Abstract of the paper ``Microgeometry of random composites and porous media''
with G. W. Milton
For practical applications of variational bounds to the effective properties
of composite materials, the information available is often not that
required by the formulas for the optimal
bounds. It is therefore important to determine what can be said
rigorously about various unknown material properties when some other
properties are known. The key quantities to be analyzed are the parameters
``zeta'' and ``eta'' depending on the microgeometry through integrals of the
three-point correlation functions. The physical significance of these
parameters for two-phase composites and porous media is elucidated here by
examining the various relationships between them and material properties.
The bounds on conductivity due to Beran and the bounds on elastic constants
due to Beran and Molyneux and to McCoy, as well as
those of Milton and Phan-Thien, are considered. For the special case of porous
media, the formulas simplify greatly and the resulting analytical relationships
between transport properties and geometrical parameters are easily interpreted.
In particular, it is shown that the microgeometry parameter ``zeta'' places
limits on the pore space connectivity. Examples of bounds on one effective
material property from measurements of another are also derived. These
include bounds correlating the effective electrical or thermal conductivities
and the effective shear modulus with the effective bulk modulus. These bounds
are somewhat more restrictive than the well-known bounds of Hashin and
Shtrikman. For porous materials, measurements of bulk modulus provide bounds
on electrical formation factor and vice versa.
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