Cody

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

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)```

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.

### Solution Stats

53.13% Correct | 46.88% Incorrect
Last solution submitted on Apr 02, 2019