1. Composite materials At least two different materials put together.
Mostly to obtain superior strength and stiffness.
Why not just use
the stronger material?

2. Fiber arrangement
Fiber arrangement is dictated by tradeoff of cost, flexibility, and performance.

3. Orthotropy
Anisotropic materials with two orthogonal planes of symmetry in properties.
Ply is transversely isotropic.
Large differences between E1 and E2

4. Rule of Mixture for E1 Based on volume fractions 𝑉 𝑓 and 𝑉 𝑚 =1- 𝑉 𝑓 .
Equivalent to two springs in parallel.

5. Example with uncertainty
For a graphite fiber and resin matrix we have from the manufacturer 222≤ 𝐸 𝑓 ≤238𝐺𝑃𝑎 ≤ 𝐸 𝑚 ≤3.55𝐺𝑃𝑎
Our uncertainty in volume fraction is 0.6≤ 𝑉 𝑓 ≤0.7
What is the uncertainty in 𝐸 1 ?

6. Transverse modulus
Two springs in series
Obtain
Other properties