Homogenization of Reticulated Structures

Cioranescu, Doina; Paulin, J. Saint Jean; Telega, JJ

doi:10.1115/1.1383678

Cited by 86 publications

(23 citation statements)

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“…To get the homogenized equation, we need the following classical extension result one can find for instance in [13].…”

Section: A Priori Estimatesmentioning

confidence: 99%

Diffusion through a composite structure with a high contrasting diffusivity

Sili

2014

Asymptotic Analysis

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We consider the stationary diffusion equation in a periodic composite medium made of two components Mε and Bε having very different diffusivity, the ratio between the coefficients of the diffusion in that structure being 1 α 2 ε , where ε is the size of the period and αε which represents the amplitude of the diffusion in the inclusions Bε is a decreasing sequence towards zero. We show that the inclusions Bε work on the macroscopic diffusion as holes. In particular for scalings 0 < αε ε corresponding to very weak diffusion in Bε, the volume fraction of the material at the limit is the well known one in the case of holes.

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“…To get the homogenized equation, we need the following classical extension result one can find for instance in [13].…”

Section: A Priori Estimatesmentioning

confidence: 99%

Diffusion through a composite structure with a high contrasting diffusivity

Sili

2014

Asymptotic Analysis

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“…Following [13], we assume that the fissures system Ω ε f , i.e. Following [13], we assume that the fissures system Ω ε f , i.e.…”

Section: Three-dimensional Periodic Examplementioning

confidence: 99%

Homogenization of a class of quasilinear elliptic equations in high-contrast fissured media

Amaziane¹,

Pankratov

Piatnitski³

2006

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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The aim of the paper is to study the asymptotic behaviour of the solution of a quasilinear elliptic equation of the formwith a high-contrast discontinuous coefficient a ε (x), where ε is the parameter characterizing the scale of the microstucture. The coefficient a ε (x) is assumed to degenerate everywhere in the domain Ω except in a thin connected microstructure of asymptotically small measure. It is shown that the asymptotical behaviour of the solution u ε as ε → 0 is described by a homogenized quasilinear equation with the coefficients calculated by local energetic characteristics of the domain Ω.

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“…See for the case of locally periodic thin domains. Also, see for general references in homogenization and for reticulated structures.…”

Section: Introductionmentioning

confidence: 99%

Thin domains with doubly oscillatory boundary

Arrieta

Villanueva-Pesqueira

2013

Math Methods in App Sciences

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Abstract. We consider a 2-dimensional thin domain with order of thickness which presents oscillations of amplitude also on both boundaries , top and bottom, but the period of the oscillations are of different order at the top and at the bottom. We study the behavior of the Laplace operator with Neumann boundary condition and obtain its asymptotic homogenized limit as → 0. We are interested in understanding how this different oscillatory behavior at the boundary, influences the limit problem.

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Homogenization of Reticulated Structures

Cited by 86 publications

References 0 publications

Diffusion through a composite structure with a high contrasting diffusivity

Diffusion through a composite structure with a high contrasting diffusivity

Homogenization of a class of quasilinear elliptic equations in high-contrast fissured media

Thin domains with doubly oscillatory boundary

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