An identification method to calibrate higher-order parameters in local second-gradient models

Simon Raude; Richard Giot; Alexandre Foucault; Roméo Fernandes

doi:10.1016/j.crme.2015.06.002

An identification method to calibrate higher-order parameters in local second-gradient models

Simon Raude ¹; Richard Giot ¹ ; Alexandre Foucault ²; Roméo Fernandes ²

¹ GeoRessources, UMR 7359 ENSG–Université de Lorraine, 54518 Vandœuvre-lès-Nancy, France
² IMSIA, UMR EDF-CNRS-CEA-ENSTA 9219, Clamart, France

Comptes Rendus. Mécanique, Volume 343 (2015) no. 7-8, pp. 443-456.

Abstract
Résumé

A numerical method is presented for identifying the material parameters that appear in second-gradient models. For local second-gradient models, additional material parameters must be defined in numerical models. The objective of the present study is to develop a simple numerical identification procedure for these additional coefficients. The method combines modelling of laboratory tests with analytical implements. Numerical studies are then used to validate the method for a shale and to investigate the effects of both the internal length and the additional coefficients on the numerical responses. The procedure provides the first coherent results achieved at the laboratory scale.

Une méthode numérique permettant d'identifier les paramètres matériaux spécifiques aux modèles second gradient est présentée. Pour les modèles second gradient locaux, des paramètres matériaux supplémentaires sont définis dans les modèles numériques. L'objectif est de développer une procédure d'identification numérique simple pour ces coefficients supplémentaires. La méthode combine la modélisation d'essais de laboratoire et des développements analytiques. Des études numériques permettent de valider la méthode sur une argile et d'investiguer les effets de la longueur interne et des coefficients supplémentaires sur la réponse numérique. La procédure fournit les premiers résultats cohérents à l'échelle du laboratoire.

Received: 2014-10-31
Accepted: 2015-06-10
Published online: 2015-07-01

DOI: 10.1016/j.crme.2015.06.002

Keywords: Second-gradient dilation model, Localisation, Material property identification, Shear bands, 3-D modelling, Softening behaviour
Mots-clés : Modèles second gradient de dilatation, Localisation, Identification des propriétés des matériaux, Bandes de cisaillement, Modélisation 3D, Radoucissement

Author's affiliations:

Simon Raude ¹; Richard Giot ¹; Alexandre Foucault ²; Roméo Fernandes ²

¹ GeoRessources, UMR 7359 ENSG–Université de Lorraine, 54518 Vandœuvre-lès-Nancy, France
² IMSIA, UMR EDF-CNRS-CEA-ENSTA 9219, Clamart, France

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     author = {Simon Raude and Richard Giot and Alexandre Foucault and Rom\'eo Fernandes},
     title = {An identification method to calibrate higher-order parameters in local second-gradient models},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {443--456},
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     volume = {343},
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     year = {2015},
     doi = {10.1016/j.crme.2015.06.002},
     language = {en},
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Simon Raude; Richard Giot; Alexandre Foucault; Roméo Fernandes. An identification method to calibrate higher-order parameters in local second-gradient models. Comptes Rendus. Mécanique, Volume 343 (2015) no. 7-8, pp. 443-456. doi : 10.1016/j.crme.2015.06.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.06.002/

References
Cited by

[1] P. Bésuelle; J. Desrue; S. Raynaud Experimental characterisation of the localisation phenomenon inside a Vosges sandstone in a tri-axial cell, Int. J. Rock Mech. Min. Sci., Volume 37 (2000), pp. 1223-1237

[2] S.A. Hall; J. Desrues; G. Viggiani; P. Bésuelle; E. Andò Experimental characterisation of (localised) deformation phenomena in granular geomaterials from sample down to inter- and intra-grain scales, Proc. IUTAM, Volume 4 (2012), pp. 54-65

[3] Z.P. Bazant et al. Continuum theory for strain softening, J. Eng. Mech., Volume 110 (1984), pp. 1666-1692

[4] S. Forest; E. Lorrentz Localization and regularization (J. Besson, ed.), Local Approach to Fracture, Presses de l'École des mines de Paris, Paris, 2004

[5] G. Pijaudier-Cabot; Z.P. Bažant Nonlocal damage theory, J. Eng. Mech., Volume 113 (1987), pp. 1512-1533

[6] J.R. Rice The localization of plastic deformation (W.D. Koiter, ed.), International Congress of Theoretical and Applied Mechanics, North-Holland, Amsterdam, 1976

[7] J.W. Rudnicki; J.R. Rice Conditions for the localisation of the deformation in pressure sensitive dilatant materials, J. Mech. Phys. Solids, Volume 23 (1975), pp. 371-394

[8] I. Vardoulakis; J. Sulem Bifurcation Analysis in Geomechanics, Blackie Academic and Professional, Glasgow, 1995

[9] E. Aifantis On a microstructural origin of certain inelastic models, J. Eng. Mater. Technol., Volume 106 (1984), pp. 326-330

[10] H. Zbib; E. Aifantis On the localisation and post localisation of plastic deformation. Part I. On the initiation of shear bands, Res. Mech., Volume 23 (1988), pp. 261-277

[11] H. Zbib; E. Aifantis On the localisation and post localisation of plastic deformation. Part II. On the evolution and thickness of shear bands, Res. Mech., Volume 23 (1988), pp. 279-292

