User Subroutines in ABAQUS · 2020-04-25 · Finite Element Software Packages ANSYS ABAQUS LS-DYNA ... User Subroutines in ABAQUS Winter 2015 4. Introduction Understanding the fundamental

User Subroutines in ABAQUS

Saeid Poorasadion

Ph.D. CandidateMechanical Engineering Department

Sharif University of Technology

Email: [email protected], [email protected]

Winter 2015

Contents

Introduction

User Subroutines

UMAT

Writing UMAT Writing UMAT

Examples

• 1D Elastic

• Isotropic Hardening Plasticity

• Neo-Hookean Hyperelasticity

VUMAT

S.Poorasadion User Subroutines in ABAQUS Winter 2015 2

Introduction

3

Introduction

Finite Element Software Packages

ANSYS

ABAQUS

LS-DYNA

Which Software??


Introduction

Understanding the fundamental concepts of nonlinearfinite element analysis:

Selecting the best solution procedure and goodstrategy for developing a reasonable model

• Selecting appropriate element and BCs• Selecting appropriate element and BCs

Developing a new solution procedure

• New constitutive model for material

• New element


Textbook for Nonlinear FEM: Nonlinear finite elements for continua and structures (Belytschko, et al.)

Introduction

Finite Element Method

Implicit method

Initial Displacements

Calculate Strain

Calculate Stress

Using Constitutive ModelIf change of one or more sections in these solution is required, we should write a new code in a programming

language!!?

Calculate Internal Force & Compare with

External Force

Calculate Tangent Matrix

Calculate Tangent Stiffness Matrix

Modify Displacements

(Newton method)

Solution Complete

Using Constitutive Model

< Tol

language!!?


Introduction

Main Problem

Creating a software to simulate a specificapplication:

– Simulating shape memory alloys

– Creating a new element (B- spline element)

• Developing a finite element code in program languages– Limitation in BCs and geometry

• Adding an appropriate code to Finite Element SoftwarePackages

User Subroutines


User Subroutines

8

User Subroutines

ABAQUS/Standard 6.10: 51 subroutines

ABAQUS/Explicit 6.10: 20 subroutines

FORTRAN code (.for)

Some popular user subroutines in ABAQUS/StandardSome popular user subroutines in ABAQUS/Standard

DLOAD VDLOAD

UMAT VUMAT

UEL VUEL

UHYPER


User Subroutines

Where User Subroutines Fit into ABAQUS/Standard


User Subroutines



User Subroutines



User Subroutines


User SubroutinesUser Subroutines& Scripting Interface??


Programming

To include user subroutines in an analysis:

Through ABAQUS execution command

• abaqus job=my_analysis user=my_subroutine

Through ABAQUS/CAE

• Job Module > General Tab>Address to User Subroutinefile


Programming

To include user subroutines in an analysis:

Through ABAQUS execution command

• abaqus job=my_analysis user=my_subroutine

Through ABAQUS/CAE

• Job Module > General Tab>Address to User Subroutinefile


Programming

Compiling and Linking User Subroutines

A correct compile and link commands should beused automatically

• Microsoft Visual Studio

• Intel Visual Fortran Compiler• Intel Visual Fortran Compiler

IMPORTANT: Consistency among the abovesoftware


Programming

Subroutine Argument Lists

Variables to be defined

Variables that can be defined

Variables passed in for information

Naming ConventionsSubroutines or COMMON blocks should begin with the letter K


UMATUser-defined MaterialUser-defined Material

18

UMAT

FEMPre-Processing

(Boundary ConditionGeometry, Mesh

External Nodal Force)

Stress, DS/De

1.Initial Displacements For increment i

2.Calculate Internal Nodal Force for element3.Calculate tangent Stiffness Matrix for element

1.Assembly Internal Nodal Force2.Assembly tangent Stiffness Matrix Stress, DS/De2.Assembly tangent Stiffness Matrix

3.Apply Boundary Condition4.Check Convergence if yes GOTO 1

5.Modify Displacements GOTO 2

Post-Processing(Stress

DisplacementInternal Nodal Force)

Define B matrix

Calculate StressCalculate Tangent Moduli

Define Internal Nodal ForceDefine Tangent Stiffness Matrix

UMAT


UMAT


UMAT

Called at all material calculation points of Called at all material calculation points of elements (Gauss points)


