Implementation of v Um At
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Transcript of Implementation of v Um At
Implementation of VUMAT
Wenhai Wang
Advisor : Dr. Antonios Zavaliangos
October 15th 2003
UMAT & VUMATUMAT and VUMAT are the user subroutines for the definition of USER based constitutive models
UMAT ABAQUS/Standard--implicit time integration, must provide "material stiffness matrix" for use in forming the Jacobian of the nonlinear equilibrium equations;
VUMAT ABAQUS/Explicit--Explicit time integration, not necessary forming the Jacobianmatrix.
Where Does VUMAT “Fit” in ABAQUS?
ABAQUS
Solving equations of equilibrium
)(),(),( tFtVtX iii )( ttX i ∆+
iε∆)( tti ∆+σ
VUMAT
Solving equations of mechanics
)(tiσ
)( ttFi ∆+
•ABAQUS constitutive library is extensive BUT;
Some models are missing;Some models are not flexible
enough;Example: Gurson Model*POROUS METAL PLASTICITY, RELATIVE DENSITY=0.951. , 1. , 1.
•We can develop our models.
Why Is VUMAT Important?
ABAQUS SUBROUTINEτεσ ∆,t
Stress at t time &strain increment
YIELDCONDITION
Combine the flow rule,Update the stress at t+dt time
*σ
hydrostatic Pressure & equivalent stress
** ,Pσ
trial stress:update the stress at t+dt time using trial stress
*
*
)()(PdttP
dtt=+
=+ σσ
VUMAT
ABAQUS SUBROUTINEτεσ ∆,t
Stress at t time &strain increment
YIELDCONDITION
Combine the flow rule,Update the stress at t+dt time
*σ
hydrostatic Pressure & equivalent stress
** ,Pσ
trial stress:update the stress at t+dt time using trial stress
*
*
)()(PdttP
dtt=+
=+ σσ
VUMAT
ABAQUS SUBROUTINEτεσ ∆,t
Stress at t time &strain increment
ABAQUS SUBROUTINEτεσ ∆,t
Stress at t time &strain increment
ABAQUS SUBROUTINEτεσ ∆,t
Stress at t time &strain increment
YIELDCONDITION
Combine the flow rule,Update the stress at t+dt time
*σ
hydrostatic Pressure & equivalent stress
** ,Pσ
trial stress:update the stress at t+dt time using trial stress
*
*
)()(PdttP
dtt=+
=+ σσ
VUMAT
YIELDCONDITION
Combine the flow rule,Update the stress at t+dt time
*σ
hydrostatic Pressure & equivalent stress
** ,Pσ
trial stress:update the stress at t+dt time using trial stress
*
*
)()(PdttP
dtt=+
=+ σσ YIELDCONDITION
Combine the flow rule,Update the stress at t+dt time
*σ
hydrostatic Pressure & equivalent stress
** ,Pσ
trial stress:update the stress at t+dt time using trial stress
*
*
)()(PdttP
dtt=+
=+ σσ*
*
)()(PdttP
dtt=+
=+ σσ
VUMAT
Debug and Run a VUMATInput File: Subroutine (VUMAT):
C:\>abaqus job=test input=dpnodev user=vumat datacheck
C:\>abaqus job=test input=dpnodev user=vumat
ABAQUS Command:
Structure of VUMAT
)31
23()(
)(
)()(
)()()(
'*
klkl
ijkl
plijklijkl
plijkl
elijkl
PLdtt
LLt
Lt
Ltdtt
δσσ
σλσ
εεσ
εεσ
εσσ
∂Φ∂
+∂Φ∂
−+=
∆−∆+=
∆−∆+=
∆+=+
εσ∆
)(t
...)(tf
Elasticity Strain decomposition
Stress:
Strain increment:
State variables:
)( dtt +σ
...)( dttf +
Flow rule
An 1-D Example of UMAT)(tu
L
)(tσ
)(tε εεε ∆+=+ )()( tdtt
?
