## Introduction

I have written about the Abaqus PRF model in previous posts (see below). I specifically covered the different flow equations that are supported by the PRF model. I never really liked their selection, however, and I have now taken the time to implement 2 additional flow equations as UCREEPNETWORK and VUCREEPNETWORK subroutines. These subroutines are part of the PolyUMod library and you can use them in any of your PRF models. In this article I will explain the theory of the new flow models, how you can calibrate them using MCalibration, and how you can use the final calibrated PRF models in Abaqus.

## How to Use the UCREEPNETWORK Subroutine?

It is easy to use the PolyUMod UCREEPNETWORK creep models for the PRF model in Abaqus. All you need to do is to set `Law=User`

, and then specify the parameters that are used by the creep law. The creep parameters, of course, can be determined using MCalibration. The following example is using a single flow network with PolyUMod flow model Type=2 (see more about that below).

` ````
```*Material, name=mat
*Density
1e-09
*Hyperelastic, Yeoh, Moduli=instantaneous
** C10, C20, C30, D1, D2, D3
1, -0.01, 0.001, 0.06, 0, 0
**
*Viscoelastic, Nonlinear, NetworkId=1, Law=User, properties=8
** type, gammaDot0, tauHat, m, p0, fff, epsf, aa
2, 1.0, 2.0, 8.0, 0.0, 0.5, 0.1, 0.001
*Network stiffness ratio, N=1
0.8

## PolyUMod Flow Model 1: BBP

This flow model is the classic Bergstrom-Boyce model with pressure-dependence. The following material parameters are needed:

**Flow Element Type**= 1**tauHat**[stress]. Specifies the flow resistance stress.**m**[dimensionless]. Stress exponent for the flow resistance.**C**[dimensionless]. Exponent on the strain-dependence for the strain-dependence of the viscosity.**E**[dimensionless]. Strain offset factor. Typically 0.001, or something similar.**gammaDot0**[1/sec]. Attempt frequency constant introduced for dimensional reasons.**p0**[dimensionless]. Same approach as in the TNV model.**aa**[dimensionless]. Typically 0.01, or so. If the normalized stress is lower than this value, then no flow will occur. If this parameter is non-zero then some FE simulations will run faster. Can also be used to force a pure plastic response.

Here are exemplar stress-strain predictions at different strain rates in uniaxial tension.

## PolyUMod Flow Model 2: PowerYEP

This flow model contains power-law stress dependence, yield evolution, and pressure dependence. The formulations for the dependencies are are similar to the PolyUMod Three Network (TN) model. The following material parameters are needed:

**Flow Element Type**=2**gammaDot0**[1/sec]. Attempt frequency introduced for dimensional reasons.**tauHat**[stress]. Specifies the flow resistance stress.**m**[dimensionless]. Stress exponent for the flow resistance.**p0**[dimensionless]. Same approach as in the TNV model.**ff**[dimensionless]. Final value of the yield evolution factor.**epsf**[dimensionless]. Effective characteristic strain for the yield evolution factor.**aa**[dimensionless]. Typically 0.01, or so. If the normalized stress is lower than this value, then no flow will occur. If this parameter is non-zero then some FE simulations will run faster. Can also be used to force a pure plastic response.

Here are exemplar stress-strain predictions at different strain rates in uniaxial tension.

## Final Notes

- The PolyUMod UCREEPNETWORK and VUCREEPNETWORK flow models are easy to use and calibrate since they are natively implemented into MCalibration.
- In many cases these new flow models will make the Abaqus PRF model more accurate.
- Note that the PRF model with these enhanced flow models will still not be as accurate as the PolyUMod TN and TNV models, since those model also include connections between the different networks elements. Those types of connection cannot be implemented in the Abaqus PRF model.
- It appears that Abaqus/Explicit 2022 has a problem supporting pressure dependence in VUCREEPNETWORK subroutines.