Neutral coated inclusions in conductivity and anti–plane elasticity
Neutral coated inclusions in conductivity and anti–plane elasticity
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DOI：
10.1098/rspa.2001.0796
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发表时间：
2001-07
期刊：
影响因子：
--
通讯作者：
G. Milton;S. Serkov
中科院分区：
文献类型：
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作者：
G. Milton;S. Serkov
考虑二维导电性(或等效为反平面弹性)的中性夹杂问题。当将这种夹杂物插入到包含均匀外加电场的基质中时，不会干扰该夹杂物外部的电场。因此，中性包裹体的组合具有其有效电导张量的一定模数，可以准确地确定。假设夹杂物的核心有一个孔(或理想导体)，周围有一层厚厚的各向同性材料涂层。整个结构嵌入到一个可能的各向异性矩阵中。利用保角变换技术，得到了芯层和涂层边界的解析公式。允许的夹杂物形状取决于外加电场以及基体和涂层的电导率。结果表明，夹杂物可以有多种形状，并且不仅限于涂覆共焦椭圆形。然而，涂层共焦椭圆是唯一对多种场都是中性的夹杂物。
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.