A novel nonlinear viscoelastic solid model

Abstract

The standard linear solid (SLS) model has been widely used to describe linear viscoelastic materials. Although the SLS can be extended to describe more complex phenomena through the inclusion of additional components, a compact model of nonlinear viscoelasticity remains elusive. Here, using the framework of the three component SLS model, the stress–strain relationships of the individual components have been generalised. This work describes the derivation of the new generalised model, termed nonlinear viscoelastic solid model, or NVS, that can potentially describe nonlinear viscoelastic phenomena in a compact differential form and reduces to the familiar SLS model if linear components are selected. As a proof of concept, exponential functions of strain and strain rate were selected for the three components and major viscoelastic phenomena such as stress relaxation, creep and sawtooth strain loading were simulated. Finally, to demonstrate its efficacy in describing biological tissue, the NVS model was used to simulate the cyclic loading of mammalian stomach and cardiac muscle tissues.