Advanced User Material Subroutines for Polymers

For more information and to request a quotation please contact:
Jorgen Bergstrom, Ph.D.
Veryst Engineering
47A Kearney Road
Needham, MA 02494
USA

Telephone: (781) 433 - 0433

Email 1: jorgen@polymerFEM.com
Email 2: jbergstrom@veryst.com

Introduction

Components made from polymers can have many advantages over other materials in terms of, for example, cost, density, and specific strength. The mechanical response of polymers, however, is typically very sensitive to the load environment, temperature, and the applied strain-rate. It is necessary to have a good understanding of the experimental characteristics of the material and to use an accurate material model when performing finite element (FE) simulations in order to get reliable and accurate results.

Unfortunately, the currently available material models in commercially available finite element programs are not capable of accurately predicting the mechanical response of many important polymers. To overcome this shortcoming Veryst Engineering has developed a collection of advanced material models that can be added to the FE program as an external shared library. This way the advanced material models become available to the FE user as if they where built-in. Using this approach is it possible to perform very accurate FE simulations without becoming an expert in material model software development. All the difficult development work has already been done!

The user-material model library is available for all FE element programs that supports external user-material subroutines (UMATs). Most major FE programs have this capability, for example, ABAQUS, ANSYS, LS-DYNA, and MSC.MARC.

User-Material Model Library

The Polymer User Material Library (PolyUMod) consists of a collection of useful material models. The material models that are included in the library specifically target the non-linear, viscoplastic, time- and temperature-dependent response of various polymeric materials. The material models enable significantly more accurate finite element simulations than what is possible with the currently available built-in models in the major FE codes.

To use the PolyUMod library it is sufficient to:

  1. Install the shared library or custom executable on the simulation computer
  2. Specify the appropriate material parametes in the pre-processor or the input file
  3. Run the FE simulation as usual

The finite element simulations will then automatically use the PolyUMod library as if it was a built-in feature. The details of the installation and usage of the library is presented in the User's Manual.

The PolyUMod library of material model subroutines are commercially available through a yearly license agreement. The PolyUMod library is currently available for the following computer platforms:

The material model software is directly available for ABAQUS (standard and explicit) and LS-DYNA (implicit and explicit). Other FE codes can be supported for an additional one-time conversion fee.

Available User-Material Models

The PolyUMod library currently contains the material models listed in the following table. Additional models can be added on request.

Each of these models provides unique and powerful predictions for different classes of engineering and biopolymers. Each material model is available for both implicit and explicit FE simulations.

Material Model Name Materials Comments

LE

Linear Elastic (LE)

Linear elastic model that also incorporates the PolyUMod failure models.

NH

Neo-Hookean (NH)

Neo-Hookean hyperelastic model that supports the PolyUMod failure models.

EC

Eight-Chain (EC)

Arruda-Boyce eight-chain hyperelastic model that supports the PolyUMod failure models.

  • Supports different failure models
  • Uses a more accurate implementation of the inverse Langevin function than most other commercial implementations.

AEC

Anisotropic Eight-Chain (AEC)

Anisotropic version of the eight-chain model [Bischoff et al, Trans. ASME, 69, 570-579, 2002].

BB

Bergstrom-Boyce (BB)

Advanced material model for elastomers, rubbers, and soft biological tissues [references].

pdfMore Info

Adds functionality to the built-in *Hysteresis option in ABAQUS/Implicit:

  • Temperature effects
  • Available for ABAQUS/Explicit
  • Supports different failure models

BBM

BB Mullins (BBM)

Same as standard BB model, but also includes the Ogden-Roxburgh Mullins model [Proceedings of the Royal Society of London, Series A, 455, 2861-2877, 1999].

Adds functionality to the built-in *Hysteresis option in ABAQUS/Implicit:

  • Temperature effects
  • Mullins effect
  • Available for ABAQUS/Explicit
  • Supports different failure models

ABBM

Anistropic BB Mullins (ABBM)

Same as the BBM model but is using using the Bischoff anisotropic eight-chain model.

  • Temperature effects
  • Anisotropic
  • Mullins effect
  • Strain-rate effects
  • Available for explicit simulations
  • Supports different failure models

DBB

Dynamic Bergstrom-Boyce (DBB)

Same as the BBM model but contains additional features to enable accurate predictions of both small-strain dynamic behavior and large-strain behavior using one set of material parameters.

  • Temperature effects
  • Small strain dynamic behavior
  • Mullins effect
  • Supports different failure models

AB

Arruda-Boyce (AB)

Arruda-Boyce viscoplastic model for thermoplastic materials [Mech. Mater., 19, 193-212, 1995].

DNF

Dual Network Fluoropolymer (DNF)

Specifically developed of Fluoropolymers, (e.g. Teflon), but is suitable for many thermoplastics [Mech. Materials, 37, 899-913, 2005].

  • Large deformation behavior
  • Strain-rate effects
  • Temperature effects
  • Both viscoelastic and viscoplastic behavior
  • Supports different failure models

HM

Hybrid Model (HM)

Specifically developed for UHMWPE, but is suitable for many thermoplastics. [references]

Advanced and accurate model for UHMWPE. Extensively used in biomechanics simulations.

  • Large deformation behavior
  • Strain-rate effects
  • Temperature effects
  • Supports different failure models

MFM

Micromechanical Foam Model (MFM)

Polymer foam model that explicitly incorporates the reduced density of the foam.

pdfMore Info

  • Large deformation behavior
  • Strain-rate effects
  • Temperature effects
  • Explicitly incorporates the reduced density of the foam.
  • Supports different failure models.

TNM

Three-Network (TNM)

The TNM is an alternative to the Hybrid model that give similar quality predictions but also includes temperature effects and is more numerically efficient.

