Constitutive laws in time and frequency domains for linear viscoelastic materials.

There have been numerous phenomenological approaches to the characterization of linear isothermal viscoelastic material behavior. The particular form of the relaxation function has an impact not only upon how well it can be fit to data from a simple relaxation test but also upon how amenable it is to the integral transform techniques commonly used to solve problems of linear viscoelasticity. A new viscoelastic constitutive law is proposed and compared to the fractional calculus model in the context of a particular problem. The solution procedures for each law demonstrate that the new constitutive law requires less computation. Comparison of the actual results themselves, however, is not meaningful since conclusions drawn would depend upon the particular material being modeled and how well each law can be fit to the particular material. The problem is solved once more using a relaxation modulus defined in terms of a Prony series. Significant computational advantages over the previous two are demonstrated for this constitutive law. The results indicate that the particular constitutive law used for a linear viscoelasticity problem can be chosen based upon a trade-off between material property presentation and computational ease. [Work supported by ONR.]