Second-order homogenization estimates for nonlinear composites incorporating field fluctuations:: I -: theory
Second-order homogenization estimates for nonlinear composites incorporating field fluctuations:: I -: theory
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DOI：
10.1016/s0022-5096(01)00099-0
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发表时间：
2002-04-01
影响因子：
5.3
通讯作者：
Castañeda, PP
中科院分区：
文献类型：
--
作者：
Castañeda, PP
本文关注的是改进的二阶均匀化方法的发展，该方法结合了非线性复合材料的场波动。这个想法是结合使用“线性比较复合材料”的两种不同的早期方法的所需特征，其属性是从适当设计的变分原理中最佳选择的。第一种方法 (Ponte Castaneda, J. Mech. Phys. Solids 39 (1991) 45) 利用相的“割线”模量，在相上应变场的二阶矩处进行评估，并提供边界，但这些边界仅精确到异质性对比中的一阶。第二种方法（Ponte Castaneda，J. Mech. Phys. Solids 44 (1996) 827）利用“切线”模量，在应变场的相位平均值（或一阶矩）处进行评估，并产生精确到二阶的估计值，但在某些特殊情况下可能会违反界限。事实证明，这些特殊情况与渗透现象等情况相对应，在这种情况下，二阶方法捕获的场涨落变得很重要，而二阶方法捕获的场涨落的准确度不如边界捕获的准确度。相比之下，新方法利用结合一阶矩和二阶矩信息的广义割线模，提供了精确到二阶的估计，从而永远不会违反边界。这项工作的第二部分给出了新理论的一些简单应用。 (C) 2002 Elsevier Science Ltd. 保留所有权利。
This paper is concerned with the development of an improved second-order homogenization method incorporating field fluctuations for nonlinear composite materials. The idea is to combine the desirable features of two different, earlier methods making use of "linear comparison composites", the properties of which are chosen optimally from suitably designed variational principles. The first method (Ponte Castaneda, J. Mech. Phys. Solids 39 (1991) 45) makes use of the "secant" moduli of the phases, evaluated at the second moments of the strain field over the phases, and delivers bounds, but these bounds are only exact to first-order in the heterogeneity contrast. The second method (Ponte Castaneda, J. Mech. Phys. Solids 44 (1996) 827) makes use of the "tangent" moduli, evaluated at the phase averages (or first moments) of the strain field, and yields estimates that are exact to second-order in the contrast, but that can violate the bounds in some special cases. These special cases turn out to correspond to situations, such as percolation phenomena, where field fluctuations, which are captured less accurately by the second-order method than by the bounds, become important. The new method delivers estimates that are exact to second-order in the contrast, making use of generalized secant moduli incorporating both first- and second-moment information, in such a way that the bounds are never violated. Some simple applications of the new theory are given in Part II of this work. (C) 2002 Elsevier Science Ltd. All rights reserved.