## Introduction

In this last part of our tutorial series I will calibrate a number of different material models to the available experimental data for the PEEK material that is the focus of this study. In the following sections, the results from the different material models are compared to the experimental data. The final section summarizes all findings and provides some recommendations.

## Material Model 1: Abaqus JC-Model

The calibration results for the Abaqus Johnson-Cook plasticity model are shown in the figure below. The average error in the model predictions is 29.4%.

Abaqus commands:

*Elastic

*Plastic, hardening=Johnson Cook

*Rate Dependent, type=Johnson Cook

## Material Model 2: ANSYS BB-Model

ANSYS natively supports the Bergstrom-Boyce (BB) model. The set of material parameters that most accurately represent the experimental data is shown in the figure below. The average error in the model predictions is 29.4%.

ANSYS commands:

TB, BB, matid, 1, 7, ISO

TB, BB, matid, 1, 1, PVOL

## Material Model 3: Abaqus Elastic-Plastic with Kinematic Hardening

The calibration results for the Abaqus elastic-plastic with kinematic hardening model are shown in the figure below. The average error in the model predictions is 26.9%.

Abaqus commands:

*Elastic

*Plastic, hardening=combined, data type=parameters, number backstresses=5

## Material Model 4: PolyUMod Bergstrom-Boyce (BB) Model

Many FE solvers have built-in support for the BB-model, and those that do not can use the PolyUMod library. In this case, all the different implementations of the BB-model give similar results, see figure below. The average error between the experimental data and the model predictions is about 23.1%. The reason this error is so large is that the BB-model was developed for elastomer-like materials, not thermoplastics. The non-linear viscoelastic response of elastomers is simpler than the viscoplastic response of thermoplastics, so thermoplastics typically require a more advanced material model (typically with 3 parallel networks, the BB-model only uses 2 parallel networks).

## Material Model 5: Abaqus PRF-Model

The calibration results for the Abaqus Parallel Rheological Framework (PRF) model are shown in the figure below. The average error in the model predictions is 16.5%.

Abaqus commands:

*Hyperelastic, Yeoh, Moduli=instantaneous

*Viscoelastic, Nonlinear, NetworkId=1, SRatio=[val], Law=Power Law

*Viscoelastic, Nonlinear, NetworkId=2, SRatio=[val], Law=Power Law

## Material Model 6: PolyUMod TN-Model

The calibration results from the PolyUMod Three Network (TN) model are shown in the figure below. The average error in the model predictions is 10.3%.

## Material Model 7: PolyUMod TNV-Model

The calibration results from the PolyUMod Three Network Viscoplasticity (TNV) model are shown in the figure below. The average error in the model predictions is 10.3%.

## Summary

In this tutorial series we calibrated a number of commonly used material models to experimental data for Polyether ether ketone (PEEK). The a direct comparison between the accuracy of the different constitutive models are shown in the following figure

The figure shows that there is a HUGE difference in accuracy between the different models. The best plasticity models have an error that is 3X larger then the best viscoplasticity model. That is, the plasticity model errors are 300% larger than the best model!

It is also clear that not all viscoplasticity models are created equally. The Bergstrom-Boyce (BB) model, despite being a totally cool model that I developed, is not accurate for PEEK. As mentioned earlier, this is not surprising since the BB-model was developed for rubbers, not thermoplastics. The Abaqus Parallel Rheological Framework (PRF) model is the most accurate native material model in commercial FE codes, but its predictive errors are more than 2X larger than for the PolyUMod Three Network Viscoplasticity (TNV) model. The PolyUMod TNV model is clearly the most accurate model in this case.