TNFM

Three Network Foam (TNFM)

Version of the TNM that is explicitly formulated to polymer foams.

PNM2

Parallel Network (PNM)

Advanced model that contains an arbitrary number of elastic and flow elements connected in parallel. See the next section for more information.



Parallel Network Model

The parallel network model (PNM) is a very powerful material model that can be used to simulate different classes of materials. The linear elastic, neo-hookean, eight-chain, Bergstrom-Boyce, Arruda-Boyce, and the three-network models are all special cases of this model. Since this model is so flexible it is described in more detail in this section.

The structure of the PNM can be represented as a number of parallel networks as shown in the following figure.

PNM Rheo
Figure: Rheological representation of the PNM.

All networks must have an elastic component, followed by optional specifications of the temperature, damage, and failure properties of the elastic component. Each network can also have an optional flow component, with optional temperature, pressure, and yield evolution dependence.

The following sections summarize the different components that are available. More detail is given in the PolyUMod User's Manual.

Elastic Components in the Parallel Network Model

Each network needs to have an elastic component. The following elastic element types are available:

Temperature Dependence of the Elastic Component

The elastic component can be made temperature dependent by specifying a scalar multiplication factor that is used to scale the stress that is calculated by the elastic component. The specification of temperature dependence of the elastic component is optional. The following temperature dependence factors are available:

Thermal Expansion of the Elastic Component

The elastic component can undergo thermal expansion if the temperature is changing. The specification of thermal expansion is optional. The following thermal expansion factors are available:

Damage Accumulation of the Elastic Component

The stiffness of the elastic component can be decreased due to damage accumulation. This damage accumulation acts to scale either the stiffness or the overall stress state. The specification of damage accumulation is optional. The following damage component types are available:

Failure Criterion of the Elastic Component

The stress prediction from the elastic component can be coupled with a failure criterion. Once the pre-defined failure condition has been reached, the integrity and stress of that network is eliminated. The global failure flag is set once all networks have failed.

Flow Type Components

Each network can contain a flow component in addition to the elastic component. The specification of a flow-type component is optional. The following flow type components are available.

Temperature Dependence of the Flow Model

The flow model can be modified to include temperature dependence using one of the following functional expressions. The specification of temperature dependence of the flow component is optional.

Pressure Dependence of the Flow Model

The flow model can be modified to include pressure dependence of yield. This effect can be experimentally observed when comparing tension and compression predictions with corresponding experimental data. The specification of pressure dependence is optional. The following pressure dependence factors are available:

Yield Evolution of the Flow Model

The flow resistance in the flow model can be taken to evolve with applied plastic strain. This approach is commonly used to represent strain softening of glassy polymers beyond initial yield. This idea is here extended by directly specifying the target flow resistance as a function of applied plastic strain. The specification of a yield evolution model is optional. The following yield evolution models are available.

Each network in the model can be given an arbitrary combination of the above models. The material parameters are specified in the input deck or in the FE pre-processor.

Available Failure Models

Each of the material models in the PolyUMod library can be combined with a failure model. The following failure models are available:

  1. Failure at a critical chain strain
  2. Failure at a critical Mises strain
  3. Failure at a critical max principal strain
  4. Failure at a critical Mises stress
  5. Failure at a critical max principal stress

Material Model Calibration

When working with any material model it is necessary to find the appropriate material parameters from experimental data. This can be challenging when the material model is non-linear, which all advanced models are. To facilitate the parameter expraction, Veryst Engineering has developed a specialized material parameter extraction software that can be used in a semi-automatic way to determine the most appropriate material parameters from a given set of experimental data. The software is written as a Matlab Toolbox. This software tool is commercially available through a lifetime license.

The following example illustrates the use of the Matlab parameter extraction tool.

Calibration of the Bergstom-Boyce Model

Consider a case where a chloroprene rubber has been tested in uniaxial tension at two different strain. The experiments were performed at room temperature. The following figure shows the experimental data.
Experimental data
Figure: Summary of experimental data

The Bergstrom-Boyce material model was calibrated using the following Matlab file:

% setup experimental data
% loadingType in ['uniaxial', 'planar', 'simple_shear', 'biaxial', 'triaxial']
loadCases(1).fileName = 'CR_compression_fast.txt';
loadCases(1).loadingType = 'uniaxial';  
loadCases(1).strainType = 'true';
loadCases(1).temperature = 293;

loadCases(2) = loadCases(1);
loadCases(2).fileName = 'CR_compression_slow.txt';

% select material model
options.materialModel = 'BergstromBoyce';

% initial guess of material parameters
props = [ ...
%      mu;  lamLock;   kappa;         s;       xi;        C;   tauBas;      m;  tauCut  ]
      9.0;     4.50;      500;      5.0;     0.05;    -0.50;     4.00;    6.0;   0.01   ];

% select parameters to optimize
options.propsToOptimize = [
%     muA;   lamLoc;    kappa;        s;       xi;        C;   tauBas;     m;  tauCut
        1;        2;        0;        4;        5;        0;        7;     8;       0 ];

% method to evaluate predictions
options.fitnessFunc = 'NMAD'; % normalized mean absolute difference

% run the parameter extraction and return the optimal material parameters
[props, fit, pred, loadCases, options] = run_parameter_extraction(loadCases, props, options);

The results from running the Matlab script is shown in the following figure.

Predicted data
Figure: Comparison experimental and predicted data.

This example illustrates a procedure that can be used to calibrate any of the material parameters in the PolyUMod library.

Contact Information

For more information and to request a quotation please contact:
Jorgen Bergstrom, Ph.D.
Veryst Engineering
47A Kearney Road
Needham, MA 02494
USA

Telephone: (781) 433 - 0433

Email 1: jorgen@polymerFEM.com
Email 2: jbergstrom@veryst.com