Question

Rule of mixtures assumption justification

Answer 1

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.[1][2][3] 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.[3] In general there are two models, one for axial loading (Voigt model),[2][4] and one for transverse loading (Reuss model).[2][5]

In general, for some material property {\displaystyle E} (often the elastic modulus[1]), the rule of mixtures states that the overall property in the direction parallel to the fibers may be as high as

{\displaystyle E_{c}=fE_{f}+\left(1-f\right)E_{m}}

where

{\displaystyle f={\frac {V_{f}}{V_{f}+V_{m}}}} is the volume fraction of the fibers{\displaystyle E_{f}} is the material property of the fibers{\displaystyle E_{m}} is the material property of the matrix

In the case of the elastic modulus, this is known as the upper-bound modulus, and corresponds to loading parallel to the fibers. The inverse rule of mixtures states that in the direction perpendicular to the fibers, the elastic modulus of a composite can be as
If the property under study is the elastic modulus, this quantity is called the lower-bound modulus, and corresponds to a transverse loading......hope it may help you....#MB