Composite materials are mixtures of two or more phases, where each phase has different material properties. In this sense, porous materials can also be thought of as composites, even if the solid framework is a uniform phase.
This chapter covers many of the main ideas used in the theory and modelling of linear composites with isotropic phases, including field averages, exact bounds, exact dilute limits and other cases where exact results can be obtained, and approximate effective medium theories. These exact ideas are used to test and validate the finite element and finite difference algorithms that were used to do the research described in this monograph. These algorithms are described, and instructions are given for their use on arbitrary digital images. FORTRAN 77 programs that carry out these algorithms are available to be downloaded, as described in this chapter. All of this material is contained in the following:
(1a) Finite element and finite difference programs for computing the linear electrical and elastic properties of digital images of random materials (210 pages of text)
(1b) User Manaual for Finite Element and Finite Difference Programs: A Parallel Version of NIST IR 6269 (275 pages of text, 118.3K of figures)
(1a) E.J. Garboczi, National Institute of Standards and Technology, Internal Report 6269, December, 1998.
(1b) R.B. Bohn, E.J. Garboczi, National Institute of Standards and Technology, Internal Report 6997, June 2003.