Define your constitutive model. This process involves two tasks:
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).
Mechanical APDL offers the following model-fitting categtories:
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-Rivlin | 2, 3, 5, 9 | 2 / 3 / 5 / 9 + 1 |
Polynomial | 1 to N | See below.[b] |
Yeoh | 1 to N | N +
N |
Neo-Hookean | - | 1 + 1 |
Ogden | 1 to N | 2 * N +
N |
Arruda-Boyce | - | 2 + 1 |
Gent | - | 2 + 1 |
Blatz-Ko[c] | - | 1 |
Ogden Hyperfoam[d] | 1 to N | 2 * 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 Test | Engineering Strain | Engineering Stress | -- |
Biaxial Test | Engineering Strain | Engineering Stress | -- |
Planar/Shear Test | Engineering Strain (in loading direction) | Engineering Stress | -- |
Simple Shear Test | Engineering Shear Strain | Engineering Shear Stress | (Optional) Engineering Normal Stress (normal to the edge of shear stress) |
Volumetric Test | Volume Ratio (J) | Hydrostatic Pressure | -- |
Table 7.6: Experimental Details for Compressible Models
Experiment Type | Column 1 | Column 2 | Column 3 |
---|---|---|---|
Uniaxial Test | Engineering Strain | Lateral Direction Engineering Strain | Engineering Stress |
Biaxial Test | Engineering Strain | Engineering Strain (in thickness direction) | Engineering Stress |
Shear Test | Engineering Strain (in loading direction) | Engineering Strain (in thickness direction) | Engineering Stress |
Simple Shear Test | Engineering Shear Strain | Engineering Shear Stress | (Optional) Engineering Normal Stress (normal to the edge of shear stress) |
Volumetric Test | Volume 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 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 7.9: 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.
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] | ||
6 | UserMat with the default nonlinear option | TB,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 | Time | True Strain | True Stress | -- |
Table 7.13: Column Header Types and Abbreviations
Column Name | Abbreviation |
---|---|
Time | time |
Total Strain | epto |
True Stress | s |
Temperature | temp |
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.
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 |
2 | Creep | TB,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
Time | time |
Equivalent Creep Strain | creq |
Equivalent Creep Strain Rate | dcreq |
Equivalent Stress | seqv |
Temperature | temp |
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 Hardening | x | x | x | x | |
Time Hardening | x | x | x | x | |
Generalized Exponential | x | x | x | x | |
Generalized Graham | x | x | x | x | |
Generalized Blackburn | x | x | x | ||
Modified Time Hardening | x | x | x | x | |
Modified Strain Hardening | x | x | x | x | |
Generalized Garofalo | x | x | x | ||
Exponential Form | x | x | x | ||
Norton | x | x | x | ||
Combined Time Hardening | x | x | x | x | |
Prim+Sec Rational Polynomial | x | x | x | ||
Generalized Time Hardening | x | x | x | x |
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.
Table 7.18: Valid Material Models for Viscoelastic Parameter-Fitting
Index ID | Material Model | TB Command |
---|---|---|
1 | Isotropic Elasticity | TB,ELASTIC |
2 | Prony Series | TB,PRONY,,,,SHEA/BULK |
3 | Shift Function | TB,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 |
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 Type | Column 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 |