For a composite of aligned continuous fibers, which correctly describes when to use the isostrain and isostress forms of the rule of mixtures?

Answer: A. Loading parallel to the fibers is approximated by the isostrain form and loading perpendicular to them by the isostress form

When loaded parallel to the fibers, fiber and matrix stretch by the same amount like springs connected in parallel, so the isostrain form E₁ = VfEf + VmEm applies. When loaded perpendicular to the fibers, fiber and matrix carry the same stress like springs in series, so the isostress form 1/E₂ = Vf/Ef + Vm/Em is used as an approximation. At the same volume fraction, the isostrain form gives an upper bound on Young's modulus and the isostress form a lower bound (the Voigt and Reuss bounds). The choice applying the isostress form to parallel loading and the isostrain form to perpendicular loading swaps parallel and perpendicular. The modulus of unidirectional material differs greatly between the fiber and transverse directions, so saying it does not depend on direction is also wrong. The actual transverse modulus is often somewhat higher than the isostress form predicts, and corrections such as the Halpin–Tsai equations are used.