Implementing User-Programmable Features (UPFs) in ANSYS · Also, the ANSYS training course “ANSYS...

© 2011 ANSYS, Inc. May 9, 20141

Lecture 4Implementing material models: using usermat.F

Implementing User-Programmable Features (UPFs) in ANSYS

© 2011 ANSYS, Inc. May 9, 20142

Lecture overview

• What is usermat.F used for?

• Stress, strain and material Jacobian matrix

• How is usermat.F used?

• usermat.F restrictions

• Example of application

• Where to find additional information

© 2011 ANSYS, Inc. May 9, 20143

The usermat.F subroutine allows writing the stress-strain

relationship of a material and applies to any analysis

procedure involving mechanical behaviour. The ANSYS

installation includes an example which corresponds to a

plasticity model, which is the same as TB,BISO , for

different stress states and that can be used as reference.

Such a routine can be found in the following folder:

… \ANSYS Inc\v150\ansys\customize\user

What is usermat.F used for?

© 2011 ANSYS, Inc. May 9, 20144

The stress measure (σ) used by the subroutine is the Cauchy

stress (true stress), and the strain measure (ε) is the

logarithmic strain (true strain). The strains and incremental

strains passed into usermat.F are the total mechanical

strains from which the thermal strains (if they exist) are

subtracted.

usermat.F must also provide the material Jacobian

matrix defined as:

the stress increment

being

the strain incrementij

ijJacobianεσ

∆∂∆∂

=

∆∂

∆∂

ij

ij

ε

σ

Stress, strain and material Jacobian matrix

© 2011 ANSYS, Inc. May 9, 20145

One important remark to mention is that ANSYS outputs

engineering shear strains whether NLGEOMis ONor OFF.

This is true for usermat.F as well. Engineering shear

strains are twice the tensor shear strains.


© 2011 ANSYS, Inc. May 9, 20146

usermat.F is based on the current configuration for

nonlinear geometry analysis (NLGEOM,ON). The program

uses a co-rotational approach to account for rigid body

rotation. Because the program already accounts for the

strains passed into usermat.F for the rigid body rotation,

there is no need to apply additional rotation within

usermat.F .

The subroutine is called at every material integration point

of the elements during the solution phase. The program

passes in stresses, strains, and state variable values at the

beginning of the time increment and strain increment at the

current increment, then updates the stresses and state

variables to the appropriate values at the end of the time

increment.


© 2011 ANSYS, Inc. May 9, 20147

usermat.F assumes use of a nonlinear constitutive

model, so results are copied from integration points to

nodes. In MAPDL, for linear elastic materials (or if stress

value < yield stress value), the default is to extrapolate

stresses and strains from integration points to nodes.

Consequently, when comparing results for usermat.Fwith linear elastic materials, differences may be seen.

Therefore, to make the comparison valid, one should use

the APDL command ERESX,NO to force copying stresses

and strains at integration points to nodes, even for linear

elastic materials. There is no way, currently, to have

usermat.F extrapolate stresses and strains from

integration points to nodes (they are always copied).

However, it is possible to do so in UserElem.F(explained in Lecture 7).


© 2011 ANSYS, Inc. May 9, 20148

Stress, strain, and the material Jacobian tensors are stored

in a vector or matrix format. In particular, the order of

components for all tensors is as follows:


© 2011 ANSYS, Inc. May 9, 20149

The order of components for the material Jacobian matrix is

as follows:


© 2011 ANSYS, Inc. May 9, 201410

How is usermat.F used?

The file usermat.F consists of 4 routines which are called

depending on the corresponding stress state. Below is a list

of such 4 routines with a brief description of the stress/strain

state as well as finite elements they can be used in

conjunction with:

usermat3d 3D solid elements or plane elements in

plane strain or axisymmetric stress state

usermatps plane stress states (such as PLANE182,

PLANE183or SHELL181)

usermatbm 3D beam elements (BEAM188, BEAM189)

usermat1d 1D truss elements (LINK180)

© 2011 ANSYS, Inc. May 9, 201411


Number of state variables to be

defined with TB,STATE command

Number of material properties to be

defined with TB,USER command

T

T∆t

t∆ε ε∆

Vector of material properties

tFttF ∆+

Main input arguments are listed below:

© 2011 ANSYS, Inc. May 9, 201412


tStress at time to be updated

at time tt ∆+

State variables at time to be

updated at time

ttt ∆+

Main input/output arguments are listed below:

© 2011 ANSYS, Inc. May 9, 201413


Main output arguments are listed below:

Bisection occurs if

user routine does

not converge

material Jacobian

matrix

© 2011 ANSYS, Inc. May 9, 201414

usermat.F restrictions

The following restrictions apply to the usermat.Fsubroutine:

• The subroutine supports current-technology elements

only and is not applicable to legacy elements. Details on

current-technology elements can be found here:

ANSYS Documentation > Mechanical APDL > Element Reference >

2. Element Classifications > 2.4. Current-Technology Elements

• The subroutine usermat.F is not applicable to legacyelements for which dedicated subroutines should beused instead. Further information is available in theonline documentation:

ANSYS Documentation > Mechanical APDL > Feature Archive > IV. Legacy Elements

© 2011 ANSYS, Inc. May 9, 201415

usermat.F restrictions

• State variables (defined via the TB,STATE command)

are supported only by full graphics in the POST1

postprocessor;

• The subroutine is not intended for modelling

incompressible elastic materials(*), such as hyperelastic

materials. A special treatment such as a penalty

approach may be needed to ensure incompressibility. In

any case, if the material exhibits nearly incompressible

behavior, use a finite tangent bulk modulus.

(*) Fully-incompressible materials can be modeled using the subroutine UserHyper.F , which will

be described in Lecture 5.

