8.4. Modeling Material Nonlinearities

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A number of material-related factors can cause your structure's stiffness to change during the course of an analysis. Nonlinear stress-strain relationships of plastic, multilinear elastic, and hyperelastic materials will cause a structure's stiffness to change at different load levels (and, typically, at different temperatures). Creep, viscoplasticity, and viscoelasticity will give rise to nonlinearities that can be time-, rate-, temperature-, and stress-related. Swelling will induce strains that can be a function of temperature, time, neutron flux level (or some analogous quantity), and stress. Any of these kinds of material properties can be incorporated into an ANSYS analysis if you use appropriate element types. Nonlinear constitutive models (TB command, except for TB,FAIL) are not applicable for the ANSYS Professional program.

8.4.1. Nonlinear Materials

If a material displays nonlinear or rate-dependent stress-strain behavior, then you must use the TB family of commands [TB, TBTEMP, TBDATA, TBPT, TBCOPY, TBLIST, TBPLOT, TBDELE] (GUI path Main Menu> Preprocessor> Material Props> Material Models> Structural> Nonlinear) to define the nonlinear material property relationships in terms of a data table. The exact form of these commands varies depending on the type of nonlinear material behavior being defined. The different material behavior options are described briefly below. See Data Tables - Implicit Analysis in the Elements Reference for specific details for each material behavior type.

8.4.1.1. Plasticity

Most common engineering materials exhibit a linear stress-strain relationship up to a stress level known as the proportional limit. Beyond this limit, the stress-strain relationship will become nonlinear, but will not necessarily become inelastic. Plastic behavior, characterized by nonrecoverable strain, begins when stresses exceed the material's yield point. Because there is usually little difference between the yield point and the proportional limit, the ANSYS program assumes that these two points are coincident in plasticity analyses (see Figure 8.9: "Elastoplastic Stress-Strain Curve").

Plasticity is a nonconservative, path-dependent phenomenon. In other words, the sequence in which loads are applied and in which plastic responses occur affects the final solution results. If you anticipate plastic response in your analysis, you should apply loads as a series of small incremental load steps or time steps, so that your model will follow the load-response path as closely as possible. The maximum plastic strain is printed with the substep summary information in your output (Jobname.OUT).

Figure 8.9  Elastoplastic Stress-Strain Curve

The automatic time stepping feature [AUTOTS] (GUI path Main Menu> Solution> Analysis Type> Sol'n Control ( : Basic Tab) or Main Menu> Solution> Unabridged Menu> Load Step Opts> Time/Frequenc>Time and Substps) will respond to plasticity after the fact, by reducing the load step size after a load step in which a large number of equilibrium iterations was performed or in which a plastic strain increment greater than 15% was encountered. If too large a step was taken, the program will bisect and resolve using a smaller step size.

Other kinds of nonlinear behavior might also occur along with plasticity. In particular, large deflection and large strain geometric nonlinearities will often be associated with plastic material response. If you expect large deformations in your structure, you must activate these effects in your analysis with the NLGEOM command (GUI path Main Menu> Solution> Analysis Type> Sol'n Control ( : Basic Tab) or Main Menu> Solution> Unabridged Menu> Analysis Type> Analysis Options). For large strain analyses, material stress-strain properties must be input in terms of true stress and logarithmic strain.

8.4.1.1.1. Plastic Material Options

The available options for describing plasticity behavior are described in this section. Use the links in the following table to navigate to the appropriate section:

You may incorporate other options into the program by using User Programmable Features (see the Guide to ANSYS User Programmable Features).

Bilinear Kinematic Hardening. 

The Bilinear Kinematic Hardening (BKIN) option assumes the total stress range is equal to twice the yield stress, so that the Bauschinger effect is included (see Figure 8.11: "Bauschinger Effect"). This option is recommended for general small-strain use for materials that obey von Mises yield criteria (which includes most metals). It is not recommended for large-strain applications. You can combine the BKIN option with creep and Hill anisotropy options to simulate more complex material behaviors. See Material Model Combinations in the Elements Reference for the combination possibilities. Also, see Material Model Combinations in this chapter for sample input listings of material combinations. Stress-strain-temperature data are demonstrated in the following example. Figure 8.10: "Kinematic Hardening"(a) illustrates a typical display [TBPLOT] of bilinear kinematic hardening properties.

MPTEMP,1,0,500            ! Define temperatures for Young's modulus
MP,EX,1,12E6,-8E3         ! C0 and C1 terms for Young's modulus
TB,BKIN,1,2               ! Activate a data table
TBTEMP,0.0                ! Temperature = 0.0
TBDATA,1,44E3,1.2E6       ! Yield = 44,000; Tangent modulus = 1.2E6
TBTEMP,500                ! Temperature = 500
TBDATA,1,29.33E3,0.8E6    ! Yield = 29,330; Tangent modulus = 0.8E6
TBLIST,BKIN,1             ! List the data table
/XRANGE,0,0.01            ! X-axis of TBPLOT to extend from varepsilon=0 to 0.01
TBPLOT,BKIN,1             ! Display the data table

See the MPTEMP, MP, TB, TBTEMP, TBDATA, TBLIST, /XRANGE, and TBPLOT command descriptions for more information.

Figure 8.10  Kinematic Hardening

(a) Bilinear kinematic hardening, (b) Multilinear kinematic hardening

Figure 8.11  Bauschinger Effect

Multilinear Kinematic Hardening. 

The Multilinear Kinematic Hardening (KINH and MKIN) options use the Besseling model, also called the sublayer or overlay model, so that the Bauschinger effect is included. KINH is preferred for use over MKIN because it uses Rice's model where the total plastic strains remain constant by scaling the sublayers. KINH allows you to define more stress-strain curves (40 vs. 5), and more points per curve (20 vs. 5). Also, when KINH is used with LINK180, SHELL181, SHELL281, PLANE182, PLANE183, SOLID185, SOLID186, SOLID187, SOLSH190, BEAM188, BEAM189, SHELL208, and SHELL209, you can use TBOPT = 4 (or PLASTIC) to define the stress vs. plastic strain curve. For either option, if you define more than one stress-strain curve for temperature dependent properties, then each curve should contain the same number of points. The assumption is that the corresponding points on the different stress-strain curves represent the temperature dependent yield behavior of a particular sublayer. These options are not recommended for large-strain analyses. You can combine either of these options with the Hill anisotropy option to simulate more complex material behaviors. See Material Model Combinations in the Elements Reference for the combination possibilities. Also, see Material Model Combinations in this chapter for sample input listings of material combinations. Figure 8.10: "Kinematic Hardening"(b) illustrates typical stress-strain curves for the MKIN option.

A typical stress-strain temperature data input using KINH is demonstrated by this example.

TB,KINH,1,2,3                             ! Activate a data table
TBTEMP,20.0                               ! Temperature = 20.0
TBPT,,0.001,1.0                           ! Strain = 0.001, Stress = 1.0
TBPT,,0.1012,1.2                          ! Strain = 0.1012, Stress = 1.2
TBPT,,0.2013,1.3                          ! Strain = 0.2013, Stress = 1.3
TBTEMP,40.0                               ! Temperature = 40.0
TBPT,,0.008,0.9                           ! Strain = 0.008, Stress = 0.9
TBPT,,0.09088,1.0                         ! Strain = 0.09088, Stress = 1.0
TBPT,,0.12926,1.05                        ! Strain = 0.12926, Stress = 1.05

In this example, the third point in the two stress-strain curves defines the temperature-dependent yield behavior of the third sublayer.

A typical stress- plastic strain temperature data input using KINH is demonstrated by this example.

TB,KINH,1,2,3,PLASTIC                   ! Activate a data table
TBTEMP,20.0                             ! Temperature = 20.0
TBPT,,0.0,1.0                           ! Plastic Strain = 0.0000, Stress = 1.0
TBPT,,0.1,1.2                           ! Plastic Strain = 0.1000, Stress = 1.2
TBPT,,0.2,1.3                           ! Plastic Strain = 0.2000, Stress = 1.3
TBTEMP,40.0                             ! Temperature = 40.0
TBPT,,0.0,0.9                           ! Plastic Strain = 0.0000, Stress = 0.9
TBPT,,0.0900,1.0                        ! Plastic Strain = 0.0900, Stress = 1.0
TBPT,,0.129,1.05                        ! Plastic Strain = 0.1290, Stress = 1.05

Alternatively, the same plasticity model can also be defined using TB, PLASTIC, as follows:

TB,PLASTIC,1,2,3,KINH                  ! Activate a data table
TBTEMP,20.0                            ! Temperature = 20.0
TBPT,,0.0,1.0                          ! Plastic Strain = 0.0000, Stress = 1.0
TBPT,,0.1,1.2                          ! Plastic Strain = 0.1000, Stress = 1.2
TBPT,,0.2,1.3                          ! Plastic Strain = 0.2000, Stress = 1.3
TBTEMP,40.0                            ! Temperature = 40.0
TBPT,,0.0,0.9                          ! Plastic Strain = 0.0000, Stress = 0.9
TBPT,,0.0900,1.0                       ! Plastic Strain = 0.0900, Stress = 1.0
TBPT,,0.129,1.05                       ! Plastic Strain = 0.1290, Stress = 1.05

In this example, the stress - strain behavior is the same as the previous sample, except now the strain value is the plastic strain. The plastic strain can be converted from total strain as follows:

Plastic Strain = Total Strain - (Stress/Young's Modulus).

A typical stress-strain temperature data input using MKIN is demonstrated by this example.

MPTEMP,1,0,500                             ! Define temperature-dependent EX,
MP,EX,1,12E6,-8E3                          ! as in BKIN example
TB,MKIN,1,2                                ! Activate a data table
TBTEMP,,STRAIN                             ! Next TBDATA values are strains
TBDATA,1,3.67E-3,5E-3,7E-3,10E-3,15E-3     ! Strains for all temps
TBTEMP,0.0                                 ! Temperature = 0.0
TBDATA,1,44E3,50E3,55E3,60E3,65E3          ! Stresses at temperature = 0.0
TBTEMP,500                                 ! Temperature = 500
TBDATA,1,29.33E3,37E3,40.3E3,43.7E3,47E3   ! Stresses at temperature = 500
/XRANGE,0,0.02
TBPLOT,MKIN,1

Please see the MPTEMP, MP, TB, TBPT, TBTEMP, TBDATA, /XRANGE, and TBPLOT command descriptions for more information.

Nonlinear Kinematic Hardening. 

The Nonlinear Kinematic Hardening (CHABOCHE) option uses the Chaboche model, which is a multi-component nonlinear kinematic hardening model that allows you to superpose several kinematic models. See the Theory Reference for ANSYS and ANSYS Workbench for details. Like the BKIN and MKIN options, you can use the CHABOCHE option to simulate monotonic hardening and the Bauschinger effect. This option also allows you to simulate the ratcheting and shakedown effect of materials. By combining the CHABOCHE option with isotropic hardening model options BISO, MISO, and NLISO, you have the further capability of simulating cyclic hardening or softening. You can also combine this option with the Hill anisotropy option to simulate more complex material behaviors. See Material Model Combinations in the Elements Reference for the combination possibilities. Also, see Material Model Combinations in this chapter for sample input listings of material combinations. The model has 1 + 2 x n constants, where n is the number of kinematic models, and is defined by NPTS in the TB command. See the Theory Reference for ANSYS and ANSYS Workbench for details. You define the material constants using the TBTEMP and TBDATA commands. This model is suitable for large strain analysis.

