Rule of Mixtures


In materials science, a general rule of mixtures is a weighted mean used to predict various properties of a composite material made up of continuous and unidirectional fibers. It provides a theoretical upper- and lower-bound on properties such as the elastic modulus, mass density, ultimate tensile strength, thermal conductivity, and electrical conductivity. In general there are two models, one for axial loading (Voigt model), and one for transverse loading (Reuss model).

In general, for some material property (often the elastic modulus), the rule of mixtures states that the overall property in the direction parallel to the fibers may be as high as shown here.

In the case of the elastic modulus, this is known as the upper-bound modulus, and corresponds to loading parallel to the fibers.

Related formulas


Ecgeneral rule of mixtures (dimensionless)
fvolume fraction of the fibers (dimensionless)
Efmaterial property of the fibers (dimensionless)
Emmaterial property of the matrix (dimensionless)