Rule-of-mixtures expressions for modulus in continuous and aligned composites apply to which orientations?

• A. Longitudinal and Transverse
• B. Only transverse
• C. Only longitudinal
• D. Neither

Answer: (A)

In a continuous, aligned composite the two principal directions define how the load and deformation distribute between the fiber and the matrix. Along the fiber direction, the strain is the same in both constituents, so their stiffnesses add in proportion to their volume fractions: E_long = E_f V_f + E_m V_m. This is the straightforward rule of mixtures, sometimes called the iso-strain form.

Perpendicular to the fibers, the load induces stresses that balance across the two phases, leading to a harmonic-type average: 1/E_trans = V_f / E_f + V_m / E_m. This is the reciprocal rule of mixtures, derived from the iso-stress condition for the transverse direction.

These two expressions specifically apply to the longitudinal (along-fiber) and transverse (across-fiber) orientations in a continuous, aligned, well-bonded composite. For other off-axis directions, you’d need additional transformation or more advanced models.