Foundations of Linear Viscoelasticity

The classical linear theory of viscoelasticity was apparently first formulated by Boltzmann1 in 1874. His original presentation covered the three-dimensional case, but was restricted to isotropic materials. The extension of the theory to anisotropic materials is, however, almost immediately evident on reading Boltzmann’s paper, and the basic hypotheses of the theory have not changed since 1874. Since that date, much work has been done on the following aspects of linear viscoelasticity: solution of special boundary value problems,2a reformulation3,4 of the one-dimensional version of the theory in terms of new material functions (such as “creep functions” and frequency-dependent complex “impedances”) which appear to be directly accessible to measurement, experimental determination2b of the material functions for those materials for which the theory appears useful, prediction of the form of the material functions from molecular models, and, recently, axiomatization5,6 of the theory.