THE THEORETICAL CONNECTION BETWEEN MORI-TANAKA'S THEORY AND THE HASHIN-SHTRIKMAN-WALPOLE BOUNDS
THE THEORETICAL CONNECTION BETWEEN MORI-TANAKA'S THEORY AND THE HASHIN-SHTRIKMAN-WALPOLE BOUNDS
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DOI：
10.1016/0020-7225(90)90111-u
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发表时间：
1990
影响因子：
6.6
通讯作者：
G. Weng
中科院分区：
文献类型：
--
作者：
G. Weng
Mori-Tanaka的具有一般各向异性成分的理论已被改写成一种新的形式，并表明这种形式与Walpole为界所发展的结构相同。前一种理论中的等效极化应力和应变正是Hashin-Shtrikman和Walpole选择的等效极化应力和应变，并且基体相的平均应力和应变等于Walpole在近似场上施加的图像应力和应变，以满足所需的边界条件。其结果是，含有排列或随机取向、形状相同的椭球内含物的复合材料的有效模量总是与H-S-W界的有效模量具有相同的表达式，只是后者的比较材料被确定为基体相，并根据适当的内含物形状解释Eshelby张量。这种联系使人们能够就M-T理论的预测画出一条重要的结论线，它也指出了这种理论总是可以安全地应用而不会违反边界的条件，以及这种应用可能不太可靠的条件。
Mori-Tanaka's theory with the general anisotropic constituents has been recast into a new form and it is shown that this form bears an identical structure to that developed by Walpole for the bounds. The equivalent polarization stress and strain in the former theory are exactly those chosen by Hashin-Shtrikman and Walpole and the average stress and strain of the matrix phase are equal to the image stress and strain imposed on the approximate fields by Walpole to meet the required boundary conditions. The consequence is that the effective moduli of the composite containing either aligned or randomly-oriented, identically shaped ellipsoidal inclusions always have the same expressions as those of the H-S-W bounds, only with the latter's comparison material identified as the matrix phase and Eshelby's tensor interpreted according to the appropriate inclusion shape. This connection allows one to draw a line of important conclusions regarding the predictions of the M-T theory, and it also points to the conditions where this theory can always be applied safely without ever violating the bounds and where such an application might be less reliable.