USE OF CLASSICAL VARIATIONAL PRINCIPLES TO DETERMINE BOUNDS FOR EFFECTIVE BULK MODULUS IN HETEROGENEOUS MEDIA
USE OF CLASSICAL VARIATIONAL PRINCIPLES TO DETERMINE BOUNDS FOR EFFECTIVE BULK MODULUS IN HETEROGENEOUS MEDIA
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DOI：
10.1090/qam/99925
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发表时间：
1966-01-01
影响因子：
0.8
通讯作者：
MOLYNEUX, J
中科院分区：
文献类型：
--
作者：
BERAN, M;MOLYNEUX, J
本文利用弹性力学的两个标准变分原理导出了非均匀介质中有效体积模量的界。作为应力场和应变场的试函数，我们使用微扰展开式，该微扰展开式通过包含一组乘法常数而被修改。一阶微扰效应被明确地计算出来，并根据相关函数导出了的界，其中和分别是剪切模量和体积模量的波动部分。对于两相介质，给出了两相对称时和两相对称时的显式计算。结果也包括介质由两个对称相组成时的介电问题。
Bounds are here derived for the effective bulk modulus in heterogeneous media, denoted by, using the two standard variational principles of elasticity. As trial functions for the stress and strain fields we use perturbation expansions that have been modified by the inclusion of a set of multiplicative constants. The first order perturbation effect is explicitly calculated and bounds forare derived in terms of the correlation functionsandwhereandare the fluctuating parts of the shear modulusand the bulk modulus,, respectively. Explicit calculations are given for two phase media whenand when the media are symmetric in the two phases. Results are also included for the dielectric problem when the media are composed of two symmetric phases.