A classification of the wide variety of solids according to physical, structural and chemical characteristics shows the category of heterophase solids to be the largest group of natural and artificial substances. Most manufacturing and manufactured materials fall in this category.
The structure of such materials can be described by the shape, size, concentration, orientation and topology of the constituent phases. Statistical methods in particular, geometric probability sometimes supplemented by certain physical ortopological restrictions, provide adequate tools for the description of naturally grown or artificially mixed systems.
Mechanical modulus properties as well as thermal and electrical properties can be treated in a fairly general manner,based either on field distortion of one phase by the presence of another phase or by means of phase models that give upper and lower limits for the property.
The problem of strength properties can be seen in terms of fracture mechanisms or as a statistical one, in which case extreme value theory provides a suitable method.