Problem 2776. Rule of mixtures (composites) - lower and upper bounds

Created by goc3 in Community

The rule of mixtures is used in the mechanical design of composite structures to estimate the elastic modulus (Ec) based on the following properties:

    Ef: elastic modulus of the fiber material
    Em: elastic modulus of the matrix material
    ff or fm: volume fraction of the fiber or matrix material (ff = 1 – fm)

Based on these values, the lower-bound estimate of elastic modulus is calculated by:

Ec = 1 / (ff / Ef + (1 – ff) / Em).

On the other hand, the upper-bound (linear) estimate of elastic modulus is calculated by:

Ec = ff * Ef + (1 – ff) * Em.

Write a function to calculate both bounds for various values. Also, return the difference between the modulus estimates and the ratios of this difference to both moduli estimates.

Solution Stats

68.0% Correct | 32.0% Incorrect
Last solution submitted on May 09, 2018