Neutral coated inclusions in conductivity and anti-plane elasticity

被引:80
作者
Milton, GW [1 ]
Serkov, SK [1 ]
机构
[1] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA
来源
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2001年 / 457卷 / 2012期
关键词
neutral inclusions; conformal mapping; inclusion assemblages;
D O I
10.1098/rspa.2001.0796
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
The problem of neutral inclusions for two-dimensional conductivity (or, equivalently, anti-plane elasticity) is considered. Such an inclusion when inserted in a matrix containing a uniform applied electric field does not disturb the field outside the inclusion. Consequently, assemblages of neutral inclusions have certain moduli of their effective conductivity tensor that can be determined exactly. The inclusion is assumed to have a hole (or perfect conductor) at its core surrounded by a thick coating of isotropic material. The whole construction is embedded in a possibly anisotropic matrix. Analytic formulae for the boundaries of the core and coating are found with the use of conformal mapping techniques. The admissible inclusion shapes depend on the applied electric field and on the conductivities of matrix and coating. It is shown that the inclusions can have a variety of shapes and are not just restricted to being coated confocal ellipses. However, coated confocal ellipses are the only inclusions which are neutral to multiple applied fields.
引用
收藏
页码:1973 / 1997
页数:25
相关论文
共 33 条
[1]  
Ahlfors L., 1979, Complex analysis: an introduction to the theory of analytic functions of one complex variable
[2]   Neutral inhomogeneities in conduction phenomena [J].
Benveniste, Y ;
Miloh, T .
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 1999, 47 (09) :1873-1892
[3]   On the Saint-Venant torsion of composite bars with imperfect interfaces [J].
Benveniste, Y ;
Chen, T .
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2001, 457 (2005) :231-255
[4]   Asymptotic models of dilute composites with imperfectly bonded inclusions [J].
Bigoni, D ;
Serkov, SK ;
Valentini, M ;
Movchan, AB .
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 1998, 35 (24) :3239-3258
[5]   HARMONIC HOLES - INVERSE PROBLEM IN ELASTICITY [J].
BJORKMAN, GS ;
RICHARDS, R .
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1976, 43 (03) :414-418
[6]   HARMONIC HOLES FOR NONCONSTANT FIELDS [J].
BJORKMAN, GS ;
RICHARDS, R .
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1979, 46 (03) :573-576
[7]   Morphologically representative pattern-based bounding in elasticity [J].
Bornert, M ;
Stolz, C ;
Zaoui, A .
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 1996, 44 (03) :307-331
[8]   ON NEUTRAL HOLES IN TAILORED, LAYERED SHEETS [J].
BUDIANSKY, B ;
HUTCHINSON, JW ;
EVANS, AG .
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1993, 60 (04) :1056-1058
[9]   MICROSTRUCTURES MINIMIZING THE ENERGY OF A 2-PHASE ELASTIC COMPOSITE IN 2 SPACE DIMENSIONS .1. THE CONFOCAL ELLIPSE CONSTRUCTION [J].
GRABOVSKY, Y ;
KOHN, RV .
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 1995, 43 (06) :933-947
[10]   A VARIATIONAL APPROACH TO THEORY OF EFFECTIVE MAGNETIC PERMEABILITY OF MULTIPHASE MATERIALS [J].
HASHIN, Z ;
SHTRIKMAN, S .
JOURNAL OF APPLIED PHYSICS, 1962, 33 (10) :3125-&