:10.1016/j.enggeo.2024.107455
  • Zhiwei Ma; Xiaoyan Ou; Bo Zhang Development of a convolutional neural network based geomechanical upscaling technique for heterogeneous geological reservoir, Journal of Rock Mechanics and Geotechnical Engineering, Volume 16 (2024) no. 6, p. 2111 | DOI:10.1016/j.jrmge.2024.02.009
  • Eyram Tsekpuia; Adrien Guery; Nathalie Gey; Stéphane Berbenni A microstructure-based three-scale homogenization model for predicting the elasto-viscoplastic behavior of duplex stainless steels, International Journal of Plasticity, Volume 164 (2023), p. 103575 | DOI:10.1016/j.ijplas.2023.103575
  • Pan Wang; Enlong Liu; Bin Zhi; Bingtang Song A rate-dependent constitutive model for saturated frozen soil considering local breakage mechanism, Journal of Rock Mechanics and Geotechnical Engineering, Volume 15 (2023) no. 9, p. 2458 | DOI:10.1016/j.jrmge.2022.11.017
  • Z. Ma; B. Zhang, SPE Annual Technical Conference and Exhibition (2023) | DOI:10.2118/214889-ms
  • S. Sharafi; M.H. Santare; J. Gerdes; S.G. Advani A multiscale modeling approach of the Fused Filament Fabrication process to predict the mechanical response of 3D printed parts, Additive Manufacturing, Volume 51 (2022), p. 102597 | DOI:10.1016/j.addma.2022.102597
  • Sudeep K. Sahoo; Laszlo S. Toth; Alain Molinari; Marat I. Latypov; Olivier Bouaziz Plastic energy-based analytical approach to predict the mechanical response of two-phase materials with application to dual-phase steels, European Journal of Mechanics - A/Solids, Volume 91 (2022), p. 104414 | DOI:10.1016/j.euromechsol.2021.104414
  • Bo Zhang; Zhiwei Ma; Dongming Zheng; Rick Chalaturnyk; Jeff Boisvert, SPE Canadian Energy Technology Conference (2022) | DOI:10.2118/208885-ms
  • Przemysław Sadowski; Katarzyna Kowalczyk-Gajewska; Stanisław Stupkiewicz Spurious softening in the macroscopic response predicted by the additive tangent Mori–Tanaka scheme for elastic–viscoplastic composites, European Journal of Mechanics - A/Solids, Volume 90 (2021), p. 104339 | DOI:10.1016/j.euromechsol.2021.104339
  • Stéphane Berbenni A time-incremental homogenization method for elasto-viscoplastic particulate composites based on a modified secant formulation, International Journal of Solids and Structures, Volume 229 (2021), p. 111136 | DOI:10.1016/j.ijsolstr.2021.111136
  • N. Q. Tran; A. B. Tran; D. C. Pham; N. Nguyen Polarization versus Mori-Tanaka approximations for elastic isotropic multicomponent materials, Journal of Mechanical Science and Technology, Volume 35 (2021) no. 7, p. 3033 | DOI:10.1007/s12206-021-0626-9
  • Miroslav Zecevic; Ricardo A. Lebensohn New robust self-consistent homogenization schemes of elasto-viscoplastic polycrystals, International Journal of Solids and Structures, Volume 202 (2020), p. 434 | DOI:10.1016/j.ijsolstr.2020.05.032
  • F. Coudon; G. Cailletaud; J. Cormier; L. Marcin A multiscale model for nickel-based directionally solidified materials, International Journal of Plasticity, Volume 115 (2019), p. 1 | DOI:10.1016/j.ijplas.2018.10.003
  • Dongqi Li; Zongli Li; Yueming Yin; Xiangqin Du; Guohui Zhang Prediction of cracking, yield and ultimate strengths based on the concrete three-phase micromechanics model, Construction and Building Materials, Volume 193 (2018), p. 416 | DOI:10.1016/j.conbuildmat.2018.10.164
  • Benjamin Tressou; Reza Vaziri; Carole Nadot-Martin Application of the incremental variational approach (EIV model) to the linear viscoelastic homogenization of different types of microstructures: long fiber-, particle-reinforced and strand-based composites, European Journal of Mechanics - A/Solids, Volume 68 (2018), p. 104 | DOI:10.1016/j.euromechsol.2017.10.006
  • Safaa Lhadi; Stéphane Berbenni; Nathalie Gey; Thiebaud Richeton; Lionel Germain Micromechanical modeling of the effect of elastic and plastic anisotropies on the mechanical behavior of β-Ti alloys, International Journal of Plasticity, Volume 109 (2018), p. 88 | DOI:10.1016/j.ijplas.2018.05.010
  • Stéphane Berbenni; Hafid Sabar A Time-Incremental Eshelby-Based Homogenization Scheme for Viscoelastic Heterogeneous Materials, Micromechanics and Nanomechanics of Composite Solids (2018), p. 347 | DOI:10.1007/978-3-319-52794-9_12
  • Charles Mareau; Stéphane Berbenni An affine formulation for the self-consistent modeling of elasto-viscoplastic heterogeneous materials based on the translated field method, International Journal of Plasticity, Volume 64 (2015), p. 134 | DOI:10.1016/j.ijplas.2014.08.011

Cité par 20 documents. Sources : Crossref

Commentaires - Politique