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Effective thermal conductivity of transversely isotropic media with arbitrary oriented ellipsoïdal inhomogeneities

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2007
auteur(s) Giraud Albert; Gruescu Ion-Cosmin; Do D.P.; Homand Françoise; Kondo Djimédo
journal (abréviation) International Journal of Solids and Structures (Int J Solid Struct)
volume (numéro) 44 (9)
pages 2627 – 2647
résumé The objective of this work is to investigate the thermal conduction phenomena in transversely isotropic geomaterials or rock-like composites with arbitrary oriented ellipsoidal inhomogeneities of low aspect ratio. Based on the evaluation of the Green function, we provide here new expressions for the interaction tensor whose knowledge permits to obtain the concentration tensor of the polarization field used itself to evaluate the effective thermal conductivity tensor by homogenization. Some particular cases of the obtained general solution are equally presented, in order to validate the developed formalism. The obtained results are next used to study the effect of matrix anisotropy, pores systems and microstructure-related parameters on the overall effective thermal conductivity in transversely isotropic rocks. A two step-homogenization scheme is developed for the prediction of the initial anisotropy effects and to test the ability of the proposed model in the evaluation of effective thermal conductivity. With the help of an Orientation Distribution Function (ODF) the anisotropy due to the pore systems is also accounted. Numerical applications and comparisons with available experimental data are finally carried out for a partially saturated Opalinus clay and an argillite which are both composed of an argillaceous matrix and multiple solid minerals constituents.
mots clés Green functions, interaction tensor, effective thermal conductivity,
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