© 2011 ANSYS, Inc. May 9, 201416

Example of application

A simple bilinear plasticity material model, identical to

TB,BISO , is used to demonstrate the user material

subroutine usermat.F .

The example is a two-element test case under simple

tension. Element 1 has material defined using the TB,BISOoption, while Element 2 has material defined using the

TB,USER option. A 100% deformation is applied to both

elements. Finite deformation (NLGEOM,ON) is considered.

The /POST26 processor results of stress components and

plastic strain components are printed for both elements and

are expected to be the same.

© 2011 ANSYS, Inc. May 9, 201417


Below is the description of the APDL syntax needed to use

usermat.F . In this specific example the user material was

assigned to material #2 and its mechanical properties,

namely Young’s modulus, Poisson’s ratio, yielding stress and

tangent modulus, are temperature-dependent. The number

of state variables is 8.

TB,USER,2,2,4TBTEMP,1.0TBDATA,1,190000,0.3,100,10TBTEMP,2.0TBDATA,1,210000,0.3,200,10TB,STATE,2,,8

© 2011 ANSYS, Inc. May 9, 201418


Output information: TB,BISO vs. TB,USER

Information regarding the number of state variables,

inputted using the TB,STATE syntax, is provided as well:

© 2011 ANSYS, Inc. May 9, 201419


/POST26 output: results are identical

© 2011 ANSYS, Inc. May 9, 201420


In order to be able to get the values of the state variables,

the following APDL command should be inserted at the

/SOLU processor level:

OUTRES,SVAR,ALL

In particular, the option ALL allows writing the results for

every substep. Also, it might be convenient to print the

values of the state variables (8 in this example) in the

output file. This can be achieved by means of the following

do-loop to be inserted at the /POST1 processor level:

*DO,AR99,1,8PRESOL,SVAR,AR99

*ENDDO

© 2011 ANSYS, Inc. May 9, 201421


Below is the list of the state variables utilized in this example:

SVAR 1 ----- > Equivalent plastic strain

SVAR 2 ----- > X component of plastic strain

SVAR 3 ----- > Y component of plastic strain

SVAR 4 ----- > Z component of plastic strain

SVAR 5 ----- > XY component of plastic strain

SVAR 6 ----- > YZ component of plastic strain

SVAR 7 ----- > XZ component of plastic strain

SVAR 8 ----- > von Mises stress

as also specified in the subroutine usermat3d :

© 2011 ANSYS, Inc. May 9, 201422


/POST1 output: printout of state variable #1 (equivalent

plastic strain) at last substep.

© 2011 ANSYS, Inc. May 9, 201423


State variables can also be plotted (the first one in this

example). This can be done by means of the following APDL

command:

PLESOL,SVAR,1

However, it is worth mentioning that this is not supported

by PowerGraphics. Therefore there is the need to insert the

/GRAPH,FULL command in the script.

We can also print/plot the evolution of the state variables

by utilizing this undocumented APDL command:

ESOL,…,…,…,SVAR,1PRVAR,1 (or PLVAR,1 to plot)

© 2011 ANSYS, Inc. May 9, 201424


/POST26 output: graph of the evolution of state variable #1

(equivalent plastic strain).

0.692053

© 2011 ANSYS, Inc. May 9, 201425


/POST26 output: printout of the evolution of state

variable #1 (equivalent plastic strain).

© 2011 ANSYS, Inc. May 9, 201426


(A) structure with TB,BISOmaterial model

(B) structure with user-defined

elasto-plastic material model

APDL commands:

/POST1

PLESOL,NL,EPEQ,0,1.0

/POST1 output: contour plot of the equivalent plastic

strain at last substep. We notice that the results are

identical for both models.

(A)(B)

© 2011 ANSYS, Inc. May 9, 201427


/POST1 output: contour plot of state variable #1

(equivalent plastic strain) at last substep. We notice that it

is non-zero only when considering the structure (cube on

the right) with the user-defined routine.

(A) structure with TB,BISOmaterial model

(B) structure with user-defined

elasto-plastic material model

APDL commands:

/POST1

PLESOL,SVAR,1

(A)(B)

© 2011 ANSYS, Inc. May 9, 201428

Where to find additional information

Additional information on rate-independent plasticity can

be found in the online manual:

Also, the ANSYS training course “ANSYS Mechanical –

Advanced Nonlinear Materials” provides detailed

information regarding plasticity and, in this respect, it is

recommended.

ANSYS Documentation > Mechanical APDL > Material Reference > 3. Material Models // 3.4. Rate-Independent Plasticity

ANSYS Documentation > Mechanical APDL > Theory Reference > 4. Structures with Material Nonlinearities > 4.2. Rate-Independent Plasticity

ANSYS Documentation > Mechanical APDL > Structural Analysis Guide > 8. Nonlinear Structural Analysis > 8.4. Modeling Material Nonlinearities

© 2011 ANSYS, Inc. May 9, 201429

Where to find additional information

Another usage example of the usermat subroutine is

available in the online documentation, precisely in Chapter

40 of the Technology Demonstration Guide:

ANSYS Documentation > Mechanical APDL > Technology Demonstration Guide > 40. Large-Deformation Neo-Hookean Analysis (via UserMat Subroutine)

The problem formulates a 3-D large deformation,

hyperelastic material to demonstrate the user material

capability in nonlinear geometry analyses. Details are given

for stress and material tangent calculations and formulation

in a co-rotated frame, as well as conversion of tensor

quantities to Voigt notation.

Implementing User-Programmable Features (UPFs) in ANSYS · Also, the ANSYS training course “ANSYS...

Documents

Transcript of Implementing User-Programmable Features (UPFs) in ANSYS · Also, the ANSYS training course “ANSYS...