7.3. Step 3. Select a Material Model

Define your constitutive model. This process involves two tasks:

  1. Define a material model (TB) and specify the model parameters (TBDATA and TBPT).

  2. Create a fitting object by importing your defined model information (TBFT,FADD).

The program uses the values entered via TBDATA and TBPT as the initial values for the optimization process. You can overwrite them (TBFT,AINI commands or TBFT,SET).

7.3.1. Hyperelastic Material Models

Experiment types supported: uniaxial, biaxial, pure shear, simple shear, volumetric

Table 7.4: Valid Material Models for Hyperelastic Parameter-Fitting

Model Name Order/Options Number of Coefficients[a]
Mooney-Rivlin2, 3, 5, 92 / 3 / 5 / 9 + 1
Polynomial1 to NSee below.[b]
Yeoh1 to NN + N
Neo-Hookean-1 + 1
Ogden1 to N2 * N + N
Arruda-Boyce-2 + 1
Gent-2 + 1
Blatz-Ko[c]-1
Ogden Hyperfoam[d]1 to N2 * N + N
TNM--
Bergstrom-Boyce-8 + 1
Extended Tube-5
Mullins Effect-3
With Prony Series-(2 * NSHEAR) + (2 * NBULK)
TB,USER with TBOPT = MXUP-User-defined

[a] The number of coefficients is usually the sum of the number of deviatoric coefficients and the number of volumetric coefficients.

[b] The number of coefficients for a polynomial depends on the polynomial order N.

[c] This is a compressible model.

[d] This is a compressible model. Also, the experimental data that you provide requires additional fields.


Hyperelastic curve-fitting supports these primary behaviors:

Curve-fitting for fully- or nearly-incompressible hyperelastic material models use the incompressibility equation λ1 * λ2 * λ3 = 1 (where λ is the stretch) to evaluate deviatoric material parameters. The volumetric coefficients are not used during the evaluation of the coefficients that define the deviatoric terms for these models

Table 7.5: Experimental Details for Incompressible Models

Experimental Type Column 1 Column 2 Column 3
Uniaxial TestEngineering StrainEngineering Stress--
Biaxial TestEngineering StrainEngineering Stress--
Planar/Shear TestEngineering Strain (in loading direction)Engineering Stress--
Simple Shear TestEngineering Shear StrainEngineering Shear Stress(Optional) Engineering Normal Stress (normal to the edge of shear stress)
Volumetric TestVolume Ratio (J)Hydrostatic Pressure--

Table 7.6: Experimental Details for Compressible Models

Experiment Type Column 1 Column 2 Column 3
Uniaxial TestEngineering StrainLateral Direction Engineering StrainEngineering Stress
Biaxial TestEngineering StrainEngineering Strain (in thickness direction)Engineering Stress
Shear TestEngineering Strain (in loading direction)Engineering Strain (in thickness direction)Engineering Stress
Simple Shear TestEngineering Shear StrainEngineering Shear Stress(Optional) Engineering Normal Stress (normal to the edge of shear stress)
Volumetric TestVolume Ratio (J)Hydrostatic Pressure--

J is the ratio of current volume to the original volume.

Table 7.7: Experimental Details for Incompressible Models with History-Dependence

Experiment Type Column 1 Column 2 Column 3 Column 4
Uniaxial Test Time Engineering Strain Engineering Stress --
Biaxial Test Time Engineering strain Engineering Stress --
Planar/Shear Test Time Engineering Strain Engineering Stress --
Simple Shear Test Time Engineering Strain Engineering Stress Engineering Normal Stress (Optional)
Volumetric Test Time Volume Ratio Hydrostatic Pressure --

Table 7.8: Experimental Details for the Three-Network Model (TNM), Bergstrom-Boyce Model, Hyperviscoelastic Combinations (HYPER+PRONY), and TB,USER with the MXUP option. Only nearly- or fully-incompressible UserMat routines are supported.

Experiment TypeColumn 1Column 2Column 3Column 4
Uniaxial TestTimeEngineering StrainEngineering Stress --
Biaxial TestTimeEngineering strainEngineering Stress --
Planar/Shear TestTimeEngineering StrainEngineering Stress --
Simple Shear TestTimeEngineering StrainEngineering StressEngineering Normal Stress (Optional)
Volumetric TestTimeVolume RatioHydrostatic Pressure--

Table 7.9: Experimental Details for Anisotropic Hyperelastic Models

Experimental Type Column 1 Column 2 Column 3
Uniaxial Test Engineering Strain Engineering Stress --
Biaxial Test Engineering Strain Dir 1 Engineering Strain Dir 2 Engineering Stress
Volumetric Test Volume Ratio (J) Hydrostatic Pressure --

Euler angles are specified via /xcsys,euler,angle1,angle2,angle3 in the experiment header. See example.