The following example is a typical data table with no temperature dependency and one kinematic model:

TB,CHABOCHE,1             ! Activate CHABOCHE data table
TBDATA,1,C1,C2,C3         ! Values for constants C1, C2, and C3

The following example illustrates a data table of temperature dependent constants with two kinematic models at two temperature points:

TB,CHABOCHE,1,2,2                ! Activate CHABOCHE data table
TBTEMP,100                       ! Define first temperature
TBDATA,1,C11,C12,C13,C14,C15     ! Values for constants C11, C12, C13,
                                 ! C14, and C15 at first temperature
TBTEMP,200                       ! Define second temperature
TBDATA,1,C21,C22,C23,C24,C25     ! Values for constants C21, C22, C23,
                                 ! C24, and C25 at second temperature

Please see the TB, TBTEMP, and TBDATA command descriptions for more information.

Bilinear Isotropic Hardening. 

The Bilinear Isotropic Hardening (BISO) option uses the von Mises yield criteria coupled with an isotropic work hardening assumption. This option is often preferred for large strain analyses. You can combine BISO with Chaboche, creep, viscoplastic, and Hill anisotropy options to simulate more complex material behaviors. See Material Model Combinations in the Elements Reference for the combination possibilities. Also, see Material Model Combinations in this chapter for sample input listings of material combinations.

Multilinear Isotropic Hardening. 

The Multilinear Isotropic Hardening (MISO) option is like the bilinear isotropic hardening option, except that a multilinear curve is used instead of a bilinear curve. This option is not recommended for cyclic or highly nonproportional load histories in small-strain analyses. It is, however, recommended for large strain analyses. The MISO option can contain up to 20 different temperature curves, with up to 100 different stress-strain points allowed per curve. Strain points can differ from curve to curve. You can combine this option with nonlinear kinematic hardening (CHABOCHE) for simulating cyclic hardening or softening. You can also combine the MISO option with creep, viscoplastic, and Hill anisotropy options to simulate more complex material behaviors. See Material Model Combinations in the Elements Reference for the combination possibilities. Also, see Material Model Combinations in this chapter for sample input listings of material combinations. The stress-strain-temperature curves from the MKIN example would be input for a multilinear isotropic hardening material as follows:

/prep7
MPTEMP,1,0,500               ! Define temperature-dependent EX,
MPDATA,EX,1,,14.665E6,12.423e6           
MPDATA,PRXY,1,,0.3

TB,MISO,1,2,5                ! Activate a data table
TBTEMP,0.0                   ! Temperature = 0.0
TBPT,DEFI,2E-3,29.33E3    ! Strain, stress at temperature = 0
TBPT,DEFI,5E-3,50E3
TBPT,DEFI,7E-3,55E3
TBPT,DEFI,10E-3,60E3
TBPT,DEFI,15E-3,65E3
TBTEMP,500                   ! Temperature = 500
TBPT,DEFI,2.2E-3,27.33E3    ! Strain, stress at temperature = 500
TBPT,DEFI,5E-3,37E3
TBPT,DEFI,7E-3,40.3E3
TBPT,DEFI,10E-3,43.7E3
TBPT,DEFI,15E-3,47E3
/XRANGE,0,0.02
TBPLOT,MISO,1

Alternatively, the same plasticity model can also be defined using TB, PLASTIC, as follows:

/prep7
MPTEMP,1,0,500               ! Define temperature-dependent EX,
MPDATA,EX,1,,14.665E6,12.423e6           
MPDATA,PRXY,1,,0.3
 
TB,PLASTIC,1,2,5,MISO        ! Activate TB,PLASTIC data table
TBTEMP,0.0                   ! Temperature = 0.0
TBPT,DEFI,0,29.33E3          ! Plastic strain, stress at temperature = 0
TBPT,DEFI,1.59E-3,50E3
TBPT,DEFI,3.25E-3,55E3
TBPT,DEFI,5.91E-3,60E3
TBPT,DEFI,1.06E-2,65E3
TBTEMP,500                   ! Temperature = 500
TBPT,DEFI,0,27.33E3          ! Plastic strain, stress at temperature = 500
TBPT,DEFI,2.02E-3,37E3
TBPT,DEFI,3.76E-3,40.3E3
TBPT,DEFI,6.48E-3,43.7E3
TBPT,DEFI,1.12E-2,47E3
/XRANGE,0,0.02
TBPLOT,PLASTIC,1

See the MPTEMP, MP, TB, TBTEMP, TBPT, /XRANGE, and TBPLOT command descriptions for more information.

Nonlinear Isotropic Hardening. 

The Nonlinear Isotropic Hardening (NLISO) option is based on either the Voce hardening law or the power law (see the Theory Reference for ANSYS and ANSYS Workbench for details). The NLISO Voce hardening option is a variation of BISO where an exponential saturation hardening term is appended to the linear term (see Figure 8.12: "NLISO Stress-Strain Curve").

Figure 8.12  NLISO Stress-Strain Curve

The advantage of this model is that the material behavior is defined as a specified function which has four material constants that you define through the TBDATA command. You can obtain the material constants by fitting material tension stress-strain curves. Unlike MISO, there is no need to be concerned about how to appropriately define the pairs of the material stress-strain points. However, this model is only applicable to the tensile curve like the one shown in Figure 8.12: "NLISO Stress-Strain Curve". This option is suitable for large strain analyses. You can combine NLISO with Chaboche, creep, viscoplastic, and Hill anisotropy options to simulate more complex material behaviors. See Material Model Combinations in the Elements Reference for the combination possibilities. Also, see Material Model Combinations in this chapter for sample input listings of material combinations.

The following example illustrates a data table of temperature dependent constants at two temperature points:

TB,NLISO,1                       ! Activate NLISO data table
TBTEMP,100                       ! Define first temperature
TBDATA,1,C11,C12,C13,C14         ! Values for constants C11, C12, C13,
                                 ! C14 at first temperature
TBTEMP,200                       ! Define second temperature
TBDATA,1,C21,C22,C23,C24         ! Values for constants C21, C22, C23,
                                 ! C24 at second temperature

Please see the TB, TBTEMP, and TBDATA command descriptions for more information.

Anisotropic. 

The Anisotropic (ANISO) option allows for different bilinear stress-strain behavior in the material x, y, and z directions as well as different behavior in tension, compression, and shear. This option is applicable to metals that have undergone some previous deformation (such as rolling). It is not recommended for cyclic or highly nonproportional load histories since work hardening is assumed. The yield stresses and slopes are not totally independent (see the Theory Reference for ANSYS and ANSYS Workbench for details).

To define anisotropic material plasticity, use MP commands (Main Menu> Solution> Load Step Opts> Other> Change Mat Props) to define the elastic moduli (EX, EY, EZ, NUXY, NUYZ, and NUXZ). Then, issue the TB command [TB,ANISO] followed by TBDATA commands to define the yield points and tangent moduli. (See Nonlinear Stress-Strain Materials in the Elements Reference for more information.)

Hill Anisotropy. 

The Hill Anisotropy (HILL) option, when combined with other material options simulates plasticity, viscoplasticity, and creep - all using the Hill potential. See Material Model Combinations in the Elements Reference for the combination possibilities. Also, see Material Model Combinations in this chapter for sample input listings of material combinations. The Hill potential may only be used with the following elements: PLANE42, SOLID45, PLANE82, SOLID92, SOLID95, LINK180, SHELL181, SHELL281, PLANE182, PLANE183, SOLID185, SOLID186, SOLID187, SOLSH190, BEAM188, BEAM189, SHELL208, and SHELL209.

Drucker-Prager. 

The Drucker-Prager (DP) option is applicable to granular (frictional) material such as soils, rock, and concrete, and uses the outer cone approximation to the Mohr-Coulomb law.

MP,EX,1,5000
MP,NUXY,1,0.27
TB,DP,1
TBDATA,1,2.9,32,0    ! Cohesion = 2.9 (use consistent units),
                     ! Angle of internal friction = 32 degrees,
                     ! Dilatancy angle = 0 degrees

See the MP, TB, and TBDATA command descriptions for more information.

Extended Drucker Prager. 

The Extended Drucker Prager (EDP) option is also available for granular materials. This option allows you to specify both the yield functions and the flow potentials using the complex expressions defined in Extended Drucker-Prager the Elements Reference.

!Extended DP Material Definition
/prep7
mp,ex,1,2.1e4
mp,nuxy,1,0.45

!Linear Yield Function
tb,edp,1,,,LYFUN          
tbdata,1,2.2526,7.894657


!Linear Plastic Flow Potential
tb,edp,1,,,LFPOT          
tbdata,1,0.566206

tblist,all,all

See the EDP argument and associated specifications in the TB command, the Extended Drucker-Prager in the Elements Reference and also The Extended Drucker-Prager Model in the Theory Reference for ANSYS and ANSYS Workbench for more information.

Gurson Plasticity. 

The Gurson Plasticity (GURSON) option is used to model porous metals. This option allows you to incorporate microscopic material behaviors, such as void dilatancy, void nucleation, and void coalescence into macroscopic plasticity models. The microscopic behaviors of voids are described using the porosity variables defined in Gurson's Model in the Elements Reference

!The Gurson PLASTICITY Material Definition
/prep7
!!! define linear elasticity constants
mp,ex,1,2.1e4	! Young modulus
mp,nuxy,1,0.3	! Poison ratio
    !!! define parameters related to Gurson model with
!!! the option of strain controlled nucleation with
!!! coalescence (COA1)
f_0=0.005          ! initial porosity
q1=1.5             ! first Tvergaard constant
q2=1.0             ! second Tvergaard constant
f_c=0.15           ! critical porosity
f_F=0.20           ! failure porosity
f_N=0.04           ! nucleation porosity
s_N=0.1            ! standard deviation of mean strain
strain_N=0.3       ! mean strain
sigma_Y=50.0       ! initial yielding strength
power_N=0.1        ! power value for nonlinear isotropic 
                   ! hardening power law (POWE)
!!! define Gurson material
tb,GURS,1,,8,COA1                            
tbdata,1,f_0,q1,q2,f_c,f_F
tbdata,6,f_N,s_N,strain_N
tb,nliso,1,,2,POWE
tbdata,,sigma_Y,power_N
tblist,all,all

See the GURSON argument and associated specifications in the TB command, and also Gurson's Model in the Theory Reference for ANSYS and ANSYS Workbench for more information.

Cast Iron. 

The Cast Iron (CAST, UNIAXIAL) option assumes a modified von Mises yield surface, which consists of the von Mises cylinder in compression and a Rankine cube in tension. It has different yield strengths, flows, and hardenings in tension and compression. Elastic behavior is isotropic, and is the same in tension and compression. The TB,CAST command is used to input the plastic Poisson's ration in tension, which can be temperature dependent. Use the TB,UNIAXIAL command to enter the yield and hardening in tension and compression.

Note

Cast Iron is intended for monotonic loading only and cannot be used with any other material model.

TB,CAST,1,,,ISOTROPIC
TBDATA,1,0.04

TB,UNIAXIAL,1,1,5,TENSION
TBTEMP,10
TBPT,,0.550E-03,0.813E+04
TBPT,,0.100E-02,0.131E+05
TBPT,,0.250E-02,0.241E+05
TBPT,,0.350E-02,0.288E+05
TBPT,,0.450E-02,0.322E+05

TB,UNIAXIAL,1,1,5,COMPRESSION
TBTEMP,10
TBPT,,0.203E-02,0.300E+05
TBPT,,0.500E-02,0.500E+05
TBPT,,0.800E-02,0.581E+05
TBPT,,0.110E-01,0.656E+05
TBPT,,0.140E-01,0.700E+05

Figure 8.13: "Cast Iron Plasticity" illustrates the idealized response of gray cast iron in tension and compression.

Figure 8.13  Cast Iron Plasticity

See the TB and TBPT command descriptions for more information.

