Rule of mixtures (Voigt / iso-strain): loaded along the fibers, fiber and matrix stretch by the same strain, so stiffness adds by volume: E₁ = VfEf + VmEm. Loaded across the fibers (Reuss / iso-stress), they carry the same stress instead, so compliances add: 1/E₂ = Vf/Ef + Vm/Em — a much softer result dominated by the weak matrix.
- Off-axis stiffness: at an angle θ between the load and the fiber axis, classical laminate theory gives 1/Eθ = cos⁴θ/E₁ + sin⁴θ/E₂ + (1/G₁₂ − 2ν₁₂/E₁)·sin²θcos²θ. The cos⁴θ term means stiffness falls off a cliff within the first 10–20° of misalignment — real laminates are stacked at multiple angles for exactly this reason.
- Anisotropic strength: along-fiber failure is set by the strong, stiff fiber; cross-fiber failure is set by the weak matrix (and the stress concentrations it suffers around each fiber), so the same material can be many times stronger in one direction than the other.