The effective elastic moduli of columnar composites made of cylindrically anisotropic phases with rough interfaces

Le, H.-T.; Quang, H. Le; He, Qi‐Chang

doi:10.1016/j.ijsolstr.2014.03.036

Cited by 5 publications

(4 citation statements)

References 30 publications

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“…The present work aims to solve, in the situation of thermal conduction, the problem of determining the effective conductivity of composite materials in which the interface between any constituent phases oscillates quickly and periodically about an arbitrarily curved surface and along two directions. Thus, the present work can be considered as a continuation and an extension of our previous ones [7][8][9][10].…”

Section: Introductionmentioning

confidence: 63%

“…In the work of Le-Quang et al [7], it was shown that, when the rough interface oscillates quickly and periodically along only one direction, the effective properties of the equivalent interphase obtained by homogenizing an interface zone correspond exactly to the ones of a two-phase layered composite material. In addition, the determination of effective properties of composite materials while accounting for interfacial roughness has been carried out in the contexts of elasticity and thermal conduction [7][8][9][10]. the results obtained in these works are limited to the cases where rough interfaces oscillate either along one direction around a curved surface [7][8][9] or along two directions but around a plane surface [10].…”

Section: Introductionmentioning

confidence: 99%

“…In addition, the determination of effective properties of composite materials while accounting for interfacial roughness has been carried out in the contexts of elasticity and thermal conduction [7][8][9][10]. the results obtained in these works are limited to the cases where rough interfaces oscillate either along one direction around a curved surface [7][8][9] or along two directions but around a plane surface [10]. The present work aims to solve, in the situation of thermal conduction, the problem of determining the effective conductivity of composite materials in which the interface between any constituent phases oscillates quickly and periodically about an arbitrarily curved surface and along two directions.…”

Section: Introductionmentioning

confidence: 99%

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The effective thermal conductivity of composites with interfaces oscillating in two directions around a curved surface

Nguyen

Quang

et al. 2020

Acta Mech

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In many situations of practical or/and theoretical interest, the assumption that the interfaces between constituent phases of a composite are smooth is no longer appropriate, and the consideration of rough interfaces at microscopic scale is necessary. However, in micromechanics, when the interfaces between the constituent phases of composites become rough, all classical well-known micromechanical schemes resorting to Eshelby's formalism cannot be applicable and the problem of determining the effective properties of composites become largely open. The present work aims to determine the effective thermal conductivity of a composite in which the interfaces between its constituent phases are perfectly bonded but oscillate quickly around a curved surface and along two directions. To achieve this objective, a two-scale homogenization method is proposed. In the first-scale homogenization, or microscopic-to-mesoscopic upscaling, the interfacial zone in which the interface oscillates is homogenized as an equivalent interphase by applying an asymptotic analysis. The thermal properties of the equivalent interphase can generally be determined by using a numerical approach based on the fast Fourier transform (FFT) method. In particular case where the equivalent interphase is very thin, this interphase is then replaced with a general imperfect interface situated at its middle surface. By applying the equivalent inclusion method, every inclusion with imperfect interface is further substituted by an equivalent inclusion with perfect interface. In the second scale homogenization, or mesoscopic-to-macroscopic upscaling, due to the fact that the interfaces are perfect, the effective thermal conductivity can be analytically obtained by using some well-known classical micromechanical schemes. To illustrate the two-scale homogenization method proposed in this work, the case of a layered

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Section: Introductionmentioning

confidence: 63%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The effective thermal conductivity of composites with interfaces oscillating in two directions around a curved surface

Nguyen

Quang

et al. 2020

Acta Mech

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“…Following Bensoussan et al [14], Sanchez-Palencia [15], and Bakhvalov and Panasenko [16], we suppose that: boldv ( x 1 , x 3 , ϵ ) = boldU ( x 1 , y , x 3 , ϵ ) . Following Bakhvalov and Panasenko [16], we express boldU as follows (see also, Vinh and Tung [19–23], Le et al [28], Le Quang et al [29, 30], and Nguyen et al [31]):…”

Section: Explicit Homogenized Equation In Matrix Formmentioning

confidence: 99%

Homogenization of very rough two-dimensional interfaces separating two dissimilar poroelastic solids with time-harmonic motions

Vinh

Tung

Kieu

2018

Mathematics and Mechanics of Solids

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The homogenization of a very rough three-dimensional interface separating two dissimilar isotropic poroelastic solids with time-harmonic motions was considered by Gilbert and Ou (Acoustic wave propagation in a composite of two different poroelastic materials with a very rough periodic interface: A homogenization approach. Int J Multiscale Comput Eng 2003; 1(4): 431–440). The homogenized equations have been derived; however, they are still in implicit form. In this paper, the homogenization of a very rough two-dimensional interface separating two dissimilar generally anisotropic poroelastic solids with time-harmonic motions is investigated. The main aim of the investigation is to derive homogenized equations in explicit form. By employing the homogenization method, along with the matrix formulation of the poroelasticity theory, the explicit homogenized equations have been derived. Since these equations are totally explicit, they are very useful in solving practical problems. As an example proving this, the reflection and transmission of SH waves at a very rough interface of the tooth-comb type is considered. The closed-form analytical expressions of the reflection and transmission coefficients are obtained. Based on these expressions, the dependence of the reflection and transmission coefficients on some parameters is examined numerically.

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Probabilistic modeling of surface effects in nano-reinforced materials

2021

Computational Materials Science

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The effective elastic moduli of columnar composites made of cylindrically anisotropic phases with rough interfaces

Cited by 5 publications

References 30 publications

The effective thermal conductivity of composites with interfaces oscillating in two directions around a curved surface

The effective thermal conductivity of composites with interfaces oscillating in two directions around a curved surface

Homogenization of very rough two-dimensional interfaces separating two dissimilar poroelastic solids with time-harmonic motions

Probabilistic modeling of surface effects in nano-reinforced materials

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