8.4.1.2. Multilinear Elasticity

The Multilinear Elastic (MELAS) material behavior option describes a conservative (path-independent) response in which unloading follows the same stress-strain path as loading. Thus, relatively large load steps might be appropriate for models that incorporate this type of material nonlinearity. Input format is similar to that required for the multilinear isotropic hardening option, except that the TB command now uses the label MELAS.

8.4.1.3. User Defined Material

The User Defined (USER) material option describes input parameters for defining a material model based on either of two subroutines, which are ANSYS user-programmable features (see the Guide to ANSYS User Programmable Features). The choice of which subroutine to use is based on which element you are using.

The USER option works with the USERMAT subroutine in defining any material model (except incompressible materials), when you use any of the following elements: LINK180, SHELL181, SHELL281, PLANE182, PLANE183, SOLID185, SOLID186, SOLID187, SOLSH190, BEAM188, BEAM189, SHELL208, and SHELL209.

The USER option works with the USERPL subroutine in defining plasticity or viscoplasticity material models, when you use any of the following elements: LINK1, LINK8, PIPE20, BEAM23, BEAM24, PLANE42, SHELL43, SOLID45, PIPE60, SOLID62, SOLID65, PLANE82, SHELL91, SOLID92, SHELL93, SOLID95, and PLANE183.

To access the user material option, issue the TB,USER command to define the material number, the number of temperatures, and the number of data points. Then define the temperatures and material constants using the TBTEMP and TBDATA commands.

The following example illustrates defining a material with two temperatures and four data points:

TB,USER,1,2,4                    ! Define material 1 as user
                                 ! material with 2 
                                 ! temperatures and 4 data                                
                                 ! points at each
                                 ! temperature point.
TBTEMP,1.0                       ! First temperature.
TBDATA,1,19e5,0.3,1e3,100,       ! 4 material constants for
                                 ! first temperature.
TBTEMP,2.0                       ! Second temperature.
TBDATA,1,21e5,0.3,2e3,100,       ! 4 material constants for
                                 ! second temperature.

If you use state variables in the USERMAT subroutine, you must first define the number of state variables using the TB,STATE command. You then use the TBDATA command to initialize the value of the state variables, as shown in the following example:

TB,STATE,1,,4,                   ! Define material 1, which
                                 ! has 4 state variables. 
TBDATA,1,C1,C2,C3,C4,            ! Initialize the 4 state variables.

You cannot use TB,STATE in the USERPL subroutine.

See the TB, and TBDATA command descriptions for more information.

8.4.1.4. Hyperelasticity

A material is said to be hyperelastic if there exists an elastic potential function (or strain energy density function), which is a scalar function of one of the strain or deformation tensors, whose derivative with respect to a strain component determines the corresponding stress component.

Hyperelasticity can be used to analyze rubber-like materials (elastomers) that undergo large strains and displacements with small volume changes (nearly incompressible materials). Large strain theory is required [NLGEOM,ON]. A representative hyperelastic structure (a balloon seal) is shown in Figure 8.14: "Hyperelastic Structure".

Figure 8.14  Hyperelastic Structure

All of the 18x family of elements except the link and beam elements are suitable for simulating hyperelastic materials (SHELL181, PLANE182, PLANE183, SOLID185, SOLID186, SOLID187, SOLSH190, SHELL208, and SHELL209). For more information, see Mixed u-P Formulation Elements in the Elements Reference.

The material response in ANSYS hyperelastic models can be either isotropic or anisotropic, and it is assumed to be isothermal. Because of this assumption, the strain energy potentials are expressed in terms of strain invariants. Unless indicated otherwise, the hyperelastic materials are also assumed to be nearly or purely incompressible. Material thermal expansion is also assumed to be isotropic.

ANSYS supports several options of strain energy potentials for the simulation of incompressible or nearly incompressible hyperelastic materials. All options are applicable to elements SHELL181, SHELL281, PLANE182, PLANE183, SOLID185, SOLID186, SOLID187, SOLSH190, SHELL208, and SHELL209. Access these options through the TBOPT argument of TB,HYPER.

One of the options, the Mooney-Rivlin option, is also applicable to explicit dynamics elements PLANE162, SHELL163, SOLID164, and SOLID168. To access the Mooney-Rivlin option for these elements, use TB,MOONEY.

ANSYS provides tools to help you determine the coefficients for all of the hyperelastic options defined by TB,HYPER. The TBFT command allows you to compare your experimental data with existing material data curves and visually “fit” your curve for use in the TB command. All of the TBFT command capability is available via either batch or interactive (GUI) mode. See Material Curve Fitting (also in this manual) for more information.

Each of the hyperelastic options is presented in the following sections.

8.4.1.4.1. Mooney-Rivlin Hyperelastic Option (TB,HYPER)

Note that this section applies to using the Mooney-Rivlin option with elements SHELL181, SHELL281, PLANE182, PLANE183, SOLID185, SOLID186, SOLID187, SOLSH190, SHELL208, and SHELL209.

The Mooney-Rivlin option (TB,HYPER,,,,MOONEY), which is the default, allows you to define 2, 3, 5, or 9 parameters through the NPTS argument of the TB command. For example, to define a 5 parameter model you would issue TB,HYPER,1,,5,MOONEY.

The 2 parameter Mooney-Rivlin option has an applicable strain of about 100% in tension and 30% in compression. Compared to the other options, higher orders of the Mooney-Rivlin option may provide better approximation to a solution at higher strain.

The following example input listing shows a typical use of the Mooney-Rivlin option with 3 parameters:

TB,HYPER,1,,3,MOONEY     !Activate 3 parameter Mooney-Rivlin data table
TBDATA,1,0.163498        !Define c10
TBDATA,2,0.125076        !Define c01
TBDATA,3,0.014719        !Define c11
TBDATA,4,6.93063E-5      !Define incompressibility parameter
                         !(as 2/K, K is the bulk modulus)

Refer to Mooney-Rivlin Hyperelastic Material (TB,HYPER) in the Elements Reference for a description of the material constants required for this option.

8.4.1.4.2. Ogden Hyperelastic Option

The Ogden option (TB,HYPER,,,,OGDEN) allows you to define an unlimited number of parameters through the NPTS argument of the TB command. For example, to define a 3 parameter model, use TB,HYPER,1,,3,OGDEN.

Compared to the other options, the Ogden option usually provides the best approximation to a solution at larger strain levels. The applicable strain level can be up to 700%. A higher parameter value can provide a better fit to the exact solution. It may however cause numerical difficulties in fitting the material constants, and it requires enough data to cover the whole range of deformation for which you may be interested. For these reasons, a high parameter value is not recommended.

The following example input listing shows a typical use of the Ogden option with 2 parameters:

TB,HYPER,1,,2,OGDEN      !Activate 2 parameter Ogden data table
TBDATA,1,0.326996        !Define μ1
TBDATA,2,2               !Define α1
TBDATA,3,-0.250152       !Define μ2
TBDATA,4,-2              !Define α2
TBDATA,5,6.93063E-5      !Define incompressibility parameter
                         !(as 2/K, K is the bulk modulus)
                         !(Second incompressibility parameter d2 is zero)

Refer to Ogden Hyperelastic Material Constants in the Elements Reference for a description of the material constants required for this option.

8.4.1.4.3. Neo-Hookean Hyperelastic Option

The Neo-Hookean option (TB,HYPER,,,,NEO) represents the simplest form of strain energy potential, and has an applicable strain range of 20-30%.

An example input listing showing a typical use of the Neo-Hookean option is presented below.

TB,HYPER,1,,,NEO         !Activate Neo-Hookean data table
TBDATA,1,0.577148        !Define mu shear modulus
TBDATA,2,7.0e-5          !Define incompressibility parameter
                         !(as 2/K, K is the bulk modulus)

Refer to Neo-Hookean Hyperelastic Material in the Elements Reference for a description of the material constants required for this option.

8.4.1.4.4. Polynomial Form Hyperelastic Option

The polynomial form option (TB,HYPER,,,,POLY) allows you to define an unlimited number of parameters through the NPTS argument of the TB command. For example, to define a 3 parameter model you would issue TB,HYPER,1,,3,POLY.

Similar to the higher order Mooney-Rivlin options, the polynomial form option may provide a better approximation to a solution at higher strain.

For NPTS = 1 and constant c01 = 0, the polynomial form option is equivalent to the Neo-Hookean option (see Neo-Hookean Hyperelastic Option for a sample input listing). Also, for NPTS = 1, it is equivalent to the 2 parameter Mooney-Rivlin option. For NPTS = 2, it is equivalent to the 5 parameter Mooney-Rivlin option, and for NPTS = 3, it is equivalent to the 9 parameter Mooney-Rivlin option (see Mooney-Rivlin Hyperelastic Option (TB,HYPER) for a sample input listing).

Refer to Polynomial Form Hyperelastic Material Constants in the Elements Reference for a description of the material constants required for this option.

8.4.1.4.5. Arruda-Boyce Hyperelastic Option

The Arruda-Boyce option (TB,HYPER,,,,BOYCE) has an applicable strain level of up to 300%.

An example input listing showing a typical use of the Arruda-Boyce option is presented below.

TB,HYPER,1,,,BOYCE      !Activate Arruda-Boyce data table
TBDATA,1,200.0           !Define initial shear modulus
TBDATA,2,5.0             !Define limiting network stretch
TBDATA,3,0.001           !Define incompressibility parameter
                         !(as 2/K, K is the bulk modulus)

Refer to Arruda-Boyce Hyperelastic Material Constants in the Elements Reference for a description of the material constants required for this option.

8.4.1.4.6. Gent Hyperelastic Option

The Gent option (TB,HYPER,,,,GENT) has an applicable strain level of up to 300%.

An example input listing showing a typical use of the Gent option is presented below.

TB,HYPER,1,,,GENT      !Activate Gent data table
TBDATA,1,3.0            !Define initial shear modulus
TBDATA,2,42.0           !Define limiting I1 - 3
TBDATA,3,0.001          !Define incompressibility parameter
                        !(as 2/K, K is the bulk modulus)

Refer to Gent Hyperelastic Material Constants in the Elements Reference for a description of the material constants required for this option.

8.4.1.4.7. Yeoh Hyperelastic Option

The Yeoh option (TB,HYPER,,,,YEOH) is a reduced polynomial form of the hyperelasticity option TB,HYPER,,,,POLY. An example of a 2 term Yeoh model is TB,HYPER,1,,2,YEOH.

Similar to the polynomial form option, the higher order terms may provide a better approximation to a solution at higher strain.

For NPTS = 1, the Yeoh form option is equivalent to the Neo-Hookean option (see Neo-Hookean Hyperelastic Option for a sample input listing).

The following example input listing shows a typical use of the Yeoh option with 2 terms and 1 incompressibility term:

TB,HYPER,1,,2,YEOH      !Activate 2 term Yeoh data table
TBDATA,1,0.163498            !Define C1
TBDATA,2,0.125076            !Define C2
TBDATA,3,6.93063E-5          !Define first incompressibility parameter

Refer to Yeoh Hyperelastic Material Constants in the Elements Reference for a description of the material constants required for this option.

8.4.1.4.8. Blatz-Ko Foam Hyperelastic Option

The Blatz-Ko option (TB,HYPER,,,,BLATZ) is the simplest option for simulating the compressible foam type of elastomer. This option is analogous to the Neo-Hookean option of incompressible hyperelastic materials.

An example input listing showing a typical use of the Blatz-Ko option is presented below.

TB,HYPER,1,,,BLATZ      !Activate Blatz-Ko data table
TBDATA,1,5.0            !Define initial shear modulus

Refer to Blatz-Ko Foam Hyperelastic Material Constants in the Elements Reference for a description of the material constants required for this option.

