MICROGEOMETRY OF RANDOM COMPOSITES AND POROUS-MEDIA
MICROGEOMETRY OF RANDOM COMPOSITES AND POROUS-MEDIA
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DOI：
10.1088/0022-3727/21/1/013
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发表时间：
1988-01-14
影响因子：
3.4
通讯作者：
MILTON, GW
中科院分区：
文献类型：
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作者：
BERRYMAN, JG;MILTON, GW
对于复合材料有效性能的变分界限的实际应用，可用的信息通常不是最佳界限公式所需的信息。因此，当一些其他特性已知时，确定可以严格描述各种未知材料特性的内容非常重要。要分析的关键量是参数 zeta 和 eta，这取决于通过三点相关函数积分得到的微观几何形状。通过检查这些参数与材料性能之间的各种关系，阐明了这些参数对于两相复合材料和多孔介质的物理意义。考虑了 Beran (1965) 提出的电导率界限以及 Beran 和 Molyneux (1966) 和 McCoy (1970) 以及 Milton 和 Phan-Thien (1982) 提出的弹性常数界限。对于多孔介质的特殊情况，公式大大简化，并且很容易解释输运特性和几何参数之间的分析关系。特别是，它表明微观几何参数 zeta 对孔隙空间连通性施加了限制。还得出了一种有效材料特性的界限示例，该限制来自另一种材料特性的测量。这些包括将有效电导率或热导率以及有效剪切模量与有效体积模量相关的界限。这些界限比众所周知的 Hashin 和 Shtrikman (1962) 的界限更具限制性。对于多孔材料，体积模量的测量提供了电形成因子的界限，反之亦然。
For practical applications of variational bounds to the effective properties of composite materials, the information available is often not that required by the formulae for the optimal bounds. It is therefore important to determine what can be said rigorously about various unknown material properties when some other properties are known. The key quantities to be analysed are the parameters zeta and eta, depending on the microgeometry through integrals of the three-point correlation functions. The physical significance of these parameters for two-phase composites and porous media is elucidated by examining the various relationships between them and material properties. The bounds on conductivity due to Beran (1965) and the bounds on elastic constants due to Beran and Molyneux (1966) and to McCoy (1970), as well as those of Milton and Phan-Thien (1982), are considered. For the special case of porous media, the formulae simplify greatly and the resulting analytical relationships between transport properties and geometrical parameters are easily interpreted. In particular, it is shown that the microgeometry parameter zeta places limits on the pore space connectivity. Examples of bounds on one effective material property from measurements of another are also derived. These include bounds correlating the effective electrical or thermal conductivities and the effective shear modulus with the effective bulk modulus. These bounds are somewhat more restrictive than the well known bounds of Hashin and Shtrikman (1962). For porous materials, measurements of bulk modulus provide bounds on electrical formation factor and vice versa.