The response of a fiber-reinforced composite with a viscoelastic matrix phase

We consider the class of fiber-reinforced composites where the behavior of the matrix phase is viscoelastic under shear. By application of the correspondence principle, simple explicit expressions for the five effective relaxation moduli of a composite with a matrix whose behavior can be approximated by the standard linear model are developed. It is found that the effective relaxation times for the composite are always larger than the relaxation time of the matrix. It is further shown that due to the interaction between phases with different viscoelastic behaviors, the composite may exhibit a non-monotonous behavior. The analytic expressions are compared with corresponding finite element results for a composite with hexagonal fibers distribution. Good agreement is revealed for reinforced composites as well as for composites weakened by soft fibers.