Pp. Castaneda et Jr. Willis, THE EFFECT OF SPATIAL-DISTRIBUTION ON THE EFFECTIVE BEHAVIOR OF COMPOSITE-MATERIALS AND CRACKED MEDIA, Journal of the mechanics and physics of solids, 43(12), 1995, pp. 1919-1951
Estimates of the Hashin-Shtrikman type are developed for the overall m
oduli of composites consisting of a matrix containing one or more popu
lations of inclusions, when the spatial correlations of inclusion loca
tions take particular ''ellipsoidal'' forms. Inclusion shapes can be s
elected independently of the shapes adopted for the spatial correlatio
ns. The formulae that result are completely explicit and easy to use.
They are likely to be useful, in particular, for composites that have
undergone a prior macroscopically uniform large deformation. To the ex
tent that the statistics that are assumed may not be realized exactly,
the formulae provide approximations. Since, however, they are derived
as variational approximations for composites with some explicit stati
stics that are realizable, they are free from some of the drawbacks of
competitor approximations such as that of Mori and Tanaka (1973 Acta
Metall. 21, 571-574), which can generate tensors of effective moduli w
hich fail to satisfy a necessary symmetry requirement. The new formula
e are also the only ones known that take explicit account, at least ap
proximately, of inclusion shape and spatial distribution independently
.