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.
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