# Practical Differences Between Linear and Non-Linear Viscoelasticity

## Introduction to Linear and Non-Linear Viscoelasticity

This article covers differences between linear and non-linear viscoelasticity. Most engineers are familiar with linear viscoelasticity, and perhaps also how to use linear viscoelasticity in a FE simulation. But most engineers are not as familiar with non-linear viscoelasticity. In this article I will try to explain some of the practical differences between these two model types. One key take away is that it is as easy to use a non-linear viscoelastic material model (like the Bergstrom-Boyce model) as it is to use a linear viscoelastic model.

### Linear Viscoelasticity   ### Non-Linear Viscoelasticity  ### 2 thoughts on “Practical Differences Between Linear and Non-Linear Viscoelasticity”

1. Hi Gorgen,

I am confused about the definition of linear viscoelasticity. The linear viscoelasticity should obey: E(t)=sigma(t)/epsilon0; Obviously, hyperelastic response+stress relaxation modulus does not satisfy the definition of linear viscoelasticity.
Is there no consistency for the definition of linear viscoelasticiy?
thanks!

Best,
Yuhai

2. You can define linear viscoelasticity as either: (linear elastic) + (Prony series), or (hyperelastic) + (Prony series). I prefer the second definition, since it is more useful in practice.
/Jorgen