DOUBLE-INCLUSION MODEL AND OVERALL MODULI OF MULTIPHASE COMPOSITES
DOUBLE-INCLUSION MODEL AND OVERALL MODULI OF MULTIPHASE COMPOSITES
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DOI：
10.1016/0167-6636(93)90066-z
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发表时间：
1993-01-01
影响因子：
3.9
通讯作者：
NEMATNASSER, S
中科院分区：
文献类型：
--
作者：
HORI, M;NEMATNASSER, S
双包体模型由椭球包体组成，椭球包体包含椭球非均质，嵌入在无限扩展的均质域中。包涵体的弹性，它的异质性和无限域的弹性可以是不同的和任意的。椭球体非均质性可能包含其他夹杂物，或者具有可变弹性。借助于推广Tanaka-Mori观测（1972；J. Elast. 2, 199-200）的定理，对双包含的平均场量进行了解析估计。结果表明，基于双包含模型的平均方案比自一致和Mori-Tanaka （1973; Acta metal . 21, 571-574）方法产生两相复合材料的总体模量具有更大的灵活性和有效性，并且确实包括作为特殊情况的这些方法，为它们提供了替代解释。然后将双包裹体模型推广到多包裹体模型，其中所有的平均场量都是解析估计的。作为多夹杂物模型的应用实例，考虑了含有夹杂物的多层涂层复合材料和由几种不同材料组成的复合材料，并对它们的总模量进行了分析估计。此外，对于嵌套在任意弹性的无限延伸均质弹性固体中的任意纵横比和相对位置的一组嵌套椭球体区域，这些区域在每个环内以均匀但不同的变换应变进行变换，结果表明，每个环上的平均应变场可以精确地以封闭形式计算；最内层区域的相变应变不必是均匀的。对于嵌入式双包含以及n个包含的嵌套集，给出了明确的结果。
The double-inclusion model consists of an ellipsoidal inclusion which contains an ellipsoidal heterogeneity and is embedded in an infinitely extended homogeneous domain. The elasticity of the inclusion, its heterogeneity, and that of the infinite domain may be distinct and arbitrary. The ellipsoidal heterogeneity may include other inclusions, or it may have variable elasticity. Average field quantities for the double inclusion are estimated analytically with the aid of a theorem which generalizes the Tanaka-Mori observation (1972; J. Elast. 2, 199-200). It is shown that the averaging scheme based on the double-inclusion model produces the overall moduli of two-phase composites with greater flexibility and hence effectiveness than the self-consistent and the Mori-Tanaka (1973; Acta Metall. 21, 571-574) methods, and, indeed, includes as special cases these methods, providing alternative interpretations for them. The double-inclusion model is then generalized to multi-inclusion models, where, again, all the average field quantities are estimated analytically. As examples of the application of the multi-inclusion model, a composite containing inclusions with multilayer coatings and a composite consisting of several distinct materials are considered, and their overall moduli are analytically estimated. In addition, for a set of nested ellipsoidal regions of arbitrary aspect ratios and relative locations, which is embedded in an infinitely extended homogeneous elastic solid of arbitrary elasticity, and which undergoes transformations with uniform but distinct transformation strains within each annulus, it is shown that the resulting strain field averaged over each annulus can be computed exactly and in closed form; the transformation strains in the innermost region need not be uniform. Explicit results are presented for an embedded double inclusion, as well as a nested set of n inclusions.