8.4.1.4.9. Ogden Compressible Foam Hyperelastic Option

The Ogden compressible foam option (TB,HYPER,,,,FOAM) simulates highly compressible foam material. An example of a 3 parameter model is TB,HYPER,1,,3,FOAM. Compared to the Blatz-Ko option, the Ogden foam option usually provides the best approximation to a solution at larger strain levels. The higher the number of parameters, the better the fit to the experimental data. It may however cause numerical difficulties in fitting the material constants, and it requires sufficient data to cover the whole range of deformation for which you may be interested. For these reasons, a high parameter value is not recommended.

The following example input listing shows a typical use of the Ogden foam option with 2 parameters:

TB,HYPER,1,,2,FOAM      !Activate 2 parameter Ogden foam data table
TBDATA,1,1.85              !Define μ1
TBDATA,2,4.5               !Define α1
TBDATA,3,-9.20             !Define μ2
TBDATA,4,-4.5              !Define α2
TBDATA,5,0.92              !Define first compressibility parameter
TBDATA,6,0.92              !Define second compressibility parameter

Refer to Ogden Compressible Foam Hyperelastic Material Constants in the Elements Reference for a description of the material constants required for this option.

8.4.1.4.10. User-Defined Hyperelastic Option

The User option (TB,HYPER,,,,USER) allows you to use the subroutine USERHYPER to define the derivatives of the strain energy potential with respect to the strain invariants. Refer to the Guide to ANSYS User Programmable Features for a detailed description on writing a user hyperelasticity subroutine.

8.4.1.5. Anisotropic Hyperelasticity

You can use anisotropic hyperelasticity to model the directional differences in material behavior. This is especially useful when modeling elastomers with reinforcements, or for biomedical materials such as muscles or arteries. You use the format TB,AHYPER,,,,TBOPT to define the material behavior.

The TBOPT field allows you to specify the isochoric part, the material directions and the volumetric part for the material simulation. You must define one single TB table for each option.

You can enter temperature dependent data for anisotropic hyperelastic material with the TBTEMP command. For the first temperature curve, you issue TB, AHYPER,,,TBOPT, then input the first temperature using the TBTEMP command. The subsequent TBDATA command inputs the data.

See the TB command, and Anisotropic Hyperelasticity in the Theory Reference for ANSYS and ANSYS Workbench for more information.

The following example shows the definintion of material constants for an anisotropic hyperelastic material option.

! defininig material constants for anistoropic hyperelastic option 
tb,ahyper,1,1,31,poly
!a1,a2,a3
tbdata,1,10,2,0.1
b1,b2,b3
tbdata,4,5,1,0.1
!c1,c2,c3,c4,c5,c6
tbdata,7,1,0.02,0.002,0.001,0.0005
!d2,d3,d4,d5,d6
tbdata,12,1,0.02,0.002,0.001,0.0005
!e1,e2,e3,e4,e5,e6
tbdata,17,1,0.02,0.002,0.001,0.0005
f1,f2,f3,f4,f5,f6
tbdata,22,1,0.02,0.002,0.001,0.0005
g1,g2,g3,g4,g5,g6
tbdata,22,1,0.02,0.002,0.001,0.0005

!compressibility parameter d
tb,ahyper,1,1,1,pvol
tbdata,1,1e-3

!orientation vector A=A(x,y,z)
tb,ahyper,1,1,3,avec
tbdata,1,1,0,0
!orientation vector B=B(x,y,z)
tb,ahyper,1,1,3,bvec
tbdata,1,1/sqrt(2),1/sqrt(2),0

8.4.1.6. Creep

Creep is a rate dependent material nonlinearity in which the material continues to deform under a constant load. Conversely, if a displacement is imposed, the reaction force (and stresses) will diminish over time (stress relaxation; see Figure 8.15: "Stress Relaxation and Creep"(a)). The three stages of creep are shown in Figure 8.15: "Stress Relaxation and Creep"(b). The ANSYS program has the capability of modeling the first two stages (primary and secondary). The tertiary stage is usually not analyzed since it implies impending failure.

Figure 8.15  Stress Relaxation and Creep

Creep is important in high temperature stress analyses, such as for nuclear reactors. For example, suppose you apply a preload to some part in a nuclear reactor to keep adjacent parts from moving. Over a period of time at high temperature, the preload would decrease (stress relaxation) and potentially let the adjacent parts move. Creep can also be significant for some materials such as prestressed concrete. Typically, the creep deformation is permanent.

ANSYS analyzes creep using two time integration methods. Both are applicable to static or transient analyses.The implicit creep method is robust, fast, accurate, and recommended for general use. It can handle temperature dependent creep constants, as well as simultaneous coupling with isotropic hardening plasticity models. The explicit creep method is useful for cases where very small time steps are required. Creep constants cannot be dependent on temperature. Coupling with other plastic models is available by superposition only.

Note

The terms “implicit” and “explicit” as applied to creep, have no relationship to “explicit dynamics,” or any elements referred to as “explicit elements.”

The implicit creep method supports the following elements: PLANE42, SOLID45, PLANE82, SOLID92, SOLID95, LINK180, SHELL181, SHELL281, PLANE182, PLANE183, SOLID185, SOLID186, SOLID187, SOLSH190, BEAM188, BEAM189, SHELL208, and SHELL209.

The explicit creep method supports the following elements: LINK1, LINK8, PIPE20, BEAM23, BEAM24, PLANE42, SHELL43, SOLID45, PIPE60, SOLID62, SOLID65, PLANE82, SOLID92, SOLID95, and PLANE183.

The creep strain rate may be a function of stress, strain, temperature, and neutron flux level. Libraries of creep strain rate equations are built into the ANSYS program for primary, secondary, and irradiation induced creep. (See Creep Equations in the Elements Reference for discussions of, and input procedures for, these various creep equations.) Some equations require specific units. In particular, for the explicit creep option, temperatures used in the creep equations should be based on an absolute scale.

8.4.1.6.1. Implicit Creep Procedure

The basic procedure for using the implicit creep method involves issuing the TB command with Lab = CREEP, and choosing a creep equation by specifying a value for TBOPT. The following example input shows the use of the implicit creep method. TBOPT = 2 specifies that the primary creep equation for model 2 will be used. Temperature dependency is specified using the TBTEMP command, and the four constants associated with this equation are specified as arguments with the TBDATA command.

TB,CREEP,1,1,4,2
TBTEMP,100
TBDATA,1,C1,C2,C3,C4

You can input other creep expressions using the user programmable feature and setting TBOPT = 100. You can define the number of state variables using the TB command with Lab = STATE. The following example shows how five state variables are defined.

TB,STATE,1,,5

You can simultaneously model creep [TB,CREEP] and isotropic, bilinear kinematic, and Hill anisotropy options to simulate more complex material behaviors. See Material Model Combinations in the Elements Reference for the combination possibilities. Also, see Material Model Combinations in this chapter for sample input listings of material combinations.

To perform an implicit creep analysis, you must also issue the solution RATE command, with Option = ON (or 1). The following example shows a procedure for a time hardening creep analysis (See Figure 8.16: "Time Hardening Creep Analysis").

Figure 8.16  Time Hardening Creep Analysis

The user applied mechanical loading in the first load step, and turned the RATE command OFF to bypass the creep strain effect. Since the time period in this load step will affect the total time thereafter, the time period for this load step should be small. For this example, the user specified a value of 1.0E-8 seconds. The second load step is a creep analysis. The RATE command must be turned ON. Here the mechanical loading was kept constant, and the material creeps as time increases.

/SOLU                 !First load step, apply mechanical loading
RATE,OFF              !Creep analysis turned off
TIME,1.0E-8           !Time period set to a very small value
...
SOLV                  !Solve this load step
                      !Second load step, no further mechanical load
RATE,ON               !Creep analysis turned on
TIME,100              !Time period set to desired value
...
SOLV                  !Solve this load step

The RATE command works only when modeling implicit creep with either von Mises or Hill potentials.

When modeling implicit creep with von Mises potential, you can use the RATE command with the following elements: LINK180, SHELL181, SHELL281, PLANE182, PLANE183, SOLID185, SOLID186, SOLID187, SOLSH190, BEAM188, BEAM189, SHELL208, and SHELL209.

When modeling anisotropic creep (TB,CREEP with TB,HILL), you can use the RATE command with the following elements: PLANE42, SOLID45, PLANE82, SOLID92, SOLID95, LINK180, SHELL181, SHELL281, PLANE182, PLANE183, SOLID185, SOLID186, SOLID187, SOLSH190, BEAM188, BEAM189, SHELL208, and SHELL209.

For most materials, the creep strain rate changes significantly at an early stage. Because of this, a general recommendation is to use a small initial incremental time step, then specify a large maximum incremental time step by using solution command DELTIM or NSUBST. For implicit creep, you may need to examine the effect of the time increment on the results carefully because ANSYS does not enforce any creep ratio control by default. You can always enforce a creep limit ratio using the creep ratio control option in commands CRPLIM or CUTCONTROL,CRPLIMIT. A recommended value for a creep limit ratio ranges from 1 to 10. The ratio may vary with materials so your decision on the best value to use should be based on your own experimentation to gain the required performance and accuracy. For larger analyses, a suggestion is to first perform a time increment convergence analysis on a simple small size test.

ANSYS provides tools to help you determine the coefficients for all of the implicit creep options defined in TB,CREEP. The TBFT command allows you to compare your experimental data with existing material data curves and visually “fit” your curve for use in the TB command. All of the TBFT command capability is available via either batch or interactive (GUI) mode. See Material Curve Fitting (also in this manual) for more information.

8.4.1.6.2. Explicit Creep Procedure

The basic procedure for using the explicit creep method involves issuing the TB command with Lab = CREEP and choosing a creep equation by adding the appropriate constant as an argument with the TBDATA command. TBOPT is either left blank or = 0. The following example input uses the explicit creep method. Note that all constants are included as arguments with the TBDATA command, and that there is no temperature dependency.

TB,CREEP,1
TBDATA,1,C1,C2,C3,C4, ,C6

For the explicit creep method, you can incorporate other creep expressions into the program by using User Programmable Features (see the Guide to ANSYS User Programmable Features).

For highly nonlinear creep strain vs. time curves, a small time step must be used with the explicit creep method. Creep strains are not computed if the time step is less than 1.0e-6. A creep time step optimization procedure is available [AUTOTS and CRPLIM] for automatically adjusting the time step as appropriate.

8.4.1.7. Shape Memory Alloy

The Shape Memory Alloy (SMA) material behavior option describes the super-elastic behavior of nitinol alloy. Nitinol is a flexible metal alloy that can undergo very large deformations in loading-unloading cycles without permanent deformation. As illustrated in Figure 8.17: "Shape Memory Alloy Phases", the material behavior has three distinct phases: an austenite phase (linear elastic), a martensite phase (also linear elastic), and the transition phase between these two.

Figure 8.17  Shape Memory Alloy Phases

Use the MP command to input the linear elastic behavior of the austenite phase, and the TB,SMA command to input the behavior of the transition and martensite phases. Use the TBDATA command to enter the specifics (data sets) of the alloy material. You can enter up to six sets of data.

SMAs can be specified for the following elements: PLANE182, PLANE183, SOLID185, SOLID186, SOLID187, and SOLSH190.

A typical ANSYS input listing (fragment) will look similar to this:

MP,EX,1,60.0E3                                   ! Define austenite elastic properties
MP,NUXY,1.0.3                                    ! 

