Methods of interconversion between linear viscoelastic material functions.Part I - a numerical method based on Prony series

An efficient and accurate numerical method of interconversion between linea r viscoelastic material functions based on a Prony series representation is presented and tested using experimental data from selected polymeric mater ials. The method is straightforward and applicable to interconversion betwe en modulus and compliance functions in time, frequency, and Laplace transfo rm domains. Good agreement is shown between solutions obtained from the met hod in different domains. A detailed computational procedure and selection of values for parameters involved in the method are presented and illustrat ed. In particular, the effects of different choices of relaxation and retar dation times on the accuracy of the method are discussed. The mathematical efficiency associated with Prony series representations of both source and target transient material functions is fully utilized. The method is genera l enough to cover both viscoelastic solids and liquids. The tensile relaxat ion data from polymethyl methacrylate (PMMA)and the shear storage complianc e data from polyisobutylene are used in illustrating the method. In a compa nion paper (Schapery and Park, 1998), an extended approximate analytical in terconversion method is presented. (C) 1998 Elsevier Science Ltd. All right s reserved.