螺旋和其他径向对称集合体的有效电导率
Effective Conductivity of Spiral and other Radial Symmetric Assemblages
摘要：
研究了圆形夹杂物内部具有螺旋层合结构的集合体，如内部夹杂物的螺旋体、带壳的螺旋体、具有径向依赖体积分数的层合结构的“轮子”集合体、称为连接毂和尖刺球的复杂轴对称三维微观几何结构。所描述的集合体模型结构满足岩石力学，生物学等。经典的有效介质理论与分层均匀化。结果表明，螺旋形集合体中的场满足一个耦合的二阶微分方程组，而不是一个二阶微分方程组;均匀外场作用于螺旋形集合体上，可转化为旋转均匀场作用于螺旋形集合体内部。二维Star组装体的有效电导率与Hashin-Shtrikman涂层圆的有效电导率相等，但类似的三维Spiky Ball的电导率与涂层球几何形状的电导率不同。
英文摘要：
Assemblies of circular inclusions with spiraling laminate structure inside them are studied, such as spirals with inner inclusions, spirals with shells, assemblies of "wheels" - structures from laminates with radially dependent volume fractions, complex axisymmetric three-dimensional micro-geometries called Connected Hubs and Spiky Balls. The described assemblages model structures met in rock mechanics, biology, etc. The classical effective medium theory coupled with hierarchical homogenization is used. It is found that fields in spiral assemblages satisfy a coupled system of two second order differential equations, rather than a single differential equation; a homogeneous external field applied to the assembly is transformed into a rotated homogeneous field inside of the inclusions. The effective conductivity of the two-dimensional Star assembly is equivalent to that of Hashin-Shtrikman coated circles, but the conductivity of analogous three-dimensional Spiky Ball is different from the conductivity of coated sphere geometry.
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