TB,SMA,1,2                                       ! Define material 1 as SMA,
                                                 ! with two temperatures
TBTEMP,10                                        ! Define first starting temp
TBDATA,1,520.0,600.0,300.0,200.0,0.07,0.12       ! Define SMA parameters
                                                 ! 
TBTEMP,20                                        ! Define second starting temp
TBDATA,1,420.0,540.0,300.0,200.0,0.10,0.15       ! Define SMA parameters

See TB, and TBDATA for more information.

8.4.1.8. Viscoplasticity

Viscoplasticity is a time-dependent plasticity phenomenon, where the development of the plastic strains are dependent on the rate of loading. The primary applications are high-temperature metal forming processes such as rolling and deep drawing, which involve large plastic strains and displacements with small elastic strains (see Figure 8.18: "Viscoplastic Behavior in a Rolling Operation"). The plastic strains are typically very large (for example, 50% or greater), requiring large strain theory [NLGEOM,ON].

Viscoplasticity is modeled with element types VISCO106, VISCO107, and VISCO108, using Anand's model for material properties as described in Nonlinear Stress-Strain Materials in the Elements Reference.

Figure 8.18  Viscoplastic Behavior in a Rolling Operation

Viscoplasticity is defined by unifying plasticity and creep via a set of flow and evolutionary equations. A constraint equation is used to preserve volume in the plastic region.

The Rate-Dependent Plasticity (Viscoplasticity) or TB,RATE option allows you to introduce the strain rate effect in material models to simulate the time-dependent response of materials. Two material options are available, the Perzyna model and the Peirce model (see the Theory Reference for ANSYS and ANSYS Workbench for details). In contrast to other rate-dependent material options in ANSYS such as Creep or Anand's model, the Perzyna and Peirce models also include a yield surface. The plasticity and thus the strain rate hardening effect are active only after plastic yielding. You must use the models in combination with the BISO, MISO, or NLISO material options to simulate viscoplasticity. Further, you can simulate anisotropic viscoplasticity by also combining the HILL option. See Material Model Combinations in the Elements Reference for the combination possibilities. Also, see Material Model Combinations in this chapter for sample input listings of material combinations. For isotropic hardening, the intent is for simulating the strain rate hardening of materials rather than softening. This option is also suitable for large strain analysis, and is applicable to the following elements: PLANE42, SOLID45, PLANE82, SOLID92, SOLID95, LINK180, SHELL181, SHELL281, PLANE182, PLANE183, SOLID185, SOLID186, SOLID187, SOLSH190, BEAM188, BEAM189, SHELL208, and SHELL209. Some typical applications of these material options are metal forming and micro-electromechanical systems (MEMS).

8.4.1.9. Viscoelasticity

Viscoelasticity is similar to creep, but part of the deformation is removed when the loading is taken off. A common viscoelastic material is glass. Some plastics are also considered to be viscoelastic. One type of viscoelastic response is illustrated in Figure 8.19: "Viscoelastic Behavior (Maxwell Model)".

Figure 8.19  Viscoelastic Behavior (Maxwell Model)

Viscoelasticity is modeled with element types VISCO88 and VISCO89 for small deformation viscoelasticity and LINK180, SHELL181, SHELL281, PLANE182, PLANE183, SOLID185, SOLID186, SOLID187, SOLSH190, BEAM188, BEAM189, SHELL208, and SHELL209 for small and large deformation viscoelasticity. You must input material properties using the TB family of commands. For SHELL181, SHELL281, PLANE182, PLANE183, SOLID185, SOLID186, SOLID187, SOLSH190, SHELL208, and SHELL209, the underlying elasticity is specified by either the MP command (hypoelasticity) or by the TB,HYPER command (hyperelasticity). For LINK180, BEAM188, and BEAM189, the underlying elasticity is specified using the MP command (hypoelasticity) only. The elasticity constants correspond to those of the fast load limit. Use the TB,PRONY and TB,SHIFT commands to input the relaxation property (see the TB command description for more information).

!Small Strain Viscoelasticity
mp,ex,1,20.0E5	!elastic properties
mp,nuxy,1,0.3

tb,prony,1,,2,shear	!define viscosity parameters (shear)
tbdata,1,0.5,2.0,0.25,4.0
tb,prony,1,,2,bulk	!define viscosity parameters (bulk)
tbdata,1,0.5,2.0,0.25,4.0

!Large Strain Viscoelasticity
tb,hyper,1,,,moon	!elastic properties
tbdata,1,38.462E4,,1.2E-6

tb,prony,1,,1,shear	!define viscosity parameters
tbdata,1,0.5,2.0
tb,prony,1,,1,bulk	!define viscosity parameters
tbdata,1,0.5,2.0

See Viscoelastic Material Constants in the Elements Reference and the Theory Reference for ANSYS and ANSYS Workbench for details about how to input viscoelastic material properties using the TB family of commands.

ANSYS provides tools to help you determine the coefficients for all of the viscoelastic options defined by TB,PRONY. The TBFT command allows you to compare your experimental data with existing material data curves and visually “fit” your curve for use in the TB command. All of the TBFT command capability is available via either batch or interactive (GUI) mode. See Material Curve Fitting (also in this manual) for more information.

8.4.1.10. Swelling

Certain materials respond to neutron flux by enlarging volumetrically, or swelling. In order to include swelling effects, you must write your own swelling subroutine, USERSW. (See the Guide to ANSYS User Programmable Features for a discussion of User-Programmable Features.) Swelling Equations in the Elements Reference discusses how to use the TB family of commands to input constants for the swelling equations. Swelling can also be related to other phenomena, such as moisture content. The ANSYS commands for nuclear swelling can be used analogously to define swelling due to other causes.

8.4.2. Material Model Combinations

You can combine several material model options discussed in this chapter to simulate complex material behaviors. Material Model Combinations in the Elements Reference presents the model options you can combine along with the associated TB command labels and links to sample input listings. These sample input listings are presented below in sections identified by the TB command labels.

8.4.2.1. BISO and CHAB Example

This input listing illustrates an example of combining bilinear isotropic hardening plasticity with Chaboche nonlinear kinematic hardening plasticity.

MP,EX,1,185.0E3                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,CHAB,1                         ! CHABOCHE TABLE
TBDATA,1,180,100,3

TB,BISO,1                         ! BISO TABLE
TBDATA,1,180,200

For information on the BISO option, see Bilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CHAB option, see Nonlinear Kinematic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.2. MISO and CHAB Example

This input listing illustrates an example of combining multilinear isotropic hardening plasticity with Chaboche nonlinear kinematic hardening plasticity.

MP,EX,1,185E3                     ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,CHAB,1                         ! CHABOCHE TABLE
TBDATA,1,180,100,3                ! THIS EXAMPLE ISOTHERMAL

TB,MISO,1                         ! MISO TABLE
TBPT,,9.7E-4,180
TBPT,,1.0,380

For information on the MISO option, see Multilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CHAB option, see Nonlinear Kinematic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.3. PLAS (Multilinear Isotropic Hardening) and CHAB Example

In addition to the TB,MISO example (above), you can also use material plasticity. The multilinear isotropic hardening option - TB,PLAS, , , ,MISO is combined with Chaboche nonlinear kinematic hardening in the following example:

MP,EX,1,185E3                     ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,CHAB,1                         ! CHABOCHE TABLE
TBDATA,1,180,100,3                ! THIS EXAMPLE ISOTHERMAL

TB,PLAS,,,,MISO                   ! MISO TABLE
TBPT,,0.0,180
TBPT,,0.99795,380

For information on the MISO option, see Multilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CHAB option, see Nonlinear Kinematic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.4. NLISO and CHAB Example

This input listing illustrates an example of combining nonlinear isotropic hardening plasticity with Chaboche nonlinear kinematic hardening plasticity.

MP,EX,1,20.0E5                    ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,CHAB,1,3,5                     ! CHABOCHE TABLE
TBTEMP,20,1                       ! THIS EXAMPLE TEMPERATURE DEPENDENT
TBDATA,1,500,20000,100,40000,200,10000
TBDATA,7,1000,200,100,100,0
TBTEMP,40,2
TBDATA,1,880,204000,200,43800,500,10200
TBDATA,7,1000,2600,2000,500,0
TBTEMP,60,3
TBDATA,1,1080,244000,400,45800,700,12200
TBDATA,7,1400,3000,2800,900,0

TB,NLISO,1,2                       ! NLISO TABLE
TBTEMP,40,1
TBDATA,1,880,0.0,80.0,3
TBTEMP,60,2
TBDATA,1,1080,0.0,120.0,7

For information on the NLISO option, see Nonlinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CHAB option, see Nonlinear Kinematic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.5. PLAS (Multilinear Isotropic Hardening) and EDP Example

You can use the TB,PLAS capability in conjunction with Extended Drucker-Prager plasticity. The multilinear isotropic hardening option - TB,PLAS, , , ,MISO is combined with Extended Drucker-Prager plasticity in the following example:

/prep7
mp,ex,1,2.1e4			! Elastic Properties
mp,nuxy,1,0.1

ys=7.894657
sl=1000.0

tb,edp,1,,,LYFUN
tbdata,1,2.2526,ys

tb,edp,1,,,LFPOT
tbdata,1,0.566206

tb,plas,1,,4,miso
tbpt,defi,0.0,7.894
tbpt,defi,1,1007.894

For information on the MISO option, see Multilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the EDP option, see Extended Drucker-Prager in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.6. MISO and EDP Example

The TB,MISO option can also be used to combine multilinear isotropic hardening with Extended Drucker-Prager plasticity, as shown in the following example:

/prep7
mp,ex,1,2.1e4			! Elastic Properties
mp,nuxy,1,0.1

ys=7.894657
sl=1000.0

tb,edp,1,,,LYFUN
tbdata,1,2.2526,ys

tb,edp,1,,,LFPOT
tbdata,1,0.566206

tb,plas,1,,4,miso
tbpt,defi,0.0,7.894
tbpt,defi,1,1007.894

For information on the MISO option, see Multilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the EDP option, see Extended Drucker-Prager in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.7. GURSON and BISO Example

The TB,BISO option can also be used to combine bilinear isotropic hardening with Gurson plasticity, as shown in the following example:

q1=1.5
q2=1
q3=q1*q1
sigma_Y=E/300.0
Yield=1.0/sigma_Y
rone=1.0
rthree=3.0
f_0= 0.04
f_N= 0.04
S_N=0.1
strain_N=0.3
Power_N=0.1

tb,GURS,1,,5,BASE                ! Gurson's BASE model
tbdata,1,sigma_Y,f_0,q1,q2,q3

tb,GURS,1,,3,SNNU                ! Gurson's SNNU model
tbdata,1,f_N,strain_N,S_N

TB,BISO,1                         ! BISO TABLE
TBDATA,1,Yield, Power_N

For information on the BISO option, see Bilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the GURSON option, see Gurson's Model in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.8. GURSON and MISO Example

The TB,MISO option can also be used to combine multilinear isotropic hardening with Gurson plasticity, as shown in the following example:

Young=1000000
sigma_Y=Young/300.0
yield=1.0d0/sigma_Y/3.1415926
! define elastic Properties
mp,ex,1,Young
mp,nuxy,1,0.3
! Define Gurson's coefficients
q1=1.5
q2=1
q3=q1*q1
f_0= 0.000000
f_N= 0.04
S_N=0.1
strain_N=0.3
Power_N=0.1
f_c=0.15
f_F=0.25
! Gurson Model   
tb,gurs,1,,5,BASE		! BASE DEFINED   
tbdata,1,sigma_Y,f_0,q1,q2,q3	
    
tb,gurs,1,,3,SNNU		! SNNU DEFINED   
tbdata,1,f_N,strain_N,S_N   


tb,gurs,1,,2,COAL		! COAL DEFINED   
tbdata,1,f_c,f_F 

tb,miso,,,6
tbpt,,0.003333333,  3333.333333
tbpt,,0.018982279,  3966.666667
tbpt,,0.103530872,  4700
tbpt,,0.562397597,  5566.666667
tbpt,,1.006031106,  5900
tbpt,,2.934546576,  6566.666667

