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Effective Medium Theory for the Elastic Properties of Composite Materials with Various Percolation Thresholds

机译：具有不同渗透阈值的复合材料弹性特性的有效介质理论

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摘要

It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the elastic and electro-conductive properties of a strongly inhomogeneous two-phase composite material, the steep rise of effective parameters occurs at different concentrations. To achieve the logical concordance between the cross-property relations, a modification of the effective medium theory of the elastic properties is introduced. It is shown that the qualitative conclusions of the theory do not change, while a possibility of describing a broader class of composite materials with various percolation thresholds arises. It is determined under what conditions there is an elasticity theory analogue of the Dykhne formula for the effective conductivity. The theoretical results are supported by known experiments and show improvement over the existing approach. The introduction of the theory with the variable percolation threshold paves the way for describing the magnetorheological properties of magnetoactive elastomers. A similar approach has been recently used for the description of magneto-dielectric and magnetic properties.
机译：讨论了用于随机异质材料弹性特性的经典有效介质理论与用于电导率的有效介质理论不一致。特别地，当描述强烈不均匀的两相复合材料的弹性和导电特性时，有效参数的陡峭上升发生在不同的浓度下。为了实现跨属性关系之间的逻辑一致性，对弹性属性的有效介质理论进行了修改。结果表明，该理论的定性结论没有改变，同时出现了描述具有不同渗透阈值的更广泛种类的复合材料的可能性。确定在什么条件下对于有效电导率有Dykhne公式的弹性理论类似物。理论结果得到了已知实验的支持，显示出对现有方法的改进。具有可变渗透阈值的理论的引入为描述磁活性弹性体的磁流变性质铺平了道路。最近已经使用类似的方法来描述磁介电和磁性。

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