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# How to Calibrate a Temperature-Dependent Abaqus Hyperelastic Model

## Introduction

MCalibration makes it easy to calibrate an Abaqus Hyperelastic material model to experimental data. But what should you do if you want to create a temperature-dependent hyperelastic model? In this article I will demonstrate a quick way to calibrate a temperature-dependent Abaqus hyperelastic model

For more information about the experimental data, also see my article: “Why Does Rubber Have Odd Temperature Dependence?“.

## Experimental Data for an Unfilled Silicone Rubber

The image below summarizes the experimental uniaxial tension data that I have for an unfilled silicone rubber. The tests were performed at 3 different temperatures: 20°C, 60°C, and 150°C. For this material the deformation resistance is due to entropy changes, so the stiffness increases with temperature. In fact, if you were to analyze the data in more detail you would find that for this material the stress is almost linearly dependent on the absolute temperature in Kelvin. We will not use that information in this example.

## Step 1: Calibrate a Hyperelastic Material Model to Each Temperature

Since the experimental stress-strain response is almost linear we can use a basic hyperelastic model, such as the Arruda-Boyce Eight-Chain model. I then used MCalibration to quickly calibrate the hyperelastic model to the data at each temperature. The following figures show the calibrated model results. As expected, the model predictions are in good agreement with the experimental data.

## Step 2: Combine the Models into a Temperature-Dependent Model

Each of the 3 material models are then exported into Abaqus inp-files. Here’s an example of what one of these files look like.

*Material, name=MCal_Mat
** Calibrated with MCalibration
** Units: [length]=millimeter, [force]=Newton, [time]=seconds, [temperature]=Kelvin
** Calibration file name: Calibrate_AB_T20.mcal
*Density
1e-09
*Hyperelastic, Arruda-Boyce
**       mu,    lambdaM,          D
0.24991229,1.220010925,0.040876577

The 3 files are then combined into one file by adding the temperature at the end of each parameter line. Here is the final model. That is it! You can now use this model in any Abaqus inp-file.

*Hyperelastic, Arruda-Boyce
**       mu,    lambdaM,          D
0.24991229,1.220010925,0.040876577, 20.0
0.269581027,1.202796484,0.036812891, 60.0
0.322794588, 1.16446699,0.028635672, 150.0

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