For information on the MISO option, see Multilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the GURSON option, see Gurson's Model in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.9. Gurson and PLAS (Multilinear Isotropic Hardening)

The TB,PLAS ,,, MISO option can also be used to combine multilinear isotropic hardening with Gurson plasticity, as shown in the following example:

q1=1.5
q2=1
q3=q1*q1
sigma_Y=E/300.0
Yield=1.0/sigma_Y
rone=1.0
rthree=3.0
f_0= 0.04
f_N= 0.04
S_N=0.1
strain_N=0.3
Power_N=0.1

tb,GURS,1,,5,BASE                ! Gurson's BASE model
tbdata,1,sigma_Y,f_0,q1,q2,q3

tb,GURS,1,,3,SNNU                ! Gurson's SNNU model
tbdata,1,f_N,strain_N,S_N

tb,plas,1,,4,miso
tbpt, defi, 0.0, Yield
tbpt, defi, 1, 10.0*Yield

For information on the MISO option, see Multilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the GURSON option, see Gurson's Model in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.10. NLISO and GURSON Example

The TB,NLISO option can also be used to combine nonlinear isotropic hardening with Gurson plasticity, as shown in the following example:

q1=1.5
q2=1
q3=q1*q1
sigma_Y=E/300.0
Yield=1.0/sigma_Y
rone=1.0
rthree=3.0
f_0= 0.04
f_N= 0.04
S_N=0.1
strain_N=0.3
Power_N=0.1

tb,GURS,1,,5,BASE                ! Gurson's BASE model
tbdata,1,sigma_Y,f_0,q1,q2,q3

tb,GURS,1,,3,SNNU                ! Gurson's SNNU model
tbdata,1,f_N,strain_N,S_N

tb,nliso,1,1,2,5
tbdata,1,sigma_Y,power_N

For information on the NLISO option, see Nonlinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the GURSON option, see Gurson's Model in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.11. BISO and RATE Example

This input listing illustrates an example of combining bilinear isotropic hardening plasticity with the TB,RATE command to model viscoplasticity.

MP,EX,1,20.0E5                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,BISO,1                        ! BISO TABLE
TBDATA,1,9000,10000

TB,RATE,1,,,PERZYNA              ! RATE TABLE
TBDATA,1,0.5,1

For information on the BISO option, see Bilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the RATE option, see Rate-Dependent Viscoplastic Materials in the Elements Reference, and Viscoplasticity in this chapter.

8.4.2.12. MISO and RATE Example

This input listing illustrates an example of combining multilinear isotropic hardening plasticity with the TB,RATE command to model viscoplasticity.

MP,EX,1,20.0E5                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,MISO,1                        ! MISO TABLE
TBPT,,0.015,30000
TBPT,,0.020,32000
TBPT,,0.025,33800
TBPT,,0.030,35000
TBPT,,0.040,36500
TBPT,,0.050,38000
TBPT,,0.060,39000

TB,RATE,1,,,PERZYNA              ! RATE TABLE
TBDATA,1,0.5,1

For information on the MISO option, see Multilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the RATE option, see Rate-Dependent Viscoplastic Materials in the Elements Reference, and Viscoplasticity in this chapter.

8.4.2.13. PLAS (Multilinear Isotropic Hardening) and RATE Example

In addition to the TB,MISO example (above), you can also use material plasticity. The multilinear isotropic hardening option - TB,PLAS, , , ,MISO is combined with RATE-dependent viscoplasticity in the following example:

MP,EX,1,20.0E5                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,PLAS,,,,MISO                  ! MISO TABLE
TBPT,,0.00000,30000
TBPT,,4.00E-3,32000
TBPT,,8.10E-3,33800
TBPT,,1.25E-2,35000
TBPT,,2.18E-2,36500
TBPT,,3.10E-2,38000
TBPT,,4.05E-2,39000

TB,RATE,1,,,PERZYNA              ! RATE TABLE
TBDATA,1,0.5,1

For information on the MISO option, see Multilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the RATE option, see Rate-Dependent Viscoplastic Materials in the Elements Reference, and Viscoplasticity in this chapter.

8.4.2.14. NLISO and RATE Example

This input listing illustrates an example of combining nonlinear isotropic hardening plasticity with the TB,RATE command to model viscoplasticity.

MP,EX,1,20.0E5                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,NLISO,1                       ! NLISO TABLE
TBDATA,1,30000,100000,5200,172

TB,RATE,1,,,PERZYNA              ! RATE TABLE
TBDATA,1,0.5,1

For information on the NLISO option, see Nonlinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the RATE option, see Rate-Dependent Viscoplastic Materials in the Elements Reference, and Viscoplasticity in this chapter.

8.4.2.15. BISO and CREEP Example

This input listing illustrates an example of combining bilinear isotropic hardening plasticity with implicit creep.

MP,EX,1,20.0E5                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,BISO,1                        ! BISO TABLE
TBDATA,1,9000,10000

TB,CREEP,1,,,2                   ! CREEP TABLE
TBDATA,1,1.5625E-14,5.0,-0.5,0.0

For information on the BISO option, see Bilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CREEP option, see Implicit Creep Equations in the Elements Reference, and Implicit Creep Procedure in this chapter.

8.4.2.16. MISO and CREEP Example

This input listing illustrates an example of combining multilinear isotropic hardening plasticity with implicit creep.

MP,EX,1,20.0E5                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,MISO,1                        ! MISO TABLE
TBPT,,0.015,30000
TBPT,,0.020,32000
TBPT,,0.025,33800
TBPT,,0.030,35000
TBPT,,0.040,36500
TBPT,,0.050,38000
TBPT,,0.060,39000

TB,CREEP,1,,,2                   ! CREEP TABLE
TBDATA,1,1.5625E-14,5.0,-0.5,0.0

For information on the MISO option, see Multilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CREEP option, see Implicit Creep Equations in the Elements Reference, and Implicit Creep Procedure in this chapter.

8.4.2.17. PLAS (Multilinear Isotropic Hardening) and CREEP Example

In addition to the TB,MISO example (above), you can also use material plasticity. The multilinear isotropic hardening option - TB,PLAS, , , ,MISO is combined with implicit CREEP in the following example:

MP,EX,1,20.0E5                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,PLAS,,,,MISO                  ! MISO TABLE
TBPT,,0.00000,30000
TBPT,,4.00E-3,32000
TBPT,,8.10E-3,33800
TBPT,,1.25E-2,35000
TBPT,,2.18E-2,36500
TBPT,,3.10E-2,38000
TBPT,,4.05E-2,39000

TB,CREEP,1,,,2                   ! CREEP TABLE
TBDATA,1,1.5625E-14,5.0,-0.5,0.0

For information on the MISO option, see Multilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CREEP option, see Implicit Creep Equations in the Elements Reference, and Implicit Creep Procedure in this chapter.

8.4.2.18. NLISO and CREEP Example

This input listing illustrates an example of combining nonlinear isotropic hardening plasticity with implicit creep.

MP,EX,1,20.0E5                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,NLISO,1                       ! NLISO TABLE
TBDATA,1,30000,100000,5200,172

TB,CREEP,1,,,2                   ! CREEP TABLE
TBDATA,1,1.5625E-14,5.0,-0.5,0.0

For information on the NLISO option, see Nonlinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CREEP option, see Implicit Creep Equations in the Elements Reference, and Implicit Creep Procedure in this chapter.

8.4.2.19. BKIN and CREEP Example

This input listing illustrates an example of combining bilinear kinematic hardening plasticity with implicit creep.

MP,EX,1,1e7                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.32 

TB,BKIN,1,                    ! BKIN TABLE
TBDATA,1,42000,1000

TB,CREEP,1,,,6                ! CREEP TABLE
TBDATA,1,7.4e-21,3.5,0,0,0,0

For information on the BKIN option, see Bilinear Kinematic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CREEP option, see Implicit Creep Equations in the Elements Reference, and Implicit Creep Procedure in this chapter.

8.4.2.20. HILL and BISO Example

This input listing illustrates an example of modeling anisotropic plasticity with bilinear isotropic hardening.

MP,EX,1,20.0E5                        ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,HILL,1,2                           ! HILL TABLE
TBTEMP,100
TBDATA,1,1,1.0402,1.24897,1.07895,1,1
TBTEMP,200
TBDATA,1,0.9,0.94,1.124,0.97,0.9,0.9

TB,BISO,1,2                           ! BISO TABLE
TBTEMP,100
TBDATA,1,461.0,374.586
TBTEMP,200
TBDATA,1,400.0,325.0

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the BISO option, see Bilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.21. HILL and MISO Example

This input listing illustrates an example of modeling anisotropic plasticity with multilinear isotropic hardening.

MP,EX,1,20.0E5                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,MISO,1                        ! MISO TABLE
TBPT,,0.015,30000
TBPT,,0.020,32000
TBPT,,0.025,33800
TBPT,,0.030,35000
TBPT,,0.040,36500
TBPT,,0.050,38000
TBPT,,0.060,39000

TB,HILL,1                        ! HILL TABLE
TBDATA,1,1.0,1.1,0.9,0.85,0.9,0.80

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the MISO option, see Multilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.22. HILL and PLAS (Multilinear Isotropic Hardening) Example

In addition to the TB,MISO example (above), you can also use material plasticity. The multilinear isotropic hardening option - TB,PLAS, , , ,MISO is combined with HILL anisotropic plasticity in the following example:

MP,EX,1,20.0E5                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,PLAS,,,,MISO                  ! MISO TABLE
TBPT,,0.00000,30000
TBPT,,4.00E-3,32000
TBPT,,8.10E-3,33800
TBPT,,1.25E-2,35000
TBPT,,2.18E-2,36500
TBPT,,3.10E-2,38000
TBPT,,4.05E-2,39000

TB,HILL,1                        ! HILL TABLE
TBDATA,1,1.0,1.1,0.9,0.85,0.9,0.80

For information on the MISO option, see Multilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.23. HILL and NLISO Example

This input listing illustrates an example of modeling anisotropic plasticity with nonlinear isotropic hardening.

MP,EX,1,20.0E5                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,NLISO,1                       ! NLISO TABLE
TBDATA,1,30000,100000,5200,172

TB,HILL,1                        ! HILL TABLE
TBDATA,1,1.0,1.1,0.9,0.85,0.9,0.80

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the NLISO option, see Nonlinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.24. HILL and BKIN Example

This input listing illustrates an example of modeling anisotropic plasticity with bilinear kinematic hardening.

MP,EX,1,20.0E5                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,BKIN,1                        ! BKIN TABLE
TBDATA,1,9000,10000

TB,HILL,1                        ! HILL TABLE
TBDATA,1,1.0,1.1,0.9,0.85,0.9,0.80

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the BKIN option, see Bilinear Kinematic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.25. HILL and MKIN Example

This input listing illustrates an example of modeling anisotropic plasticity with multilinear kinematic hardening.

