Problem 2778. Rule of mixtures (composites) - lower and upper bounds (volumes)

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)

Sometimes, the volume fraction is not known and must be calculated from known volumes (Vf and Vm). In this case, ff = Vf / (Vf + Vm).

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 either bound, depending on which bound is requested in the input string and using the known volumes.