Composite Weight-Optimization Lab

Composite Make-Up

Fiber

Matrix resin

Fiber volume fraction V_f 60%

Compare against

Fiber Matrix

Equal-Stiffness Weight Savings

Panel mass vs. baseline (same bending stiffness)

— %

lighter than the baseline plate

Composite Properties

Density ρ_c

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Modulus E_L

—

Strength σ_L

—

Specific modulus

—

Specific strength

—

How it works

Aligned continuous-fiber composites combine a stiff, strong but brittle fiber with a tough, formable matrix. Along the fiber direction the classic rule of mixtures gives the composite's properties from the volume fraction V_f:

ρ_c = Vf·ρ_fiber + (1-Vf)·ρ_matrix
E_L = Vf·E_fiber + (1-Vf)·E_matrix          (Voigt / iso-strain bound)
σ_L ≈ Vf·σ_fiber + (1-Vf)·σ_matrix           (fiber-dominated failure)

The payoff isn't raw stiffness — steel still beats most composites GPa-for-GPa. It's stiffness per unit weight. For a flat plate, bending stiffness scales as D ∝ E·t³, so to match a baseline plate's stiffness with a different modulus:

t_composite = t_baseline · (E_baseline / E_L)^(1/3)
mass ratio  = (ρ_c / ρ_baseline) · (E_baseline / E_L)^(1/3)

Because ρ_c is 3–5× lower than steel, the composite plate can be made much thicker for the same stiffness and still come out far lighter — the "weight savings" readout above is exactly this mass ratio. This is the real reason aircraft, cars and wind-turbine blades switch to composites: not more stiffness, but the same stiffness for a fraction of the weight. The 3D block shows the fiber packing (density of rods) at the chosen V_f — real laminates top out near 65–70% before fibers can no longer be wetted out by resin.

Representative volume element Fiber axis

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