MPTEMP,1,20,400,650,800,950      ! ELASTIC CONSTANTS

MPDATA,EX,1,1,30.00E6,27.36E6,25.20E6,23.11E6,20.76E6
MPDATA,EY,1,1,30.00E6,27.36E6,25.20E6,23.11E6,20.76E6
MPDATA,EZ,1,1,30.00E6,27.36E6,25.20E6,23.11E6,20.76E6

MPDATA,PRXY,1,1,0.351,0.359,0.368,0.375,0.377 
MPDATA,PRYZ,1,1,0.351,0.359,0.368,0.375,0.377
MPDATA,PRXZ,1,1,0.351,0.359,0.368,0.375,0.377

MPDATA,GXY,1,1,1.190E4,1.160E4,1.110E4,1.080E4,1.060E4
MPDATA,GYZ,1,1,1.190E4,1.160E4,1.110E4,1.080E4,1.060E4
MPDATA,GXZ,1,1,1.190E4,1.160E4,1.110E4,1.080E4,1.060E4


TB,MKIN,1,5,5                    ! MKIN TABLE
TBTEMP,,strain
TBDATA,1,0.0015,0.006,0.04,0.08,0.1
TBTEMP,20
TBDATA,1,45000,60000,90000,115000,120000
TBTEMP,400
TBDATA,1,41040,54720,82080,104880,109440
TBTEMP,650
TBDATA,1,37800,50400,75600,96600,100800
TBTEMP,800
TBDATA,1,34665,46220,69330,88588,92440
TBTEMP,950
TBDATA,1,31140,41520,62280,79580,83040


TB,HILL,1,5                      ! HILL TABLE
TBTEMP,20.0
TBDATA,1,1.0,1.0,1.0,0.93,0.93,0.93
TBTEMP,400.0                             
TBDATA,1,1.0,1.0,1.0,0.93,0.93,0.93
TBTEMP,650.0
TBDATA,1,1.0,1.0,1.0,0.93,0.93,0.93
TBTEMP,800.0                             
TBDATA,1,1.0,1.0,1.0,1.00,1.00,1.00
TBTEMP,950.0                             
TBDATA,1,1.0,1.0,1.0,1.00,1.00,1.00

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the MKIN option, see Multilinear Kinematic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.26. HILL and KINH Example

This input listing illustrates an example of modeling anisotropic plasticity with multilinear kinematic hardening.

MP,EX,1,20E6                         ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,KINH,1,,3                         ! KINH TABLE
TBPT,,5E-5,1E3
TBPT,,0.01,2E3
TBPT,,0.60,6E4

TB,HILL,1                            ! HILL TABLE
TBDATA,1,1.0,1.1,0.9,0.85,0.90,0.95

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the KINH option, see Multilinear Kinematic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.27. HILL, and PLAS (Kinematic Hardening) Example

In addition to the TB,KINH example (above), you can also use material plasticity. The kinematic hardening option - TB,PLAS, , , ,KINH is combined with HILL anisotropic plasticity in the following example:

MP,EX,1,20E6                         ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,PLAS,,,,KINH                      ! KINH TABLE
TBPT,,0.00000,1E3
TBPT,,9.90E-3,2E3
TBPT,,5.97E-1,6E4

TB,HILL,1                            

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the KINH option, see Multilinear Kinematic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.28. HILL and CHAB Example

This input listing illustrates an example of modeling anisotropic plasticity with Chaboche nonlinear kinematic hardening.

MP,EX,1,185E3                    ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,CHAB,1                        ! CHABOCHE TABLE
TBDATA,1,180,400,3,0

TB,HILL,1                        ! HILL TABLE
TBDATA,1,1.0,1.1,0.9,0.85,0.9,0.80

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CHAB option, see Nonlinear Kinematic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.29. HILL and BISO and CHAB Example

This input listing illustrates an example of modeling anisotropic plasticity with bilinear isotropic hardening and Chaboche nonlinear kinematic hardening.

MP,EX,1,185E3                       ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,CHAB,1                           ! CHABOCHE TABLE
TBDATA,1,180,100,3

TB,BISO,1                           ! BISO TABLE
TBDATA,1,180,200

TB,HILL,1                           ! HILL TABLE
TBDATA,1,1.0,1.1,0.9,0.85,0.9,0.80

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the BISO option, see Bilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CHAB option, see Nonlinear Kinematic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.30. HILL and MISO and CHAB Example

This input listing illustrates an example of modeling anisotropic plasticity with multilinear isotropic hardening and Chaboche nonlinear kinematic hardening.

MP,EX,1,185E3                       ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,CHAB,1                           ! CHABOCHE TABLE
TBDATA,1,185,100,3

TB,MISO,1                           ! MISO TABLE
TBPT,,0.001,185
TBPT,,1.0,380

TB,HILL,1                           ! HILL TABLE
TBDATA,1,1.0,1.1,0.9,0.85,0.9,0.80

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the MISO option, see Multilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CHAB option, see Nonlinear Kinematic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.31. HILL and PLAS (Multilinear Isotropic Hardening) and CHAB Example

In addition to the TB,MISO example (above), you can also use material plasticity. The multilinear isotropic hardening option - TB,PLAS, , , ,MISO is combined with HILL anisotropic plasticity and Chaboche nonlinear kinematic hardening in the following example:

MP,EX,1,185E3                       ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,CHAB,1                           ! CHABOCHE TABLE
TBDATA,1,185,100,3

TB,PLAS,,,,MISO                     ! MISO TABLE
TBPT,,0.001,185
TBPT,,0.998,380

TB,HILL,1                           ! HILL TABLE
TBDATA,1,1.0,1.1,0.9,0.85,0.9,0.80

For information on the MISO option, see Multilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CHAB option, see Nonlinear Kinematic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.32. HILL and NLISO and CHAB Example

This input listing illustrates an example of combining anisotropic plasticity with nonlinear isotropic hardening and Chaboche nonlinear kinematic hardening.

MPTEMP,1,20,200,400,550,600,650            ! ELASTIC CONSTANTS
MPTEMP,,700,750,800,850,900,950
!
MPDATA,EX,1,1,1.250E4,1.210E4,1.140E4,1.090E4,1.070E4,1.050E4 
MPDATA,EX,1,,1.020E4,0.995E4,0.963E4,0.932E4,0.890E4,0.865E4 
!
MPDATA,EY,1,1,1.250E4,1.210E4,1.140E4,1.090E4,1.070E4,1.050E4 
MPDATA,EY,1,,1.020E4,0.995E4,0.963E4,0.932E4,0.890E4,0.865E4 
!
MPDATA,EZ,1,1,1.250E4,1.210E4,1.140E4,1.090E4,1.070E4,1.050E4
MPDATA,EZ,1,,1.020E4,0.995E4,0.963E4,0.932E4,0.890E4,0.865E4
!
MPDATA,PRXY,1,1,0.351,0.359,0.368,0.375,0.377,0.380 
MPDATA,PRXY,1,,0.382,0.384,0.386,0.389,0.391,0.393
!
MPDATA,PRYZ,1,1,0.351,0.359,0.368,0.375,0.377,0.380 
MPDATA,PRYZ,1,,0.382,0.384,0.386,0.389,0.391,0.393
!
MPDATA,PRXZ,1,1,0.351,0.359,0.368,0.375,0.377,0.380
MPDATA,PRXZ,1,,0.382,0.384,0.386,0.389,0.391,0.393
!
MPDATA,GXY,1,1,1.190E4,1.160E4,1.110E4,1.080E4,1.060E4,1.040E4
MPDATA,GXY,1,,1.020E4,1.000E4,0.973E4,0.946E4,0.908E4,0.887E4
!	      
MPDATA,GYZ,1,1,1.190E4,1.160E4,1.110E4,1.080E4,1.060E4,1.040E4
MPDATA,GYZ,1,,1.020E4,1.000E4,0.973E4,0.946E4,0.908E4,0.887E4
!								      
MPDATA,GXZ,1,1,1.190E4,1.160E4,1.110E4,1.080E4,1.060E4,1.040E4
MPDATA,GXZ,1,,1.020E4,1.000E4,0.973E4,0.946E4,0.908E4,0.887E4




TB,NLISO,1                                ! NLISO TABLE
TBDATA,1,180,0.0,100.0,5

!

TB,CHAB,1                                 ! CHABOCHE TABLE
TBDATA,1,180,100,3



TB,HILL,1,5                               ! HILL TABLE
TBTEMP,750.0
TBDATA,1,1.0,1.0,1.0,0.93,0.93,0.93
TBTEMP,800.0				 
TBDATA,1,1.0,1.0,1.0,0.93,0.93,0.93
TBTEMP,850.0				 
TBDATA,1,1.0,1.0,1.0,0.93,0.93,0.93
TBTEMP,900.0				 
TBDATA,1,1.0,1.0,1.0,1.00,1.00,1.00
TBTEMP,950.0				 
TBDATA,1,1.0,1.0,1.0,1.00,1.00,1.00

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the NLISO option, see Nonlinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CHAB option, see Nonlinear Kinematic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.33. HILL and RATE and BISO Example

This input listing illustrates an example of modeling anisotropic viscoplasticity with bilinear isotropic hardening plasticity.

MPTEMP,1,20,400,650,800,950      ! ELASTIC CONSTANTS
!
MPDATA,EX,1,1,30.00E6,27.36E6,25.20E6,23.11E6,20.76E6
!
MPDATA,EY,1,1,30.00E6,27.36E6,25.20E6,23.11E6,20.76E6
!
MPDATA,EZ,1,1,30.00E6,27.36E6,25.20E6,23.11E6,20.76E6
!
MPDATA,PRXY,1,1,0.351,0.359,0.368,0.375,0.377 
!
MPDATA,PRYZ,1,1,0.351,0.359,0.368,0.375,0.377
!
MPDATA,PRXZ,1,1,0.351,0.359,0.368,0.375,0.377
!
MPDATA,GXY,1,1,1.190E4,1.160E4,1.110E4,1.080E4,1.060E4
!             
MPDATA,GYZ,1,1,1.190E4,1.160E4,1.110E4,1.080E4,1.060E4
!                                                                     
MPDATA,GXZ,1,1,1.190E4,1.160E4,1.110E4,1.080E4,1.060E4


TB,BISO,1,                       ! BISO TABLE
TBDATA,1,45000,760000


TB,RATE,1,2,,PERZYNA             ! RATE TABLE
TBTEMP,20
TBDATA,1,0.1,0.3
TBTEMP,950
TBDATA,1,0.3,0.5


TB,HILL,1,5                      ! HILL TABLE
TBTEMP,750.0
TBDATA,1,1.0,1.0,1.0,0.93,0.93,0.93
TBTEMP,800.0                             
TBDATA,1,1.0,1.0,1.0,0.93,0.93,0.93
TBTEMP,850.0                             
TBDATA,1,1.0,1.0,1.0,0.93,0.93,0.93
TBTEMP,900.0                             
TBDATA,1,1.0,1.0,1.0,1.00,1.00,1.00
TBTEMP,950.0                             
TBDATA,1,1.0,1.0,1.0,1.00,1.00,1.00

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the RATE option, see Rate-Dependent Viscoplastic Materials in the Elements Reference, and Viscoplasticity in this chapter.

For information on the BISO option, see Bilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.34. HILL and RATE and MISO Example

This input listing illustrates an example of modeling anisotropic viscoplasticity with multilinear isotropic hardening plasticity.

MP,EX,1,20.0E5                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,MISO,1                        ! MISO TABLE
TBPT,,0.015,30000
TBPT,,0.020,32000
TBPT,,0.025,33800
TBPT,,0.030,35000
TBPT,,0.040,36500
TBPT,,0.050,38000
TBPT,,0.060,39000

TB,HILL,1                        ! HILL TABLE
TBDATA,1,1.0,1.1,0.9,0.85,0.9,0.80

TB,RATE,1,,,PERZYNA              ! RATE TABLE
TBDATA,1,0.5,1

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the RATE option, see Rate-Dependent Viscoplastic Materials in the Elements Reference, and Viscoplasticity in this chapter.

For information on the MISO option, see Bilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.35. HILL and RATE and NLISO Example

This input listing illustrates an example of modeling anisotropic viscoplasticity with nonlinear isotropic hardening plasticity.

