On the Consistency of Complex Moduli for Transversely-Isotropic Viscoelastic Materials

The ability of advanced composite materials and structures to damp vibration is important in many applications. Use of the complex modulus approach to represent the dissipative properties of transversely-isotropic materials, such as unidirectional fiber-reinforced composites, requires the definition of a set of 5 (imaginary) loss moduli in addition to the 5 (real) storage moduli needed to describe the elastic behavior. In practice, designers of composite materials rarely have experimental data for all 5 loss moduli, and must assume values for the remaining moduli in their analyses. If values for these unknown loss moduli are specified arbitrarily, physically unreasonable behavior can result. This paper develops the conditions necessary for physical consistency of the complex moduli of transversely isotropic materials.