## Abstract

When a test lab reports the results from a stress relaxation experiment they typically provide a file containing the stress as a function of time, at the specified strain. But it is not always clear how long it took for the test machine to reach the target strain. In this article I am investigating how much influence the preload time has on material models that are calibrated to stress relaxation data. It turns out that the preload time has a very large influence on the material models that are calibrated from the data. For more info about stress relaxation experiments also see Chapter 2 of my Mechanics of Solid Polymers book.

## Method of Investigating the Preload Time

For the investigation I used a neo-Hookean hyperelastic model with a 5 term Prony series. Specifically, in MCalibration I used: `C10`

=1 MPa, `rel_gi`

=0.18, `sum_g`

=0.5, and `sum_k`

=0. The preload time was set to 0.1 sec. The details of how I generated the “experimental data” are shown in the video below.

## Material Model Calibration 1

In this calibration I used that the preload time as 0.1 sec, which is the same as was used when generating the original “experimental data”. For this case we should be able to recover the original material parameters. The figure shows that the calibration very accurately captures the experimental data. The error is 0.02%!

To further validate the accuracy of the calibrated material model, I compared the stress-strain predictions of the original material model and the calibrated material model in monotonic tension at 3 different strain rates.

This figure shows that the calibrated material model is in good agreement with the original material model if the preload time is set correctly.

## Material Model Calibration 2

In this second calibration I used a time for the preload of 1 sec, which is NOT the same that was used when generating the original “experimental data”. The idea here is to see how big effect this has on the calibrated material model. The figure shows that the calibration also in this case can accurately capture the experimental data. The calibrated C10 parameters, however, is 1.5 MPa, which is 50% larger than what it should be.

The accuracy of the material model was also evaluated by comparing the stress-strain predictions of the original material model and the calibrated material model in monotonic tension at 3 different strain rates.

The figure shows that with an incorrect preload time, the calibrated material model very poorly represents the intermediate and high strain rate response.

## Summary of Preload Time Influences

- It is VERY important to know the time it takes to reach the target strain in stress relaxation experiment.
- Not knowing the preload time can cause very large error in the calibrated material model.
- If the preload time is not known then it can be better to remove initial stress relaxation data points up to the estimated preload time