Problem 2780. Rule of mixtures (composites) - other 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)

You are provided with the estimated elastic modulus at one bound. Determine if it is the lower or upper bound, based on the provided material properties, and return which bound was provided (0 = lower, 1 = upper) and the value for the other bound.

The lower-bound estimate of elastic modulus is calculated by:

Ec = 1 / (ff / Ef + (1 – ff) / Em).

The upper-bound (linear) estimate of elastic modulus is calculated by:

Ec = ff * Ef + (1 – ff) * Em.