A dynamic investigation of fiber-reinforced viscoelastic materials

Abstract

In recent years, several mathematical models have been proposed to describe the quasi-static response of fiber-reinforced materials, consisting of continuous, elastic fibers embedded in a linear viscoelastic matrix. By assuming that geometric dispersion (dispersion resulting from the internal geometry of the material) is small in comparison to viscoelastic dispersion (dispersion resulting from the viscoelastic nature of the material), these proposed constitutive equations can be extended from a quasi-static regime to a dynamic regime. Here, we examine how the extension to the dynamic regime may be accomplished, compare the results with a theoretical model that includes geometric dispersion, and use the results of an experimental program to evaluate the models. In general, the quasi-static constitutive equations predict phase velocities that are larger than that predicted by the model which contains geometric dispersion and attenuation coefficients that are lower; and, the experimental results agree with the theoretical predictions, provided the fibers were spread more or less uniformly over the cross section.