Comptes Rendus
Thermal conduction properties of microcracked media: Accounting for the unilateral effect
Comptes Rendus. Mécanique, Volume 347 (2019) no. 12, pp. 944-952.

Studies dedicated to the homogenization approach of microcracked media are largely focused on the determination of effective elastic properties. Some works investigate other properties, but most of them consider only open cracks. This paper intends to provide effective thermal properties related to the conduction problem taking into account the unilateral effect (opening/closure of cracks). Such analysis considers steady-state heat transfer within an initially isotropic media weakened by randomly oriented cracks. According to the boundary conditions, estimates and bounds based on Eshelby-like formalism are developed to derive closed-form expressions for effective thermal conductivity and resistivity in a fixed microcracking state.

Les techniques d'homogénéisation des milieux microfissurés sont principalement employées pour l'étude des comportements mécaniques élastiques. D'autres applications sont également possibles, mais elles demeurent le plus souvent limitées à la considération de défauts ouverts. Ce travail vise à déterminer les propriétés effectives thermiques de milieux microfissurés dans le cadre d'une conduction stationnaire. Les matériaux étudiés sont initialement isotropes et présentent des microfissures d'orientation arbitraire pouvant être ouvertes ou bien fermées (effet unilatéral). S'appuyant sur une démarche de type Eshelby, les expressions des conductivités et résistivités effectives issues de différents schémas d'homogénéisation et bornes d'encadrement sont ici présentées et discutées.

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DOI: 10.1016/j.crme.2019.10.004
Keywords: Microcracking, Heat conduction, Thermal properties, Homogenization, Unilateral effect
Mot clés : Microfissuration, Conduction thermique, Propriétés thermiques, Homogénéisation, Effet unilatéral

Sharan Raj Rangasamy Mahendren 1; Hélène Welemane 1; Olivier Dalverny 1; Amèvi Tongne 1

1 Université de Toulouse, INP/ENIT, LGP, 47, avenue d'Azereix, 65016 Tarbes, France
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Sharan Raj Rangasamy Mahendren; Hélène Welemane; Olivier Dalverny; Amèvi Tongne. Thermal conduction properties of microcracked media: Accounting for the unilateral effect. Comptes Rendus. Mécanique, Volume 347 (2019) no. 12, pp. 944-952. doi : 10.1016/j.crme.2019.10.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.10.004/

[1] M. Kachanov Elastic solids with many cracks and related problems, Adv. Appl. Mech., Volume 30 (1993), pp. 259-445

[2] S. Nemat-Nasser; M. Hori Micromechanics: Overall Properties of Heterogeneous Materials, North-Holland Series in Applied Mathematics and Mechanics, vol. 37, Elsevier Science, Amsterdam, 1993

[3] P. Ponte Castañeda; J. Willis The effect of spatial distribution on the effective behavior of composite materials and cracked media, J. Mech. Phys. Solids, Volume 43 (1995), pp. 1919-1951

[4] L. Dormieux; D. Kondo; F.-J. Ulm Microporomechanics, Wiley & Sons, Chichester, UK, 2006

[5] I. Sevostianov; M. Kachanov On the effective properties of polycrystals with intergranular cracks, Int. J. Solids Struct., Volume 156–157 (2019), pp. 243-250

[6] D. Su; M.H. Santare; G.A. Gazonas An effective medium model for elastic waves in microcrack damaged media, Eng. Fract. Mech., Volume 75 (2008), pp. 4104-4116

[7] X.D. Wang; L.Y. Jiang The effective electroelastic property of piezoelectric media with parallel dielectric cracks, Int. J. Solids Struct., Volume 40 (2003), pp. 5287-5303

[8] A. Giraud; C. Gruescu; D.P. Do; F. Homand; D. Kondo Effective thermal conductivity of transversely isotropic media with arbitrary oriented ellipsoidal inhomogeneities, Int. J. Solids Struct., Volume 44 (2007), pp. 2627-2647

[9] S. Andrieux; Y. Bamberger; J. Marigo Un modèle de matériau microfissuré pour les bétons et les roches, J. Méc. Théor. Appl., Volume 5 (1986), pp. 471-513

[10] V. Deudé; L. Dormieux; D. Kondo et al. Propriétés élastiques non linéaires d'un milieu mésofissuré, C. R. Mecanique, Volume 330 (2002), pp. 587-592

[11] L. Dormieux; D. Kondo Stress-based estimates and bounds of effective elastic properties: the case of cracked media with unilateral effects, Comput. Mater. Sci., Volume 46 (2009), pp. 173-179

[12] Z. Hashin Analysis of composite material – a survey, J. Appl. Mech., Volume 50 (1983), pp. 481-505

[13] S. Torquato Random Heterogeneous Materials. Microstructure and Macroscopic Properties, Springer Science+Business Media, New York, 2002

[14] B. Valès; V. Munoz; H. Welemane et al. Heat source estimation in anisotropic materials, Compos. Struct., Volume 136 (2016), pp. 287-296

[15] R. Hill Elastic properties of reinforced solids: some theoretical principles, Int. J. Mech. Phys. Solids, Volume 11 (1963), pp. 357-372

[16] J.D. Eshelby The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. A, Volume 421 (1957), pp. 379-396

[17] J.G. Berryman Generalization of Eshelby's formula for a single ellipsoidal elastic inclusion to poroelasticity and thermoelasticity, Phys. Rev. Lett., Volume 79 (1997), pp. 1142-1145

[18] B. Budiansky; R.J. O'Connell Elastic moduli of a cracked solid, Int. J. Solids Struct., Volume 12 (1976), pp. 81-97

[19] H. Hatta; M. Taya Equivalent inclusion method for steady state heat conduction in composites, Int. J. Eng. Sci., Volume 24 (1986), pp. 1159-1172

[20] 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

[21] Z. Hashin; S. Shtrikman A variational approach to the theory of elastic behavior of multiphase materials, J. Mech. Phys. Solids, Volume 11 (1963), pp. 127-140

[22] Q.Z. Zhu Applications des approches d'homogénéisation à la modélisation tridimensionnelle de l'endommagement des matériaux quasi fragiles : formulations, validations et implémentations numériques, 2006 (PhD thesis, Lille, France)

[23] H. Welemane; F. Cormery Some remarks on the damage unilateral effect modelling for microcracked materials, Int. J. Damage Mech., Volume 11 (2002), pp. 65-86

[24] C. Goidescu; H. Welemane; D. Kondo; C. Gruescu Microcracks closure effects in initially orthotropic materials, Eur. J. Mech. A, Solids, Volume 37 (2013), pp. 172-184

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