01.04 · Rule of mixtures · continuous fibers

The starting point for a laminate calculation is the behaviour of its individual plies. Here you will follow the connection from fibre and resin properties to the effective properties of a unidirectional ply, using controlled comparisons to see which predictions depend on composition and which depend on the micromechanics formulation.

Open this exercise in Workbench

Prepare the baseline

Establish the supplied case before changing anything. Keep a small comparison table with the constituent properties, fibre fraction, selected model and resulting moduli. When the task changes the model, leave the material data unchanged; when it changes the fraction, keep the model fixed. This makes it possible to explain the source of a difference instead of merely observing that two numbers disagree.

Worked procedure

1. Begin by opening the copied Micro record and following its links to the fibre and matrix materials. Note the constituent moduli and density, including their units, because these are the values that the mixture calculation will use. Keeping this input record beside your results will make the later hand calculation traceable.

2. Run three cases with fibre volume fractions of 0.3, 0.5 and 0.7, leaving the constituent data and other settings unchanged. After each change, use Run and record E1, E2 and density from the Micro outputs before moving to the next fraction. Arrange the three results in one table so that you can compare longitudinal and transverse response without relying on memory or mismatched screenshots.

3. Use the linked constituent moduli to calculate E1 = Vf Ef + (1 − Vf) Em for each of the three fibre fractions. Compare those hand calculations with the corresponding CDS values, first checking that both use the same units. Explain any discrepancy in terms of the selected inputs and model; this particular comparison concerns the longitudinal mixture relation, not every property in the output table.

Review checkpoints

At zero void fraction, constituent fractions sum to one.

Longitudinal modulus follows the linear mixture calculation; distinguish it from the transverse compliance estimate.

Model limits

Ideal continuous, aligned reinforcement with zero voids. This is a teaching comparison, not a measured material allowable.

Interpret the comparison

Read longitudinal, transverse and shear results as different responses, rather than expecting one mixture estimate to describe them all. Where the exercise provides published comparison values, calculate the discrepancy using those values and the specified units. Agreement in stiffness does not establish measured strength or validate properties that the chosen model does not predict.

How information passes between models

Materials → Micro: Constituent stiffness, strength, density and thermal / moisture properties.

Models → Micro: Applied model assignment: Rule of mixtures. Model parameters and formulation are used by Micro.

Further reading and evidence

• Create and connect a lamina
• Edit material properties and units
• Run and review a model
• Review effective properties
• Related case study: NASA lamina analysis

Review the recorded validation scope. Retain the original inputs and solver notices with the results. Representative teaching data are not design allowables.