7.3.2. Plastic Material Models

Experiment types supported: uniaxial

Table 7.10: Valid Material Models for Plastic Parameter-Fitting

Index ID Material Model TB Command
1 Isotropic Elasticity TB,ELASTIC
2 Isotropic Hardening TB,PLAS,,,,BISO or TB,NLISO
3 Kinematic Hardening TB,CHABOCHE
4 Rate-Dependent Plasticity TB,RATE,,,,MatModel (where MatModel = PERZYNA, PEIRCE, EVH, or ANAND)[a]
5 Static Recovery TB,PLAS,,,,KSR2
TB,PLAS,,,,ISR[b]
6UserMat with the default nonlinear optionTB,USER

[a] 1) The Anand model is used with TB,ELASTIC. 2) Temperatures must always be positive. Issue TBFT,SET,MATID,AML,GENR,UserDefinedName,TREF,TEMP to set a positive value during the curve-fitting process. All experimental data must also have positive temperatures values.

[b] 1) Isotropic static recovery is active only when the temperature of the experimental data is nonzero and creep coefficients are available. Isotropic hardening and Chaboche kinematic hardening must also be defined. 2) You can enter creep coefficients (TB,CREEP) before issuing TBFT,FADD, but they are not supported in the optimization process. To disable creep, enter the appropriate coefficients (such as setting C1 = 0 for the strain-hardening model). 3) The uniaxial stress evaluated to calculate the error used for the optimization process depends on the experimental stress, elastic modulus, and Poisson's ratio. Provide smoothed stress-strain curves to obtain accurate results. 4) The elastic strain tensor is calculated using the experimental stress, elastic modulus, and Poisson’s ratio. 5) The plastic strain tensor is calculated by subtracting the calculated elastic strain from the total experimental strain and by using the incompressibility condition on the plastic strain components. The two tensors are then added to obtain the total strain tensor used in the optimization process.


Table 7.11: Experimental Details for Rate-Independent Plasticity

Experiment Type Column 1 Column 2 Column 3 Column 4
Uniaxial Test True Strain True Stress -- --

Table 7.12: Experimental Details for Rate-/Time-Dependent Plasticity

Experiment Type Column 1 Column 2 Column 3 Column 4
Uniaxial Test TimeTrue Strain True Stress--

Table 7.13: Column Header Types and Abbreviations

Column NameAbbreviation
Timetime
Total Strainepto
True Stresss
Temperaturetemp

Example 7.1: Experimental Data Input File with Total Strain and Stress

/1,epto
/2,s
/temp,0
      0.0        0.0
 0.280000E-004  4.20000     
 0.560000E-004  8.40000     
 0.980000E-004  14.7000     
 0.144667E-003  21.7000     
 0.191333E-003  28.7000     

The header format to define a data attribute is /attr, value, where attr is the data-type abbreviation, and value is the value of the attribute.

7.3.3. Creep Material Models

Experiment types supported: creep test, uniaxial

Table 7.14: Valid Material Models for Creep Parameter-Fitting

Index ID Material Model TB Command
1 Isotropic Elasticity TB,ELASTIC
2CreepTB,CREEP

Use /index,attributename to indicate what is defined in each column. Example: if column 1 is time, specify /1,time in the header before the experimental values are specified. See the examples.

Table 7.15: Experimental Details for Creep Data

Experiment Type Column 1 Column 2 Column 3 Column 4
Creep Test (creep ) Creep strain as a function of time,stress and temperature
Creep Test (creep ) Creep strain rate as a function of time,stress,creep strain and temperature
Uniaxial Test (unia) Time True Strain True Stress --

Table 7.16: Creep Data Types and Abbreviations

Timetime
Equivalent Creep Strain creq
Equivalent Creep Strain Ratedcreq
Equivalent Stressseqv
Temperaturetemp

The header format to define each column's data type is /n, abbr, where n is the index of the data column in the file, and abbr is the abbreviation for the type of data in the column, as described in Table 7.16: Creep Data Types and Abbreviations.

Example 7.2: Typical Data Input File

/1,seqv             ! indicates first column is stress 
/2,creq             ! indicates second column is creep strain 
/3,temp             ! indicates third column is temperature 
/4,dcreq            ! indicates fourth column is creep strain rate 
4000    0.00215869	100    0.000203055 
4000    0.00406109	100    0.000181314 
4000    0.00664691	100    0.000165303 
4000    0.0102068	100    0.000152217 
4000    0.0151416	100    0.000140946

When a given column is unchanged over the loading history, you can define it as an attribute. As shown in the example above, the stress and temperature are constant throughout the range. You define this data as an attribute.

