Homogenization of Rough Two-Dimensional Interfaces Separating Two Anisotropic Solids

Vinh, Pham Chi; Tung, Do Xuan

doi:10.1115/1.4003722

Cited by 13 publications

(17 citation statements)

References 18 publications

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“…Most remarkably, the effective elastic stiffness tensorC(x 3 ) of the rough interface zone in such a general situation is provided by the very compact formula (3.1). Thus, the results derived in this section not only constitute an extension to three-dimensional anisotropic and heterogeneous phases of those presented in [49,51] but also reveals the important fact that the zone in which a rough interface oscillates fast and along a direction is equivalent to a layered zone.…”

Section: Asymptotic Analysis and Proof That The Conjecture Is Truementioning

confidence: 75%

Multiscale Homogenization of Elastic Layered Composites with Unidirectionally Periodic Rough Interfaces

Quang¹,

He²,

Le³

2013

Multiscale Model. Simul.

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Layered composites constitute a class of composites of both theoretical and practical interest. Remarkably, analytical and exact expressions are available for the effective elastic moduli of a layered composite when the interface between any two of its neighboring layers is perfect and corresponds to a smooth plane. The objective of this work is to determine the effective elastic moduli of a layered composite of which the interface between any two neighboring layers remains perfect but oscillates fast about a plane and along one direction. To achieve this objective, a multiscale homogenization approach is elaborated. First, by carrying out an asymptotic analysis, it is shown that the zone in which a periodic rough interface is situated can be homogenized as an equivalent layer whose elastic properties admit coordinate-free analytical exact expressions. Next, the resulting layered composite is further homogenized and its macroscopic elastic moduli are determined in an exact and compact way. Examples are finally provided to illustrate and confirm the analytical results by comparing them with the corresponding numerical results obtained by the finite element method.

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Section: Asymptotic Analysis and Proof That The Conjecture Is Truementioning

confidence: 75%

Multiscale Homogenization of Elastic Layered Composites with Unidirectionally Periodic Rough Interfaces

Quang¹,

He²,

Le³

2013

Multiscale Model. Simul.

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“…In this case, a two-dimensional and twophase laminate with perfect contact at the interface is studied, see , respectively. Now, I and II can be considered as two different materials with their corresponding elastic properties given by (22) and (23), respectively. A new heterogeneous composite is studied using I and II as elements.…”

Section: →∞ K Ijmentioning

confidence: 99%

“…Also, it have been considered different specific structures, as cylindrical [17,18], spherical [19,20] or truncated conical shell [21]. On the other hand, important studies have been developed in order to see the influence of the contact behavior in the interface of the components on the global properties of the composite [22][23][24]. The imperfect spring type contact is one of the most widely studied problems.…”

Section: Introductionmentioning

confidence: 99%

Analysis of effective elastic properties for shell with complex geometrical shapes

Guinovart-Sanjuán

Vajravelu

Rodrı́guez-Ramos

et al. 2018

Composite Structures

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The manuscript offers a methodology to solve the local problem derived from the homogenization technique, considering composite materials with generalized periodicity and imperfect spring contact at the interface. The general expressions of the local problem for an anisotropic composite with perfect and imperfect contact at the interface are derived. The analytical solutions of the local problems are obtained by solving a system of partial differential equations. In order to validate the model, the effective properties of the structure presented in the literature are obtained as particular cases. The solution of the local problem is used to extend the study to more complex structures, such as, wavy laminates shell composites with imperfect spring type contact at the interface. Also, the results are compared with the results for perfect and imperfect contact models available in the literature.

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“…Using the matrix formulation (not the component formulation) of theories, Vinh and his coworkers carried out the homogenization of two-dimensional very rough interfaces and the explicit homogenized equations have been obtained for the elasticity theory [4][5][6][7], for the piezoelectricity theory [8], for the micropolar elasticity [9] and for the poroelasticity with Auriault's model for time-harmonic motions [10].…”

Section: Introductionmentioning

confidence: 99%

Homogenization of very rough three-dimensional interfaces for the poroelasticity theory with Biot's model

Kieu¹,

Vinh²,

Tung³

2019

Vietnam J. Mech.

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In this paper, we carry out the homogenization of a very rough three-dimensional interface separating two dissimilar generally anisotropic poroelastic solids modeled by the Biot theory. The very rough interface is assumed to be a cylindrical surface that rapidly oscillates between two parallel planes, and the motion is time-harmonic. Using the homogenization method with the matrix formulation of the poroelasicity theory, the explicit homogenized equations have been derived. Since the obtained homogenized equations are totally explicit, they are very convenient for solving various practical problems. As an example proving this, the reflection and transmission of SH waves at a very rough interface of tooth-comb type is considered. The closed-form analytical expressions of the reflection and transmission coefficients have been derived. Based on them, the effect of the incident angle and some material parameters on the reflection and transmission coefficients are examined numerically.

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Homogenization of Rough Two-Dimensional Interfaces Separating Two Anisotropic Solids

Cited by 13 publications

References 18 publications

Multiscale Homogenization of Elastic Layered Composites with Unidirectionally Periodic Rough Interfaces

Multiscale Homogenization of Elastic Layered Composites with Unidirectionally Periodic Rough Interfaces

Analysis of effective elastic properties for shell with complex geometrical shapes

Homogenization of very rough three-dimensional interfaces for the poroelasticity theory with Biot's model

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