Problem 2776. Rule of mixtures (composites) - lower and upper bounds
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 CommentsShow comments
Problem Recent Solvers53