σ
ε
u
t
)();( ttu σ know
ABAQUS:1.Calculate from Boundary Conditions)( dttu +
2.Strain incrementL
tudttu )()( −+=∆ε
VUMAT:plel εεε ∆+∆=∆
11
)()(σ
λσσε∂Φ∂
+−+
=∆E
tdtt
If , step is elastic;If , step is plastic;0
0≠=
λλ
An 1-D Example of UMAT (cont.)
If , Plastic. Go to STEP II;If , Elastic. End and return to ABAQUS;Y
Y
dttdtt
σσσσ
<+>+
)()(
11
)()(σ
λσσε∂Φ∂
+−+
=∆E
tdtt
STEPI: Assume step is elastic
11
)()(σ
λσσε∂Φ∂
+−+
=∆E
tdtt εσσ ∆+=+ Etdtt )()(
STEPII: Only if plastic
11
)()(σ
λεσσ∂Φ∂
−∆+=+ Etdtt
Plastic means Ydtt σσ =+ )(
11/)(
σσεσλ
∂Φ∂−∆+
= YEt
Problem is complex for 3D and complex models
Idea of The Algorithm
)(*)(131
1)()( '' dttG
dtt +⎟⎠⎞
⎜⎝⎛
∂Φ∂+
=+ σ
σσλ
σ
PKdttPdttP
∂Φ∂
−+=+ λ)()( *
Yield CondtionsELLIPSE MODEL
GURSON MODEL
DRUCKER-PRAGER
01)()(),,( 22 =−+=Φ pDBDADp σσ
0))1(1()23cosh()1(2),,( 22
12
1
2
=−+−−+=Φ DqpqDqDpYY σσ
σσ
01)()(
0tan22 =−+−=
=−−=
σ
βσ
RBppAF
dpF
ac
s
01))()(())((),,( 22 =−−+=Φ fpcrpfBfAfpYY σσ
σσ
CRITICAL STATE MODEL/CAM CLAY MODEL
Associated and Non-associated
Non-associated Associated
Outline of A Typical VUMAT1. Trial stress: εσσ ∆+=+ *)()(* Ltdtt
2. Check if 0* ≤Φ if yes, the new stress is equal to the trial stress:
)()( * dttdtt +=+ σσif no, call VUMAT_SUBROUTINE
3. VUMAT Subroutine:
calculate the λ by using Newton-Raphson method
4. Update the new stress
)(*)(131
1)()( '' dttG
dtt +⎟⎠⎞
⎜⎝⎛
∂Φ∂
+=+ σ
σσλ
σ
PKdttPdttP
∂Φ∂
−+=+ λ)()( *
5. Return to ABAQUS
Difficulties & Disadvantages
Convergence of newton-raphson method;
Time step increment selection;
Time consuming.
Single Element Compress
1 2
4 3
2
1
Initial geometry: Final geometry:
CPU Time:ABAQUS : VUMAT = 00:00:04 : 00:00:10
S22
ABAQUSVUMAT
VVF (Porosity)
ABAQUSVUMAT
Cylinder CompressionInitial geometry: Final geometry:
CPU Time:ABAQUS : VUMAT = 00:08:15 : 01:25:04If Purely elastic problem, ABAQUS : VUMAT = 00:04:25 : 00:05:01
Most of the CPU time on VUMAT subroutine !
S22
ABAQUS:
VUMAT:
VVF
ABAQUS:
VUMAT:
S22 at Selected PointsS22 at element15: S22 at element 1915:
ABAQUSVUMAT
VVF at Selected PointsVVF at element 30: VVF at element 801:
ABAQUSVUMAT
Rolling
ABAQUS:
VUMAT:
CPU Time:ABAQUS : VUMAT = 00:58:04 : 06:04:23
RF2ABAQUSVUMAT
Future WorkImplementation of the Drucker-Prager Model for Explicit;
Calibrate from the experimental data and derive the models;
Develop other models for powder compaction.