Multiscale Homogenization of Elastic Layered Composites with Unidirectionally Periodic Rough Interfaces

Quang, H. Le; He, Qi; Le, H.-T.

doi:10.1137/120888971

Cited by 7 publications

(7 citation statements)

References 45 publications

(87 reference statements)

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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%

“…At the same time, we define as follows two sub-domains, denoted by ω (1) and ω (2) , which are outside ω (c) but belong to Ω (1) and Ω (2) , respectively, ω (1) = Ω (1) \(Ω (1) ∩ ω (c) ), ω (2) = Ω (2) \(Ω (2) ∩ ω (c) ). (7) With respect to the curvilinear coordinate system {y 1 , y 2 , y 3 } associated to the orthonormal curvilinear basis {f 1 , f 2 , f 3 }, the local thermal behavior in Ω is described by the following Fourier's law…”

Section: Problem Settingmentioning

confidence: 99%

“…We can cite the studies [1][2][3][4][5][6] in which the interfacial zone is homogenized by applying asymptotic analysis. 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].…”

Section: Introductionmentioning

confidence: 99%

“…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%