The effective properties of composites have been studied analytically for a long time, back to the days of Maxwell, who first solved for the effect that a single spherical inclusion, with a different conductivity from the matrix, has on the overall or effective conductivity. Random materials like concrete, powder compacts, etc. are also composites, random agglomerations of different property material at various length scales. Because of their randomness, their properties cannot be computed analytically, but instead require numerical computation. To compute the effective properties of such materials requires knowledge of the microstructure. The only practical way such information is obtained is either through microscopy, x-ray microtomography, or models. Whatever the method, the microstructural information is almost always in 2-D or 3-D digital image form, collections of discrete square or cubic pixels in which each pixel can, in principle, be a different phase of the material. Hence the need to have computer programs that are specialized to work on digital images.
There are 10 main programs described in this manual, and available for the user. They include D.C. finite element electrical programs in 2-D and 3-D (ELECFEM2D.F, ELECFEM3D.F), finite element elastic programs in 2-D and 3-D (ELAS2D.F, ELAS3D.F), finite element elastic programs that incorporate thermal strains (eigenstrains) in 2-D and 3-D (THERMAL2D.F, THERMAL3D.F), and nite dierence electrical programs for a.c. or d.c. problems in 2-D or 3-D (AC2D.F, AC3D.F, DC2D.F, DC3D.F).