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 linear viscoelastic material functions based on a Prony series representation is presented and tested using experimental data from selected polymeric materials. The method is straightforward and applicable to interconversion between modulus and compliance functions in time, frequency, and Laplace transform domains. Good agreement is shown between solutions obtained from the method in different domains. A detailed computational procedure and selection of values for parameters involved in the method are presented and illustrated. In particular, the effects of different choices of relaxation and retardation 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 general enough to cover both viscoelastic solids and liquids. The tensile relaxation data from polymethyl methacrylate (PMMA) and the shear storage compliance data from polyisobutylene are used in illustrating the method. In a companion paper (Schapery and Park, 1998) , an extended approximate analytical interconversion method is presented.