Rule of Mixtures Modulus Calculator

How it is calculated

Two formulas are evaluated from the fibre volume fraction Vf (0 to 1, as a fraction), the fibre modulus Ef and the matrix modulus Em. The Voigt value is E = Vf × Ef + (1 − Vf) × Em, a volume-weighted average that applies when load is carried along the fibres. The Reuss value is E = 1 / (Vf / Ef + (1 − Vf) / Em), which applies when load crosses the fibres. The results are labelled GPa, so enter both moduli in GPa. Vf may be 0 or 1, but moduli must be above zero. The real composite lies between the two numbers, and the tool does not say where. It also echoes Vf as a percentage.

Common mistakes

• Typing the fibre fraction as 60 instead of 0.6. A value above 1 returns no result.
• Entering moduli in MPa or psi while the answer is labelled GPa. Convert to GPa first, for example 230 GPa and not 230000.
• Mixing up weight fraction and volume fraction. Vf is a volume fraction, so a composite that is 60% fibre by weight has a lower Vf because fibre is usually denser than resin.
• Using the Voigt number for a load applied across the fibres. That direction is closer to the Reuss value, which is far lower when the two moduli are very different.
• Reading either number as a measured stiffness. They are bounds, and voids, fibre misalignment and short fibres push the real modulus below the Voigt value.