The header format to define a data attribute is /attr, value, where attr is the data-type abbreviation, and value is the value of the attribute. The constant stress and temperature values above can be written into the file header:

Example 7.3: Constant Stress and Temperature Written Into the File Header

/seqv,4000          ! indicate this creep has a constant stress of 4000 
/temp,100           ! indicate this creep data is at a constant temperature of 100 
/1,creq             ! indicate first column is creep strain 
/2,dcreq            ! indicate second column is creep strain rate 
0.00215869 0.000203055 
0.00406109 0.000181314 
0.00664691 0.000165303 
0.0102068 0.000152217 
0.0151416 0.000140946 
0.0220102 0.000130945 

Thirteen model types are available for creep curve-fitting. The model you select determines the experimental data required for the curve-fitting process. The following table describes the creep data required to perform curve-fitting for each model type:

Table 7.17: Creep Model and Data/Type Attribute

Creep Model creq dcreq time seqv temp
Strain Hardeningxx xx
Time Hardening xxxx
Generalized Exponential xxxx
Generalized Graham xxxx
Generalized Blackburn xxx 
Modified Time Hardeningx xxx
Modified Strain Hardeningxx xx
Generalized Garofalo x xx
Exponential Form x xx
Norton x xx
Combined Time Hardeningx xxx
Prim+Sec Rational Polynomial xxx 
Generalized Time Hardeningx xxx

For strain hardening and modified strain hardening, input both creep strain and creep strain rate in the experimental data.

Provide sufficient experimental data to fit the creep model selected for the fitting process. For example, the strain-hardening model is creep strain rate is a function of stress and creep. To use the model, data must be provided at multiple strain rates (whether in single or multiple files); otherwise, C2 and C3 in the strain-hardening creep equation can become zero in the fitting process and provide a perfect fit in this underconstrained problem. Similarly, experimental data having no multiple stress or creep strain values indicates that the data is independent of those variables.

7.3.4. Viscoelastic Material Models

Table 7.18: Valid Material Models for Viscoelastic Parameter-Fitting

Index ID Material Model TB Command
1 Isotropic ElasticityTB,ELASTIC
2 Prony SeriesTB,PRONY,,,,SHEA/BULK
3 Shift FunctionTB,SHIFT

Define the Prony series model (TB,ELAS and TB,PRONY). If needed, you can use the shift method (TB,SHIFT) to handle temperature experimental data.

For viscoelastic curve-fitting with multiple temperatures, you can evaluate coefficients at each discrete temperature point and write it as a temperature-dependent Prony data table, or you can use the Williams-Landau-Ferry (WLF) or Tool-Narayanaswamy (TN) shift functions to account for the temperature-dependency. (See Shift Functions in the Mechanical APDL Theory Reference.) A separate data file must be provided for each discrete temperature. The viscoelastic test data can be any of the following data types:

Table 7.19: Experimental Details for Hypoviscoelasticity

Experiment Type Column 1 Column 2 Column 3
Shear Modulus vs. Time Time Shear Modulus --
Bulk Modulus vs. Time Time Bulk Modulus --
Shear Modulus vs. Freq Freq Real Component of Shear Modulus Imaginary Component of Shear Modulus
Bulk Modulus vs. Freq Freq Real Component of Bulk Modulus Imaginary Component of Bulk Modulus

7.3.5. Geomechanical Material Models

Table 7.20: Valid Material Models for Geomechanical Parameter-Fitting

Index ID Material Model TB Command
1 Isotropic Elasticity TB,ELASTIC
2 Isotropic Hardening TB,PLAS,,,,BISO or TB,NLISO
3 Extended Drucker-Prager (EDP) TB,EDP
4 Extended Drucker-Prager Cap (EDP Cap) TB,EDP,,,,CYFUN
5 Cam-clay TB,SOIL with TB,PELAS

Table 7.21: Experimental Details for Geomechanical Test Data

Experiment TypeColumn 1 Column 2 Column 3 Column 4
YSUR Pressure Yield stress
I1J2 Stress invariant 1 Square Root of J2
TRIA Axial strain Lateral strain Axial stress Lateral stress

7.3.6. User-Defined (UserMat) Material Models

Experiment types supported: uniaxial

Table 7.22: Valid Material Models For User-Defined Material Parameter-Fitting

Index IDMaterial ModelTB Command
1 UserMat with the default nonlinear option TB,USER
2 TB,USER with TBOPT = MXUPTB,USER