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Anisotropy means that a physical property depends on direction. A strip cut along the fibres of a long-fibre composite can resist stretching much more strongly than a strip cut across them. The directional difference can come from the crystal structure of a constituent or from the arrangement of otherwise isotropic constituents.

For thermal conduction, a thermal conductivity tensor relates the temperature gradient to the heat flux. Along its principal directions the conductivities can differ, and in a general direction the heat flux need not be parallel to the negative temperature gradient. Anisotropic elasticity similarly requires a tensor-valued constitutive equation rather than a single Young's modulus. Measuring a specimen in several orientations therefore reveals information that one axial measurement cannot; averaging over randomly oriented constituents can reduce macroscopic anisotropy, but the result depends on the actual orientation distribution.

A composite material contains distinguishable constituent phases whose arrangement contributes to the bulk properties. In a fibre-reinforced example, strong fibres carry much of the axial load while a composite matrix holds them together and transmits shear stress between them. Carbon-fibre-reinforced polymer combines carbon fibres with a polymer composite matrix; glass fibres provide another reinforcement.

The constituent proportions alone do not determine the result. Aligned fibres produce anisotropy, whereas changing their orientations changes which directions are reinforced.^[ref] In an ideal long-fibre composite, the longitudinal rule of mixtures estimates the axial Young's modulus. A comparison of tensile testing along and across the fibres exposes the importance of geometry and fibre-matrix load transfer. The same idea of combining phase properties with geometry appears in effective conductivity, although the relevant constitutive equations differ.

A long-fibre composite contains reinforcing fibres whose lengths are large enough that end regions do not dominate their load-carrying response. In a well-bonded continuous aligned specimen pulled along the fibres, the fibres and composite matrix undergo approximately the same axial strain. Their different Young's moduli then produce different axial stresses, and adding their forces gives the longitudinal rule of mixtures.

Load enters a fibre through shear stress at its interface with the composite matrix. Near a free fibre end the axial stress must rise from zero, so a short fibre can spend much of its length below its useful load. The critical fibre length expresses the associated scale in a simple strength-transfer model. Whether a fibre is mechanically long therefore depends on its diameter, the interface and the required stress, rather than on an absolute length in millimetres. Changing fibre direction still changes the response: long reinforcement does not remove anisotropy.