An asymptotic expansion for perturbations in the displacement field due to the presence of thin interfaces

被引：1

作者：

Lagha, Jihene ^{[1
]}

Zribi, Habib ^{[1
]}

机构：

[1] Univ Tunis El Manar, Fac Sci Tunis, Optimisat Modelisat & Aide Decis UR11ES24, Tunis, Tunisia

来源：

APPLICABLE ANALYSIS | 2018年 / 97卷 / 06期

关键词：

Thin inhomogeneities; small perturbations; Lame system; asymptotic expansions; boundary integral method; ELASTIC MOMENT TENSORS; CONDUCTIVITY INCLUSION; RECONSTRUCTION; ELASTOSTATICS; SYSTEMS; SHAPE;

D O I：

10.1080/00036811.2017.1293816

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We rigorously derive an asymptotic expansion for two-dimensional displacement field associated with thin elastic inclusion having no uniform thickness. Our approach is based on layer potential techniques through integral representation formulas of the fields. We extend these techniques to determine a relationship between traction-displacement measurements and the shape of the thin inclusion.

引用

页码：865 / 887

页数：23

共 21 条

[1] Complete asymptotic expansions of solutions of the system of elastostatics in the presence of an inclusion of small diameter and detection of an inclusion [J].

Ammari, H ;

Kang, H ;

Nakamura, G ;

Tanuma, K .

JOURNAL OF ELASTICITY, 2002, 67 (02) :97-129

[2]

Ammari H., 2007, Applied Mathematical Sciences

[3]

Ammari H, 2015, Princeton series in applied mathematics

[4] Multistatic Imaging of Extended Targets [J].

Ammari, Habib ;

Garnier, Josselin ;

Kang, Hyeonbae ;

Lim, Mikyoung ;

Solna, Knut .

SIAM JOURNAL ON IMAGING SCIENCES, 2012, 5 (02) :564-600

[5] THE GENERALIZED POLARIZATION TENSORS FOR RESOLVED IMAGING. PART I: SHAPE RECONSTRUCTION OF A CONDUCTIVITY INCLUSION [J].

Ammari, Habib ;

Kang, Hyeonbae ;

Lim, Mikyoung ;

Zribi, Habib .

MATHEMATICS OF COMPUTATION, 2012, 81 (277) :367-386

[6] Reconstruction of small interface changes of an inclusion from modal measurements II: The elastic case [J].

Ammari, Habib ;

Beretta, Elena ;

Francini, Elisa ;

Kang, Hyeonbae ;

Lim, Mikyoung .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2010, 94 (03) :322-339

[7] CONDUCTIVITY INTERFACE PROBLEMS. PART I: SMALL PERTURBATIONS OF AN INTERFACE [J].

Ammari, Habib ;

Kang, Hyeonbae ;

Lim, Mikyoung ;

Zribi, Habib .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 362 (05) :2435-2449

[8]

[Anonymous], 2004, LECT NOTES MATH

[9] An asymptotic formula for the displacement field in the presence of thin elastic inhomogeneities [J].

Beretta, Elena ;

Francini, Elisa .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2006, 38 (04) :1249-1261

[10] SMALL VOLUME ASYMPTOTICS FOR ANISOTROPIC ELASTIC INCLUSIONS [J].

Beretta, Elena ;

Bonnetier, Eric ;

Francini, Elisa ;

Mazzucato, Anna L. .

INVERSE PROBLEMS AND IMAGING, 2012, 6 (01) :1-23

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