The central problem involved in the prediction of the behavior of heterogeneous materials is the specification of an internal stress (or strain) field consistent with the external field imposed on the macroscopic body. These internal fields are locally influenced by (I) the relative magnitudes of the properties of the components; (ii) the size, shape, and relative orientation of the distinct phase regions; and the packing geometry of the reinforcing agent. In principle, the average elastic properties can be obtained by specifying the details of the geometry; the distribution of loads on the surfaces of the macroscopic body; and the connectivity between the fiber and matrix phase. The average bulk response can be determined by taking appropriate volume averages, thereby relating the volume fraction of the components and their respective properties to the average properties of the composite. These averages involve vectorial and tensorial quantities.
In practice, either simplifying assumptions must be introduced to make an analysis tractable, or detailed numerical analyses must be performed for special cases. A wide range of relationships has evolved as the consequence of applying various levels of simplifying assumptions. The majority of the approaches share the following common assumptions:

- The phase surfaces are assumed to be in direct contact and bonded (either chemically or physically) so that slip does not occur at a phase interface.
- Attention is directed toward the overall average response of the material to loads or deformations.

These assumptions are appropriate for material properties associated with small deformations behavior and do not seriously limit the application of the relationships to the prediction of elastic properties.