A ply and a laminate

Turn the fibre angle of a unidirectional ply. Stiffness along the plate axis x is E₁ at 0°, near E₂ at 90°, and strongly coupled to shear near 45°. The stack on the right is a laminate: classical lamination theory integrates those rotated plies through the thickness. Discrete, high-aspect-ratio fibres in a matrix are a different problem — they need an embedded fibre model, not an ABD matrix.

Ē_x(θ) from Q̄(θ)

fibre angle θ