Multiphase composites with extremal bulk modulus
Multiphase composites with extremal bulk modulus
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DOI：
10.1016/s0022-5096(99)00043-5
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发表时间：
2000-03-01
影响因子：
5.3
通讯作者：
Sigmund, O
中科院分区：
文献类型：
--
作者：
Gibiansky, LV;Sigmund, O
本文致力于由三个或多个各向同性相组成的各向同性弹性复合材料的分析和数值研究。其有效体积模量和剪切模量的范围受到 Hashin-Shtrikman-Walpole (HSW) 界限的限制。对于两相复合材料，这些界限是可以达到的，也就是说，存在具有极端体积模量和剪切模量的复合材料。对于多相复合材料，它们可能会也可能不会实现，具体取决于相模量和体积分数。描述了边界可达到性的充分条件以及各种先前已知的和新型的最佳复合材料。我们的大部分新结果都与二维问题有关。采用解决逆均匀化问题的数值拓扑优化程序，并用于寻找具有最大有效体积模量的二维三相复合材料。对于已知可达到 HSW 界限的参数组合，在数值上发现了具有接近界限的体积模量的新微观结构。此外，在不满足上述可达到条件的情况下，在数值上发现了体积模量接近边界的新型微结构。根据数值结果，提出并分析了几种具有极值体积模量的新型结构。新结构的体积模量要么等于HSW束缚，要么高于具有相同相模量和体积分数的任何其他已知复合材料的体积模量。事实证明，HSW 界限可以在比之前认为的更宽的范围内实现。结果很容易应用于具有极值电导率的二维三相各向同性导电复合材料。它们还可用于研究具有任意横截面的圆柱形夹杂物（平面应变问题）或横向各向同性薄板（平面应力或板弯曲问题）的横向各向同性三维三相复合材料。 (C) 2000 Elsevier Science Ltd. 保留所有权利。
This paper is devoted to the analytical and numerical study of isotropic elastic composites made of three or more isotropic phases. The ranges of their effective bulk and shear moduli are restricted by the Hashin-Shtrikman-Walpole (HSW) bounds. For two-phase composites, these bounds are attainable, that is, there exist composites with extreme bulk and shear moduli. For multiphase composites, they may or may not be attainable depending on phase moduli and volume fractions. Sufficient conditions of attainability of the bounds and various previously known and new types of optimal composites are described. Most of our new results are related to the two-dimensional problem. A numerical topology optimization procedure that solves the inverse homogenization problem is adopted and used to look for two-dimensional three-phase composites with a maximal effective bulk modulus. For the combination of parameters where the HSW bound is known to be attainable, new microstructures are found numerically that possess bulk moduli close to the bound. Moreover, new types of microstructures with bulk moduli close to the bound are found numerically for the situations where the aforementioned attainability conditions are not met. Based on the numerical results, several new types of structures that possess extremal bulk modulus are suggested and studied analytically. The bulk moduli of the new structures are either equal to the HSW bound or higher than the bulk modulus of any other known composite with the same phase moduli and volume fractions. It is proved that the HSW bound is attainable in a much wider range than it was previously believed. Results are readily applied to two-dimensional three-phase isotropic conducting composites with extremal conductivity. They can also be used to study transversely isotropic three-dimensional three-phase composites with cylindrical inclusions of arbitrary cross-sections (plane strain problem) or transversely isotropic thin plates (plane stress or bending of plates problems). (C) 2000 Elsevier Science Ltd. All rights reserved.