UMAT

Allows you to implement general constitutiveequation

Define any constitutive model of arbitrary complexity

User-defined material models can be used with anyUser-defined material models can be used with anyABAQUS structural element type

Multiple user materials can be implemented in asingle UMAT routine and can be used together


UMAT Interface


UMAT Interface


Storage of Stress and Strain Components

Stresses and strains are stored as vectors

For plane stress elements: σ_xx, σ_yy, σ_xy

For plane strain and axisymmetric elements: σ_xx,σ_yy, σ_zz, σ_xy

The shear strain is stored as

engineering shear strain


UMAT Variables

Variables to be defined

DDSDDE(NTENS,NTENS)

STRESS(NTENS)

• “true” (Cauchy) stress.

STATEV(NSTATV)

1 JC

J

STATEV(NSTATV)

SSE, SPD and SCD

• Elastic strain energy, plastic dissipation, and “creep”dissipation.

• No effect on the solution and using for energy output

Only in a fully coupled thermal-stress analysis

• RPL (Volumetric heat generation per unit time)

• DDSDDT(NTENS), DRPLDE(NTENS), DRPLDTS.Poorasadion User Subroutines in ABAQUS Winter 2015 26

UMAT Variables

Variables that can be defined

PNEWDT

• Ratio of suggested new time increment to the timeincrement being used

Variables passed in for informationVariables passed in for information

STRAN(NTENS), DSTRAN(NTENS)

• The mechanical strains

• In finite-strain problems, approximations to logarithmicstrain.

TIME, DTIME

TEMP, DTEMP

PREDEF, DPREDS.Poorasadion User Subroutines in ABAQUS Winter 2015 27

UMAT Variables

Variables passed in for information (continued)

CMNAME

NDI, NSHR, NTENS

• Number of direct, shear, total stress components

NSTATV NSTATV

PROPS(NPROPS), NPROPS

COORDS

DROT(3,3)

• Rotation increment matrix

CELENT

• Characteristic element lengthS.Poorasadion User Subroutines in ABAQUS Winter 2015 28

UMAT Variables

Variables passed in for information (continued)

DFGRD0(3,3), DFGRD1(3,3)

NOEL, NPT

• Element, integration point numbers

LAYER, KSPT LAYER, KSPT

• Layer, section point numbers

KSTEP, KINC

• Step, increment numbers


Running UMAT


Running UMAT

Variable:PROPS


Running UMAT


Running UMAT


Running UMAT


Writing UMAT

35

Writing UMAT

Write a code in MATLAB (Debugging in MATLABis fast and easy)

Check MATLAB code with benchmark problems(for example uniaxial test)

Transfer MATLAB code to FORTRAN code

MATLAB CodeStrain,

InformationStress, DS/De


Transfer MATLAB Code to FORTRAN Code

MATLAB

FORTRAN


When assigning a value to a double precisionvariable, D-scientific notation should be used.

Debugging

Fortran Code Output


Debugging

Which is correct?


Debugging

Error: Problem during compilation

Go to file job_name.log in work directory (temp)


Debugging

Divide by zero

5/0.d0

a/b when b is zero in first time (STRAN and DSTRANare zero in first time)


Debugging

Write or print a parameter in Data File tab

write (6,*) 'tt‘ , KINC, …


Example 1: 1D Elastic


Small Strain, Large Rotation

Turn on Nlgeom in Steps

STRAN, DSTRAN and STRESS have been rotated toaccount for rigid body motion in the incrementbefore UMATbefore UMAT

the basis system for the material point rotates withthe material

DROT: Rigid body rotation

Use this variable to rotate internal variable inconstitutive model.

• Plastic strain


Large Strain, Large Rotation

Turn on Nlgeom in Steps

STRESS is Cauchy stress and have been rotated toaccount for rigid body motion in the incrementbefore UMAT.

Use DFGRD0 and DFGRD1Use DFGRD0 and DFGRD1

The deformation gradient is available for solid(continuum) elements, membranes, and finite-strain shells. It is not available for beams or small-strain shells

DROT: Rigid body rotation


Large Strain, Large Rotation

The consistent Jacobian should be used to ensurerapid convergence.

