EFFECTIVE PROPERTIES OF NONLINEAR INHOMOGENEOUS DIELECTRICS

被引:63
作者
CASTANEDA, PP
DEBOTTON, G
LI, G
机构
[1] Department of Mechanical Engineering and Applied Mechanics, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia
来源
PHYSICAL REVIEW B | 1992年 / 46卷 / 08期
关键词
D O I
10.1103/PhysRevB.46.4387
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
We develop a general procedure for estimating the effective constitutive behavior of nonlinear dielectrics. The procedure is based on a variational principle expressing the effective energy function of a given nonlinear composite in terms of the effective energy functions of the class of linear comparison composites. This provides an automatic procedure for converting well-known information for linear composites, in the form of estimates and bounds for their effective dielectric constants, into corresponding estimates and bounds for the effective behavior of nonlinear composites. Further, the procedure is easily implemented, and leads in some cases to exact results. Thus, exact estimates are given herein for isotropic weakly nonlinear composites with general nonlinearity, and bounds of the Hashin-Shtrikman type are given for the class of two-phase, isotropic dielectric composites with strongly and perfectly nonlinear constitutive behavior. The optimality of the bounds is addressed briefly.
引用
收藏
页码:4387 / 4394
页数:8
相关论文
共 17 条
[1]   USE OF VIBRATIONAL APPROACH TO DETERMINE BOUNDS FOR EFFECTIVE PERMITTIVITY IN RANDOM MEDIA [J].
BERAN, M .
NUOVO CIMENTO, 1965, 38 (02) :771-+
[2]   STRONGLY NONLINEAR COMPOSITE DIELECTRICS - A PERTURBATION METHOD FOR FINDING THE POTENTIAL-FIELD AND BULK EFFECTIVE PROPERTIES [J].
BLUMENFELD, R ;
BERGMAN, DJ .
PHYSICAL REVIEW B, 1991, 44 (14) :7378-7386
[3]   EXACT CALCULATION TO 2ND-ORDER OF THE EFFECTIVE DIELECTRIC-CONSTANT OF A STRONGLY NONLINEAR INHOMOGENEOUS COMPOSITE [J].
BLUMENFELD, R ;
BERGMAN, DJ .
PHYSICAL REVIEW B, 1989, 40 (03) :1987-1989
[5]   THE EFFECTIVE MECHANICAL-PROPERTIES OF NONLINEAR ISOTROPIC COMPOSITES [J].
CASTANEDA, PP .
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 1991, 39 (01) :45-71
[9]   A VARIATIONAL APPROACH TO THEORY OF EFFECTIVE MAGNETIC PERMEABILITY OF MULTIPHASE MATERIALS [J].
HASHIN, Z ;
SHTRIKMAN, S .
JOURNAL OF APPLIED PHYSICS, 1962, 33 (10) :3125-&
[10]  
Landauer R., 1978, AIP Conference Proceedings, P2, DOI 10.1063/1.31150