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Title: Bounds and estimates on the effective properties for nonlinear composites (English)
Author: Wall, Peter
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 45
Issue: 6
Year: 2000
Pages: 419-437
Summary lang: English
Category: math
Summary: In this paper we derive lower bounds and upper bounds on the effective properties for nonlinear heterogeneous systems. The key result to obtain these bounds is to derive a variational principle, which generalizes the variational principle by P. Ponte Castaneda from 1992. In general, when the Ponte Castaneda variational principle is used one only gets either a lower or an upper bound depending on the growth conditions. In this paper we overcome this problem by using our new variational principle together with the bounds presented by Lukkassen, Persson and Wall in 1995. Moreover, we also present some examples where the bounds are so tight that they may be used as a good estimate of the effective behavior. (English)
Keyword: homogenization
Keyword: effective properties
Keyword: variational methods
Keyword: nonlinear composites
MSC: 35B27
MSC: 73B27
MSC: 74Q20
idZBL: Zbl 0996.74062
idMR: MR1800963
DOI: 10.1023/A:1022381416707
Date available: 2009-09-22T18:05:02Z
Last updated: 2020-07-02
Stable URL:
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