The exact consistent Jacobian C

:c cJ J D C

iW W I

W W I

C

:

1

c cJ J D

J

J

C

CD

2 2

2 4

i

i

CE

CEijkl im jn kp lq mnpq

W W I

I

W

C F F F F C

SC C

SC

C C C

T TK B C BdV dV S.Poorasadion User Subroutines in ABAQUS Winter 2015 46

Examples

47

Example 2: Neo-Hookean Hyperelasticity

Neo-Hookean Free energy relationship

The Cauchy and PK2 stress tensor

21

10 21

3

13 1

IU C J

DJ

10

1

2

2

C

KD

The Cauchy and PK2 stress tensor

1

1

2/3 1 1110

1

2 2

2 21

3

IU U U JS

I J

IC J I J J

J D

C C C

C C

1

1

ij

I

JJ

C

CC

101

2 1 21

3C tr I J I

J D

B B

2/3

1

JB B



The material Jacobian derives from the variation inKirchhoff stress

The material Jacobian:JC D

2

4 2SE U

SC

C C CRelations 5.4.43 and 4 2SE

SEijkl im jn kp lq mnpq

U

C F F F F C

SC

C C C

10

1

2 1

22 2 2 2

2 13 3 9

ijkl ij jl ik jl il jk il jk

ij kl ij kl ij kl mm ij kl

C C B B B BJ

B B B JD

Relations 5.4.43 and 5.4.50 in Textbook



Main Box

Define Array and Constant



Calculate Material Parameter

Calculate J and Distortion Tensor



Calculate deviatoric left Cauchy-Green

deformation tensor

TB FF

Calculate Cauchy Stress

TB FF

10

1

2 1

32

1

C tr IJ

J ID

B B



Calculate material Calculate material Jacobian


Hyperelastic Materials

Derivation of consistent Jacobian is difficult2

4 2SE


U

C F F F F C

SC

C C C


Hyperelastic Materials

Derivation of consistent Jacobian is difficult2

4 2SE


U

C F F F F C

SC

C C C

Hyperelastic materials are often implemented more easily in user Subroutine UHYPER

Because of requiring the values of the derivativesof the strain energy density function respect to

the strain invariants


Example 3: Isotropic Hardening Plasticity

Elasticity:

Yield function:

2el elij ij kk ij

30

2pl

ij ij YS S 1

3ij ij ij kkS

Equivalent plastic strain

Plastic flow law

02 ij ij YS S

0

2,

3

t

pl pl pl pl plij ijdt

3ij ij ij kkS

3

2

ijpl plij

Y

S



We first calculate the von Mises stress based onpurely elastic behavior (elastic predictor).

If the elastic predictor is larger than the current yieldstress, plastic flow occurs.

The radial return method is used to integrate the The radial return method is used to integrate theequations.

The consistent Jacobian:

* * *2 31 / 3ij ij kk ij ij kl kl

h

h

* * *2, , ,3

prij Y Y

ij pr pr pl

S dk h

d



We first calculate the von Mises stress based onpurely elastic behavior (elastic predictor).

If the elastic predictor is larger than the current yieldstress, plastic flow occurs.

The radial return method is used to integrate the

This result is also true for large-strain calculations. The radial return method is used to integrate the

equations.

The consistent Jacobian:

* * *2 31 / 3ij ij kk ij ij kl kl

h

h

* * *2, , ,3

prij Y Y

ij pr pr pl

S dk h

d


calculations.



1

3

2

3

2

ijpl plij

Y

ijpl pl plij ijn n

Yplij n

S

S

Rotate Forward


F > TolNo F > 0





VUMAT

In ABAQUS/Explicit the user-defined material modelis implemented in user subroutine VUMAT

The material Jacobian does not need to be defined inVUMATVUMAT

UMAT or VUMAT???


Ho! O Saki, pass around and offer the bowlFor love at first appeared easy, but difficulties have occurred

یا ا�ھا ا�سا�ی ا� کاسا و �و�ھا اال

ود اول و�ی ا�تاد � ��

� ��ق آسان

Ho! O Saki, pass around and offer the bowlFor love at first appeared easy, but difficulties have occurred

Documents

User Subroutines in ABAQUS · 2020-04-25 · Finite Element Software Packages ANSYS ABAQUS LS-DYNA ... User Subroutines in ABAQUS Winter 2015 4. Introduction Understanding the fundamental