A new class of quasi-linear models for describing the nonlinear viscoelastic response of materials

In this short note, we develop a new class of quasi-linear viscoelastic models wherein the linearized strain is expressed in terms of a nonlinear measure of the stress. The class of models that is developed could be regarded as counterpart to the class of models referred to popularly as quasi-linear models, proposed by Fung to describe the response of viscoelastic bodies; however, now the strain is expressed as an integral of a nonlinear measure of the stress. The class of models that are developed can describe response that cannot be described by the class of models proposed by Fung, and moreover, these models are more reasonable from the point of view of causality.