Problem 2775. Rule of mixtures (composites) - lower bound

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).

Write a function to calculate this bound for various values.