Linear mixing for composite stiffness
The rule of mixtures predicts composite stiffness as a weighted average of fiber and matrix properties: E_composite = f_fiber * E_fiber + (1 - f_fiber) * E_matrix, where f is the fiber volume fraction. This linear relationship holds because fibers and matrix experience the same strain in the direction of the fibers (parallel loading). The rule gives an upper bound on composite modulus, known as the Voigt limit.
Reuss limit and the lower bound
When fibers and matrix experience the same stress (series loading perpendicular to fiber direction), the composite stiffness is lower: 1/E = f_fiber/E_fiber + (1-f_fiber)/E_matrix. This is the Reuss limit, the inverse-average result. Real composites fall between Voigt and Reuss bounds depending on fiber orientation and loading direction. Unidirectional fibers give Voigt-like performance parallel to fiber axis and Reuss-like transverse.
Practical implications for design
High fiber volume fractions (40-70 percent) maximize stiffness gain, but too-high fractions create processing difficulty and trapped voids. Glass-fiber epoxy typically reaches 60 percent fiber by volume; carbon-fiber prepregs up to 65 percent. Bidirectional and multidirectional fiber layouts trade peak axial stiffness for more uniform omnidirectional properties, a key choice in laminate design.