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

Giraud, Albert; Gruescu, Cosmin; Do, Duc-Phi; Homand, Françoise; Kondo, Djimédo

doi:10.1016/j.ijsolstr.2006.08.011

Cited by 84 publications

(43 citation statements)

References 26 publications

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“…The solid phase being composed by several minerals with different thermal conductivities, the equivalent grain thermal conductivity is unknown. It can be computed from classical mixing law or homogenization (see Gruescu et al, 2007;Giraud et al, 2007). In the present work, we choose to optimize directly λ S to limit the uncertainties due to additional computations.…”

Section: Application To a Clay-rockmentioning

confidence: 99%

Thermal conductivity of unsaturated clay-rocks

Jougnot

Revil

2010

Hydrol. Earth Syst. Sci.

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Abstract. The parameters used to describe the electrical conductivity of a porous material can be used to describe also its thermal conductivity. A new relationship is developed to connect the thermal conductivity of an unsaturated porous material to the thermal conductivity of the different phases of the composite, and two electrical parameters called the first and second Archie's exponents. A good agreement is obtained between the new model and thermal conductivity measurements performed using packs of glass beads and core samples of the Callovo-Oxfordian clay-rocks at different saturations of the water phase. We showed that the three model parameters optimised to fit the new model against experimental data (namely the thermal conductivity of the solid phase and the two Archie's exponents) are consistent with independent estimates. We also observed that the anisotropy of the effective thermal conductivity of the Callovo-Oxfordian clay-rock was mainly due to the anisotropy of the thermal conductivity of the solid phase.

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Section: Application To a Clay-rockmentioning

confidence: 99%

Thermal conductivity of unsaturated clay-rocks

Jougnot

Revil

2010

Hydrol. Earth Syst. Sci.

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“…The pore space is assumed to be made of a set of pores that can be described as inclusions of similar ellipsoidal shape (see Sayers, 1994), so there is only one class of pores, approximated by randomly oriented flat oblate spheroidal inclusions with low aspect ratio e % 0.05. The analogous problem for effective thermal conductivity has been presented in Gruescu et al (2007) and Giraud et al (2007a). It may be noticed that, in most cases, sedimentary rocks such as shales and argillites are transversely isotropic (see Giraud et al, 2007b for corresponding estimates of poroelastic coefficients).…”

Section: Porous Rock-like Composites Such As Deep Argillites and Shalesmentioning

confidence: 91%

Effect of pore shape on effective porothermoelastic properties of isotropic rocks

Giraud

Hoxha²,

Do³

et al. 2008

International Journal of Solids and Structures

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The present work is devoted to the determination of the macroscopic poroelastic and porothermoelastic properties of geomaterials or rock-like composites constituted by an isotropic matrix with embedded ellipsoidal inhomogeneities and/or pores randomly oriented. By considering the solution of a single ellipsoidal inhomogeneity in the homogenization problem it is possible to observe the significant influence of the shape of inhomogeneities on the effective porothermoelastic properties. In the particular case of microscopic and macroscopic isotropic behaviors, a closed form solution based on analytical integrate of the Eshelby solution for the single ellipsoidal inhomogeneity can be obtained for the randomly oriented distribution. This result completes the well known solutions in the limiting cases of spherical and penny shape inhomogeneities. Based on recent works on porous rock-like composites such as shales or argillites, an application of the developed solution to a two-level microporomechanics model is presented. The microporosity in homogenized at the first level, and multiple solid mineral phase inclusions are added at the second level. The overall porothermoelastic coefficients are estimated in the particular context of heterogeneous solid matrix. Numerical results are presented for data representative of isotropic rock-like composites.

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“…The homogenization theory using RVE is usually carried out to numerically determine the effective properties of composites (Kanit et al 2003;Muliana 2009;Zohdi and Wriggers 2008). Based on the imposed boundary conditions, either the macroscopic flux or the macroscopic gradient field is calculated by averaging or homogenizing the microscopic counterparts, and then the effective property is calculated by using the macroscopic constitutive relationships (Kushch and Chernobai 2014;Giraud et al 2007;Lutz and Zimmerman 2005):q…”

Section: Governing Equations and Boundary Conditionsmentioning

confidence: 99%

Thermo-Electro-Mechanical Properties of Interpenetrating Phase Composites with Periodic Architectured Reinforcements

Al‐Rub

Abueidda

Dalaq

2015

Advanced Structured Materials

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In this study, the multifunctional properties (thermal, electric, and mechanical properties) of a new type of three-dimensional (3D) periodic architectured interpenetrating phase composites (IPCs) are investigated computationally. These new IPCs are created using two interconnected, bicontinuous, and intertwined material phases. The inner reinforcing phase takes the shape of the 3D morphology (architecture) of the mathematically-known triply periodic minimal surfaces (TPMS). The TPMS reinforcements are 3D solid sheet networks with a certain volume fraction and architecture. The interconnectivity of the proposed TPMS-based IPCs provide a novel way of creating multifunctional composites with superior properties. In this study, the effect of six well-known TPMS architectures of various volume fractions on the thermal/electrical conductivity and Young's modulus of the IPCs is investigated using the finite element analysis of a unit cell with periodic boundary conditions. The contrast effect (high and low) between the conductivities and Young's modulus of the two phases is also investigated. The calculated effective properties are compared with some analytical bounds. The proposed TPMS-IPCs possess effective properties close to the upper Hashin-Shtrikman bounds. It is also shown that the effect of TPMS architecture decreases as the contrast decreases. Finally, the manufacturability of these new TPMS-IPCs is demonstrated through using 3D printing technology.

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

Cited by 84 publications

References 26 publications

Thermal conductivity of unsaturated clay-rocks

Thermal conductivity of unsaturated clay-rocks

Effect of pore shape on effective porothermoelastic properties of isotropic rocks

Thermo-Electro-Mechanical Properties of Interpenetrating Phase Composites with Periodic Architectured Reinforcements

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