A recently obtained constitutive relation [Zhang et al., Phys. Rev. E 66
, 051806 (2002)] is used for polymers to model plate impact experiments on a composite material consisting of elastic particles and a polymer binder. The stress relaxation in the polymer is described by a kernel in a history integral. The kernel implies a 1/
stress relaxation for a short time t,
and an exponential stress relaxation for a long time. It is found that the binder behavior, especially the stress relaxation at a short-time scale, plays an essential role in the wave dispersion observed during the experiments. Although it is difficult to implement the history dependent constitutive relation directly into a numerical calculation, a mathematical approximation of the kernel is found in the form resembling a prony series. The approximation enables easy implementation of the constitutive relation into numerical calculations. While the conventional use of a prony series requires a series of experiments to determine the parameters, in the present article, the parameters in the series expansion are uniquely determined by the kernel. Furthermore, not all the terms in the series are needed for a specific problem of interest. Only those terms with the relaxation times in the range of the time scales of the physical process are important. © 2003 American Institute of Physics.