TNV Model

The Three Network Viscoplastic (TNV) model is a general purpose viscoplastic material model capable of capturing the experimentally observed behaviors of many thermoplastics, including time-dependence, pressure-dependence of plastic flow, pressure-dependent bulk modulus, volumetric plastic flow, damage accumulation, and triaxiality dependent failure.

The PolyUMod implementation of the TNV model uses 1, 2, or 3 parallel networks, and one optional failure model. The first three parameters of the material model specifies the network type for each network, and the forth parameter specifies the failure model type.

The model supports the following hyperelastic components: Yeoh, anisotropic HGOB hyperelastic HGOB (Holzapfel-Gasser-Ogden-Bergstrom), and the hyperfoam model. Each of these can be combined with optional Mullins damage. Each network can also have isotropic or anisotropic power-law viscoplasticity. The model can also use a strain or stress based failure model with a failure value that depends on the strain-rate and stress triaxiality.

It is easy to explore all of these combinations using MCalibration! The details of each model component are listed in the PolyUMod User’s Manual. The TNV model is an alternative to the PolyUMod Three Network (TN) model. The TNV model is more general and often slightly more accurate than the TN model. Also the TNV model can predict volumetric plastic flow. Temperature dependence is not part of the TNV model, but can be added using the multi-temperature framework.

The following are the key state variables that are used by the TNV model.

IndexState Variable Name
39Max principal stress/strain (depending on the failure model)
40Stress triaxiality
41max stress/strain divided by the failure stress/strain (depending on the failure model)
42Failure damage factor D

Parameters Controlling the Viscoplastic Flow

The TNV model uses the following material parameters to control the viscoplastic flow rate: [tauHat, mm, bb, p0, fff, epsF, ceps, fss]. The meaning of these parameters is explained graphically in the figures below.

Failure Model Options

The TNV model supports either a strain-based or a stress-based failure model. The failure stress or strain is compared to either a Mises or Hill stress or strain value to determine if the material point should start to break down. The critical stress or strain can be modified to depend on the stress triaxiality ($$\sigma_{triax}=tr[\sigma]/(3 \sigma_{mises})$$) or the strain rate as indicated in the following figures.

Predefined Model Structures in MCalibration

MCalibration introduces 4 predefined TNV model structures for the common polymer types:

• Elastomers:
• Network 1: Yeoh hyperelasticity with Mullins damage
• Network 2: Yeoh hyperelasticity with power-law flow
• Isothermal thermoplastics:
• Network 1: Yeoh hyperelasticity
• Network 2: Yeoh hyperelasticity with power-law flow
• Network 3: Yeoh hyperelasticity with power-law flow
• Polyurethanes and Thermoplastic Elastomers (TPEs)
• Network 1: Yeoh hyperelasticity with Mullins dmage
• Network 2: Yeoh hyperelasticity with power-law flow
• Network 3: Yeoh hyperelasticity with power-law flow
• Polymer Foams
• Network 1: Hyperfoam
• Network 2: Hyperfoam with power-law flow

These proposed model structures are starting points for reasonable models. You should always use actual experimental data when developing a material model.

Exemplar Predictions from the TNV Model

There is an example of the model predictions from the TNV model. The figure compares experimental data for a polyvinylidene fluoride (PVDF) material with predictions from the TNV model. The model accurately captures the experimentally observed behavior.

Material Model for Unfilled PEEK

Calibrated non-linear viscoplastic material model for unfilled PEEK.

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