## Introduction

In this article I will explain how you can know if a material is linear or non-linear viscoelastic. There are a couple of simple experimental tests that can be used to determine if material is linear viscoelastic.

## A Few Examples

This example contains experimental data for a CPVC material tested in uniaxial tension and compression. The experimental data shows that the material undergoes plasticity, and **the material is therefore not linear viscoelastic**.

This example shows cyclic tensile stress-strain data for a silicone rubber. The material clearly exhibits Mullins damage, but it is not possible to say if the material is linear viscoelastic by simply reviewing the provided data.

Finally, in this example, the material was tested using a DMA frequency sweep. A linear viscoelastic material model can certainly be make to fit this data, but it does not mean that the material is linear viscoelastic in some other test! Additional tests are required to determine if the material is really linear viscoelastic.

**You cannot say that a specific material is linear viscoelastic.****But a specific material can behave like linear viscoelasticity under specific conditions.**

## Best Ways to Determine if a Material is Linear Viscoelastic

To determine if a material is linear viscoelastic, we will start with Boltzmann’s superposition principle:

Based on this idea, let’s consider a case in which a jump in strain (of magnitude e_{0}) is applied. The resulting stress will also have a jump, and then gradually relax over time. This data, by it self, cannot be use to determine if a material is linear or non-linear viscolastic.

After performing that experiment, let’s perform another similar experiment. But this time apply 2X the strain magnitude. **If the resulting stress is exactly 2X the previous stress, for all times, then the material is linear viscoelastic **(for strains up to 2e_{0}).

Another test (that is based on the same idea), is a strain amplitude DMA test. The figure below shows one example where the storage (and loss) modulus was independent of the strain amplitude up to a strain of 0.01. **In this case the material is linear viscoelastic for strains less than 1%.**

## Summary

- A material is not inherently linear or non-linear viscoelastic.
- A material may be linear viscoelastic under certain conditions (typically if the strains are small enough).
- Stress relaxation, creep, or DMA strain amplitude sweeps can be used to determine the domain in which a material is linear viscoelastic.