Electric field concentration in the presence of an inclusion with eccentric core-shell geometry

Kim, Junbeom; Lim, Mikyoung

doi:10.1007/s00208-018-1688-6

Cited by 25 publications

(20 citation statements)

References 47 publications

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“…Ciraolo and Sciammetta [17,18] further extended the results in [22] to the Finsler p-Laplacian. For more related works, see [20,21,23,28,31,32] and the references therein.…”

Section: Introduction and Principal Resultsmentioning

confidence: 99%

Gradient asymptotics of solutions to the Lamé systems in the presence of two nearly touching $C^{1,γ}$-inclusions in all dimensions

Hao,

Zhao

2021

Preprint

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In this paper, we establish the asymptotic expressions for the gradient of a solution to the Lamé systems with partially infinity coefficients as two rigid C 1,γ -inclusions are very close but not touching. The novelty of these asymptotics, which improve and make complete the previous results of Chen-Li (JFA 2021), lies in that they show the optimality of the gradient blow-up rate in dimensions greater than two.

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“…Ciraolo and Sciammetta [17,18] further extended the results in [22] to the Finsler p-Laplacian. For more related works, see [20,21,23,28,31,32] and the references therein.…”

Section: Introduction and Principal Resultsmentioning

confidence: 99%

Gradient asymptotics of solutions to the Lamé systems in the presence of two nearly touching $C^{1,γ}$-inclusions in all dimensions

Hao,

Zhao

2021

Preprint

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“…We refer to page 894 of [37] for these open problems. In addition, Kim and Lim [27] made use of the single and double layer potentials with image line charges to establish an asymptotic expression for the solution to the conductivity problem in the presence of core-shell structure with circular boundaries. Calo, Efendiev and Galvis [15] obtained an asymptotic formula of a solution to the second-order elliptic equations of divergence form in the presence of high-conductivity inclusions or low-conductivity inclusions.…”

Section: Introductionmentioning

confidence: 99%

Singular analysis of the stress concentration in the narrow regions between the inclusions and the matrix boundary

Miao¹,

Zhao²

2021

Preprint

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We consider the Lamé system arising from high-contrast composite materials whose inclusions (fibers) are nearly touching the matrix boundary. The stress, which is the gradient of the solution, always concentrates highly in the narrow regions between the inclusions and the external boundary. This paper aims to provide a complete characterization in terms of the singularities of the stress concentration by accurately capturing all the blow-up factor matrices and making clear the dependence on the Lamé constants and the curvature parameters of geometry. Moreover, the precise asymptotic expansions of the stress concentration are also presented in the presence of a strictly convex inclusion close to touching the external boundary for the convenience of application.

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“…Kang and Yun [29] recently gave a quantitative characterization for the enhanced field due to presence of the bow-tie structure, which is a special Lipschitz domain. For more related issues and investigations, see [3,18,20,26,28,30] and the reference therein.…”

Section: Introductionmentioning

confidence: 99%

Singularities of the stress concentration in the presence of $C^{1,α}$-inclusions with core-shell geometry

Zhao,

Hao

2021

Preprint

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In high-contrast composites, if an inclusion is in close proximity to the matrix boundary, then the stress, which is represented by the gradient of a solution to the Lamé systems of linear elasticity, may exhibits the singularities with respect to the distance ε between them. In this paper, we establish the asymptotic formulas of the stress concentration for core-shell geometry with C 1,α boundaries in all dimensions by precisely capturing all the blow-up factor matrices, as the distance ε between interfacial boundaries of a core and a surrounding shell goes to zero. Further, a direct application of these blow-up factor matrices gives the optimal gradient estimates.

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Electric field concentration in the presence of an inclusion with eccentric core-shell geometry

Cited by 25 publications

References 47 publications

Gradient asymptotics of solutions to the Lamé systems in the presence of two nearly touching $C^{1,γ}$-inclusions in all dimensions

Gradient asymptotics of solutions to the Lamé systems in the presence of two nearly touching $C^{1,γ}$-inclusions in all dimensions

Singular analysis of the stress concentration in the narrow regions between the inclusions and the matrix boundary

Singularities of the stress concentration in the presence of $C^{1,α}$-inclusions with core-shell geometry

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