[12] R. de Borst; H. Muhlhaus Gradient dependant plasticity: formulation and algorithmic aspects, Int. J. Numer. Methods Eng., Volume 35 (1992), pp. 521-539

[13] I. Vardoulakis; E. Aifantis A gradient flow theory of plasticity for granular materials, Acta Mech., Volume 87 (1991), pp. 197-217

[14] P. Germain La méthode des puissances virtuelles en mécanique des milieux continus: première partie: théorie du second-gradient, J. Méc., Volume 12 (1973), pp. 235-274

[15] R.D. Mindlin Second gradient of strain and surface-tension in linear elasticity, Int. J. Solids Struct., Volume 1 (1965), pp. 417-738

[16] R.D. Mindlin Micro-structure in linear elasticity, Arch. Ration. Mech. Anal., Volume 16 (1964), pp. 51-78

[17] R. Chambon; D. Caillerie; N. Hassan One-dimensional localisation studied with a second grade model, Eur. J. Mech. A, Solids, Volume 17 (1998), pp. 637-656

[18] R. Chambon; S. Crochepeyre; R. Charlier An algorithm and a method to search bifurcation points in nonlinear problems, Int. J. Numer. Methods Eng., Volume 51 (2001), pp. 315-332

[19] F. Laigle Modèle conceptuel pour le développement de lois de comportement adaptées à la conception des ouvrages souterrains, Laboratoire de tribologie et dynamique des systèmes (LTDS) de l'École centrale de Lyon, Lyon, France, 2004 (PhD thesis 353 p)

[20] J. Desrues; R. Chambon; M. Mokni; F. Mazerolle Void ratio evolution inside shear bands in triaxial sand specimens studied by computed tomography, Gotechnique, Volume 46 (1996), pp. 529-546

[21] E.M. Charalampidou; S.A. Hall; S. Stanchits; H. Lewis; C. Viggiani Characterization of shear and compaction bands in a porous sandstone deformed under tri-axial compression, Tectonophysics, Volume 503 (2011), pp. 8-17

[22] S. Forest; R. Sievert Non linear microstrain theories, Int. J. Solids Struct., Volume 43 (2006), pp. 7224-7245

[23] R. Fernandes; C. Chavant; R. Chambon A simplified second gradient model for dilatant materials: theory and implementation, Int. J. Solids Struct., Volume 45 (2008), pp. 5289-5307

[24] R. Plassart; R. Fernandes; A. Giraud; H. Dashnor; F. Laigle Hydromechanical modelling of an excavation in an underground research laboratory with an elastoviscoplastic behaviour law and regularization by second-gradient of dilation, Int. J. Rock Mech. Min. Sci., Volume 58 (2013), pp. 23-33

[25] Y. Jia; H.B. Bian; K. Su; D. Kondo; J.F. Shao Elastoplastic damage modelling of desaturation and resaturation in argillites, Int. J. Numer. Anal. Methods Geomech., Volume 34 (2009) no. 2, pp. 187-220

[26] H. Zhou; Y. Jia; J.F. Shao A unified elastic-plastic and viscoplastic damage model for quasi-brittle rocks, Int. J. Rock Mech. Min. Sci., Volume 45 (2008) no. 8, pp. 1237-1251

[27] J. Desrues Experimental characterization of localized deformation in geomaterials, Lect. Notes Appl. Comput. Mech., Volume 13 (2003), pp. 77-106

[28] G. Viggiani Mechanisms of localized deformation in geomaterials: an experimental insight using full-field measurement techniques (D. Kolymbas; G. Viggiani, eds.), Mechanics of Natural Solids, Springer, Berlin, 2009, pp. 105-125

[29] T. Matsushima; R. Chambon; D. Caillerie Large strain finite element analysis of local second-gradient models, application to localization, Int. J. Numer. Methods Eng., Volume 54 (2002), pp. 499-521

[30] R. Chambon; D. Caillerie; R. Matsushima Plastic continuum with microstructure, local second-gradient theories for geomaterials: localization studies, Int. J. Solids Struct., Volume 38 (2001), pp. 8503-8527

[31] A. Foucault Modélisation du comportement cyclique des ouvrages en terre intégrant des techniques de régularisation, École centrale de Paris, Paris, 2010 (PhD thesis)

[32] http://www.code-aster.org (Code_Aster)

[33] G. Viggiani; N. Lenoir; P. Bsuelle; M. Di Michiel; S. Marello; J. Desrues; M. Kretzschmer X-ray microtomography for studying localized deformation in fine-grained geomaterials under triaxial compression, C. R. Mecanique, Volume 332 (2004), pp. 819-826

[34] D.C. Drucker; W. Prager Soil mechanics and plastic analysis design, Q. J. Mech. Appl. Math., Volume 10 (1952), pp. 157-165

[35] P. Vermeer A simple shear band analysis using compliances, Delft, The Netherlands (1982)

[36] J.-C. Hujeux Une loi de comportement pour le chargement cyclique des sols (V. Davidovici, ed.), Génie parasismique, Presses ENPC, Paris, France, 1985, pp. 278-302

[37] A.S. Gylland; H.P. Jostad; S. Nordal Experimental study of strain localization in sensitive clays, Acta Geotech., Volume 9 (2014), pp. 227-240

[38] A. Kleine Modélisation numérique du comportement des ouvrages souterrains par une approche viscoplastique, Institut national polytechnique de Lorraine, Nancy, France, 2007 (PhD thesis)

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