It has been observed that certain filamentary composite materials exhibit a different Poisson compliance when loaded transversely to the fibers than when loaded longitudinally (parallel to the fibers). In such cases the following widely used reciprocal relation is not satisfied:  
where EL and ET are the L (longitudinal) and T (transverse) Young’s moduli and νLT and νTL are the Poisson’s ratios obtained from uniaxial loading in the L and T directions. Here two entirely different approaches are used to develop mathematical models of an elastic composite material behaving as described above. One method permits the compliance matrix to be unsymmetric but vary smoothly with the angular orientation. The other method, which is believed to be more valid, incorporates one set of symmetric compliances when the fibers are loaded in tension and a different set of symmetric compliances when the fibers are loaded in compression. The two different models are applied to some data for rubber reinforced by aramid (Kevlar) cord. For this composite, the above reciprocal relation is least satisfied, since νTL/ET is approximately 147 times νLT/EL.
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