A quasi-correspondence principle for Quasi-Linear viscoelastic solids

In this paper we show that the correspondence principle that allows one to obtain solutions to boundary-initial value problems for Linear viscoelastic solids from solutions to that for a linearized elastic solid can be extended, in many circumstances, to the case of the Quasi-Linear viscoelastic solids introduced by Fung. We illustrate the ability to generalize the correspondence principle by considering a variety of problems including torsion, transverse loading of beams and several problems that involve a single non-zero stress component. This extension is however not possible for certain classes of problems and we present a specific example where the correspondence principle breaks down. The correspondence principle between Linear elasticity and Linear viscoelasticity also breaks down under certain conditions, however the correspondence between the solutions for Linear viscoelasticity and Quasi-Linear viscoelasticity is even more fragile in that it breaks down while the classical correspondence works, and hence we refer to the correspondence as a quasi-correspondence principle.