MP,EX,1,20.0E5                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,NLISO,1                       ! NLISO TABLE
TBDATA,1,30000,100000,5200,172

TB,HILL,1                        ! HILL TABLE
TBDATA,1,1.0,1.1,0.9,0.85,0.9,0.80

TB,RATE,1,,,PERZYNA              ! RATE TABLE
TBDATA,1,0.5,1

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the RATE option, see Rate-Dependent Viscoplastic Materials in the Elements Reference, and Viscoplasticity in this chapter.

For information on the NLISO option, see Nonlinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.36. HILL and CREEP Example

This input listing illustrates an example of modeling anisotropic implicit creep.

MPTEMP,1,20,200,400,550,600,650           ! ELASTIC CONSTANTS
MPTEMP,,700,750,800,850,900,950
!
MPDATA,EX,1,1,1.250E4,1.210E4,1.140E4,1.090E4,1.070E4,1.050E4 
MPDATA,EX,1,,1.020E4,0.995E4,0.963E4,0.932E4,0.890E4,0.865E4 
!
MPDATA,EY,1,1,1.250E4,1.210E4,1.140E4,1.090E4,1.070E4,1.050E4 
MPDATA,EY,1,,1.020E4,0.995E4,0.963E4,0.932E4,0.890E4,0.865E4 
!
MPDATA,EZ,1,1,1.250E4,1.210E4,1.140E4,1.090E4,1.070E4,1.050E4
MPDATA,EZ,1,,1.020E4,0.995E4,0.963E4,0.932E4,0.890E4,0.865E4
!
MPDATA,PRXY,1,1,0.351,0.359,0.368,0.375,0.377,0.380 
MPDATA,PRXY,1,,0.382,0.384,0.386,0.389,0.391,0.393
!
MPDATA,PRYZ,1,1,0.351,0.359,0.368,0.375,0.377,0.380 
MPDATA,PRYZ,1,,0.382,0.384,0.386,0.389,0.391,0.393
!
MPDATA,PRXZ,1,1,0.351,0.359,0.368,0.375,0.377,0.380
MPDATA,PRXZ,1,,0.382,0.384,0.386,0.389,0.391,0.393
!
MPDATA,GXY,1,1,1.190E4,1.160E4,1.110E4,1.080E4,1.060E4,1.040E4
MPDATA,GXY,1,,1.020E4,1.000E4,0.973E4,0.946E4,0.908E4,0.887E4
!	      
MPDATA,GYZ,1,1,1.190E4,1.160E4,1.110E4,1.080E4,1.060E4,1.040E4
MPDATA,GYZ,1,,1.020E4,1.000E4,0.973E4,0.946E4,0.908E4,0.887E4
!								      
MPDATA,GXZ,1,1,1.190E4,1.160E4,1.110E4,1.080E4,1.060E4,1.040E4
MPDATA,GXZ,1,,1.020E4,1.000E4,0.973E4,0.946E4,0.908E4,0.887E4


TB,CREEP,1,,,2                           ! CREEP TABLE
TBDATA,1,5.911E-34,6.25,-0.25


TB,HILL,1,5                              ! HILL TABLE
TBTEMP,750.0
TBDATA,1,1.0,1.0,1.0,0.93,0.93,0.93
TBTEMP,800.0				 
TBDATA,1,1.0,1.0,1.0,0.93,0.93,0.93
TBTEMP,850.0				 
TBDATA,1,1.0,1.0,1.0,0.93,0.93,0.93
TBTEMP,900.0				 
TBDATA,1,1.0,1.0,1.0,1.00,1.00,1.00
TBTEMP,950.0				 
TBDATA,1,1.0,1.0,1.0,1.00,1.00,1.00

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CREEP option, see Implicit Creep Equations in the Elements Reference, and Implicit Creep Procedure in this chapter.

8.4.2.37. HILL, CREEP and BISO Example

This input listing illustrates an example of modeling anisotropic implicit creep with bilinear isotropic hardening plasticity.

MPTEMP,1,20,200,400,550,600,650            ! ELASTIC CONSTANTS
MPTEMP,,700,750,800,850,900,950
!
MPDATA,EX,1,1,1.250E4,1.210E4,1.140E4,1.090E4,1.070E4,1.050E4 
MPDATA,EX,1,,1.020E4,0.995E4,0.963E4,0.932E4,0.890E4,0.865E4 
!
MPDATA,EY,1,1,1.250E4,1.210E4,1.140E4,1.090E4,1.070E4,1.050E4 
MPDATA,EY,1,,1.020E4,0.995E4,0.963E4,0.932E4,0.890E4,0.865E4 
!
MPDATA,EZ,1,1,1.250E4,1.210E4,1.140E4,1.090E4,1.070E4,1.050E4
MPDATA,EZ,1,,1.020E4,0.995E4,0.963E4,0.932E4,0.890E4,0.865E4
!
MPDATA,PRXY,1,1,0.351,0.359,0.368,0.375,0.377,0.380 
MPDATA,PRXY,1,,0.382,0.384,0.386,0.389,0.391,0.393
!
MPDATA,PRYZ,1,1,0.351,0.359,0.368,0.375,0.377,0.380 
MPDATA,PRYZ,1,,0.382,0.384,0.386,0.389,0.391,0.393
!
MPDATA,PRXZ,1,1,0.351,0.359,0.368,0.375,0.377,0.380
MPDATA,PRXZ,1,,0.382,0.384,0.386,0.389,0.391,0.393
!
MPDATA,GXY,1,1,1.190E4,1.160E4,1.110E4,1.080E4,1.060E4,1.040E4
MPDATA,GXY,1,,1.020E4,1.000E4,0.973E4,0.946E4,0.908E4,0.887E4
!	      
MPDATA,GYZ,1,1,1.190E4,1.160E4,1.110E4,1.080E4,1.060E4,1.040E4
MPDATA,GYZ,1,,1.020E4,1.000E4,0.973E4,0.946E4,0.908E4,0.887E4
!								      
MPDATA,GXZ,1,1,1.190E4,1.160E4,1.110E4,1.080E4,1.060E4,1.040E4
MPDATA,GXZ,1,,1.020E4,1.000E4,0.973E4,0.946E4,0.908E4,0.887E4


TB,BISO,1                                ! BISO TABLE
TBDATA,1,180,200


TB,CREEP,1,,,2                           ! CREEP TABLE
TBDATA,1,5.911E-34,6.25,-0.25


TB,HILL,1,5                              ! HILL TABLE
TBTEMP,750.0
TBDATA,1,1.0,1.0,1.0,0.93,0.93,0.93
TBTEMP,800.0				 
TBDATA,1,1.0,1.0,1.0,0.93,0.93,0.93
TBTEMP,850.0				 
TBDATA,1,1.0,1.0,1.0,0.93,0.93,0.93
TBTEMP,900.0				 
TBDATA,1,1.0,1.0,1.0,1.00,1.00,1.00
TBTEMP,950.0				 
TBDATA,1,1.0,1.0,1.0,1.00,1.00,1.00

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CREEP option, see Implicit Creep Equations in the Elements Reference, and Implicit Creep Procedure in this chapter.

For information on the BISO option, see Bilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.38. HILL and CREEP and MISO Example

This input listing illustrates an example of modeling anisotropic implicit creep with multilinear isotropic hardening plasticity.

MP,EX,1,20.0E5                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,MISO,1                        ! MISO TABLE
TBPT,,0.015,30000
TBPT,,0.020,32000
TBPT,,0.025,33800
TBPT,,0.030,35000
TBPT,,0.040,36500
TBPT,,0.050,38000
TBPT,,0.060,39000

TB,HILL,1                        ! HILL TABLE
TBDATA,1,1.0,1.1,0.9,0.85,0.9,0.80

TB,CREEP,1,,,2                   ! CREEP TABLE
TBDATA,1,1.5625E-14,5.0,-0.5,0.0

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CREEP option, see Implicit Creep Equations in the Elements Reference, and Implicit Creep Procedure in this chapter.

For information on the MISO option, see Multilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.39. HILL, CREEP and PLAS (Multilinear Isotropic Hardening) Example

In addition to the TB,MISO example (above), you can also use material plasticity. The multilinear isotropic hardening option - TB,PLAS, , , ,MISO is combined with HILL anisotropic plasticity and implicit CREEP in the following example:

MP,EX,1,20.0E5                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,PLAS,1,,7,MISO                ! MISO TABLE
TBPT,,0.00000,30000
TBPT,,4.00E-3,32000
TBPT,,8.10E-3,33800
TBPT,,1.25E-2,35000
TBPT,,2.18E-2,36500
TBPT,,3.10E-2,38000
TBPT,,4.05E-2,39000

TB,HILL,1                        ! HILL TABLE
TBDATA,1,1.0,1.1,0.9,0.85,0.9,0.80

TB,CREEP,1,,,2                   ! CREEP TABLE
TBDATA,1,1.5625E-14,5.0,-0.5,0.0

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CREEP option, see Implicit Creep Equations in the Elements Reference, and Implicit Creep Procedure in this chapter.

For information on the MISO option, see Multilinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.40. HILL and CREEP and NLISO Example

This input listing illustrates an example of modeling anisotropic implicit creep with nonlinear isotropic hardening plasticity.

MP,EX,1,20.0E5                   ! ELASTIC CONSTANTS
MP,NUXY,1,0.3

TB,NLISO,1                       ! NLISO TABLE
TBDATA,1,30000,100000,5200,172

TB,HILL,1                        ! HILL TABLE
TBDATA,1,1.0,1.1,0.9,0.85,0.9,0.80

TB,CREEP,1,,,2                   ! CREEP TABLE
TBDATA,1,1.5625E-14,5.0,-0.5,0.0

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CREEP option, see Implicit Creep Equations in the Elements Reference, and Implicit Creep Procedure in this chapter.

For information on the NLISO option, see Nonlinear Isotropic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.41. HILL and CREEP and BKIN Example

This input listing illustrates an example of modeling anisotropic implicit creep with bilinear kinematic hardening plasticity.

MP,EX,1,1e7                     ! ELASTIC CONSTANTS
MP,NUXY,1,0.32 

TB,BKIN,1                       ! BKIN TABLE
TBDATA,1,42000,1000   

TB,CREEP,1,,,6                  ! CREEP TABLES
TBDATA,1,7.4e-21,3.5,0,0,0,0  

TB,HILL,1                       ! HILL TABLE
TBDATA,1,1.15,1.05,1.0,1.0,1.0,1.0

For information on the HILL option, see Hill's Anisotropy in the Elements Reference, and Plastic Material Options in this chapter.

For information on the CREEP option, see Implicit Creep Equations in the Elements Reference, and Implicit Creep Procedure in this chapter.

For information on the BKIN option, see Bilinear Kinematic Hardening in the Elements Reference, and Plastic Material Options in this chapter.

8.4.2.42. Hyperelasticity and Viscoelasticity (Implicit) Example

This input listing illustrates the combination of implicit hyperelasticity and viscoelasticity.

      c10=293   
      c01=177   
      TB,HYPER,1,,,MOON               !!!! type 1 is Mooney-Rivlin   
      TBDATA,1,c10,c01
      a1=0.1
      a2=0.2
      a3=0.3
      t1=10
      t2=100
      t3=1000
      tb,prony,1,,3,shear          ! define Prony constants
      tbdata,1,a1,t1,a2,t2,a3,t3

For information on hyperelasticity, see Hyperelastic Material Constants in the Elements Reference, and Hyperelasticity in this chapter.

For information on the viscoelasticity, see Viscoelastic Material Constants in the Elements Reference, and Viscoelasticity in this chapter.