# Inverse Rule of Mixtures

## Description

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).

The inverse rule of mixtures states that in the direction perpendicular to the fibers, the elastic modulus of a composite can be as low as shown here.

If the property under study is the elastic modulus, this quantity is called the lower-bound modulus, and corresponds to a transverse loading.

Related formulas## Variables

E_{c} | inverse rule of mixtures (dimensionless) |

f | volume fraction of the fibers (dimensionless) |

E_{f} | material property of the fibers (dimensionless) |

E_{m} | material property of the matrix (dimensionless) |