Thermal conduction properties of microcracked media: Accounting for the unilateral effect

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

doi:10.1016/j.crme.2019.10.004

Thermal conduction properties of microcracked media: Accounting for the unilateral effect

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

Comptes Rendus. Mécanique, Volume 347 (2019) no. 12, pp. 944-952.

Abstract
Résumé

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.

Received: 2019-04-10
Accepted: 2019-10-07
Published online: 2019-10-22

DOI: 10.1016/j.crme.2019.10.004

Keywords: Microcracking, Heat conduction, Thermal properties, Homogenization, Unilateral effect
Mots-clés : Microfissuration, Conduction thermique, Propriétés thermiques, Homogénéisation, Effet unilatéral

Author's affiliations:

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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     author = {Sharan Raj Rangasamy Mahendren and H\'el\`ene Welemane and Olivier Dalverny and Am\`evi Tongne},
     title = {Thermal conduction properties of microcracked media: {Accounting} for the unilateral effect},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {944--952},
     publisher = {Elsevier},
     volume = {347},
     number = {12},
     year = {2019},
     doi = {10.1016/j.crme.2019.10.004},
     language = {en},
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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/

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