MICROMECHANICAL FORMULAS FOR THE RELAXATION TENSOR OF LINEAR VISCOELASTIC COMPOSITES WITH TRANSVERSELY ISOTROPIC FIBERS

Explicit analytical expressions for the relaxation moduli in the Laplace domain of composites with viscoelastic matrix and transversely isotropic fibers are developed. The correspondence principle in viscoelasticity is applied and the problem in the Laplace domain is studied using the solution of the elastic problem having periodic microstructure. Formulas for the Laplace transform of the relaxation functions of the composite are obtained in terms of the properties of the matrix and the fibers. The inversion to the time domain of the relaxation and the creep functions of composites reinforced by transversely isotropic fibers is carried out numerically when a power law model is applied to represent the viscoelastic behavior of the matrix. Finally, comparisons with experimental results are presented.