Pp. Castaneda et M. Kailasam, NONLINEAR ELECTRICAL-CONDUCTIVITY IN HETEROGENEOUS MEDIA, Proceedings - Royal Society. Mathematical, physical and engineering sciences, 453(1959), 1997, pp. 793-816
Citations number
35
Journal title
Proceedings - Royal Society. Mathematical, physical and engineering sciences
A new method is proposed for estimating the effective behaviour of str
ongly nonlinear composite materials. The central idea is to write down
second-order Taylor expansions for the constituent phase energy funct
ions, about appropriately chosen reference fields. This allows the res
tatement of the problem for the nonlinear composite in terms of a corr
esponding problem for a fictitious linear composite with anisotropic c
onstituents, subjected to a given distribution of polarization fields.
The procedure thus permits the straightforward conversion of well-kno
wn estimates for linear composites, such as the Maxwell-Garnett and ef
fective-medium approximations, into corresponding estimates for nonlin
ear composites. The resulting nonlinear Maxwell-Garnett and effective-
medium estimates are exact to second order in the contrast.