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Dynamore GmbH
Industriestraße 2
70565 Stuttgart
http://www.dynamore.de
GISSMO – Material Modeling with
a sophisticated Failure Criteria
André Haufe, Paul DuBois, Frieder Neukamm, Markus Feucht
LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
2 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Motivation
3 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Weight Composites
High strength steel
Light alloys
Polymers
Safety requirements
Cost effectiveness
New materials
Design to the point
New power train
technology
Technological challenges in the automotive industry
4 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Technological challenges in the automotive industry
Damage
max
E
Failure
fail true
E
Anisotropy c
a
b
( )eE
y
Fracture growth Debonding
Weight Composites
High strength steel
Light alloys
Polymers
Safety requirements
Cost effectiveness
New materials
Design to the point
New power train
technology
Plasticity
5 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Mapping
Forming simulation
Closing the process chain: Standard materials / state of the art
v. Mises or Gurson model
Strain rate dependency
Isotropic hardening
Damage evolution
Failure models
(mapping of damage variable)
II
I
III
Hill based models
Anisotropiy of yield surface
Kinematic/Isotropic hardening
State of the art: Failure by FLD
(post-processing)
NEW: Computation of damage
(GISSMO)
II
IIII
II
I
III
Crash simulation
6 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Preliminary considerations
for plane stress
7 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Some thoughts on damage formulations
Is path dependence critical for the target application (crashworthiness)?
Is a phenomenological model good enough?
Should we take orthotropic effects into account (i.e. tensorial damage)
or is a scalar formulation fine?
Shall we accumulate the damage value based on the stress state
or on the strain state?
Shall the damage accumulation be isotropic, orthotropic or at least
pressure dependent?
8 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
J. Lemaitre, A Continuous Damage
Mechanics Model for Ductile Fracture
Overall Section Area
containing micro-defects
Reduced (“effective“)
Section Area
SS ˆS S
SSD
ˆ
Measure of
Damage
Reduction of effective cross-section leads to
reduction of tangential stiffness
Phenomenological description D 1*
σσ
Isotropic (scalar) damage Effective stress concept (similar to MAT_81/120/224 etc.)
9 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Plane stress condition
Principle axis
0
0
0
3
2
1
σ0
),(
),(
3
2
1
Plane stress
1
1
2
1
0 0
0 0
0 0 0
1 ( 1)vm
k
k k
σ1
12 k
Definition of stress triaxiality:
11
2
1
( 1) ( 1)sign( )
3 1 ( 1)3 1 ( 1)vm
p k k
k kk k
Parameterised
xx
yyxy
yx
Typical discretization with shell elements:
10 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Haigh-Westergaard coordinates in principle stress space
1
2
3
1.5
2
1tr( )
3 3
2 :
1 3 3arccos
3 2
I
J
J
J
σ
s s
Deviatoric
plane
Lode angle
vm
p
Definition of stress triaxiality:
11 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
A toy to visualize stress invariants (downloadable from the www.dynamore.se)
• Download the PDF-file
• Print on thick piece of paper
• Cut out where indicated
• Add four wooden sticks (15cm)
• Add some glue where necessary
(engineers should find out the locations without
further instructions – all others contact their
local distributor)
• Have fun!
Crafting instructions page 1:
12 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
A toy to visualize stress invariants (downloadable from the www.dynamore.se)
• Page 2 of the set may be added for further
clarification of the triaxiality variable.
Crafting instructions page 2:
Final shape of toy
13 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Plane stress parameterised for shells
Triaxiality
11
2
1
( 1) ( 1)sign( )
3 1 ( 1)3 1 ( 1)vm
p k k
k kk k
Bounds:
k
vm
p
1 1
( 1) 1lim lim sign( ) sign( )
33 1 ( 1)k k
k
k k
1 1
( 1) 1lim lim sign( ) sign( )
33 1 ( 1)k k
k
k k
1 11 1
( 1) 2lim lim sign( ) sign( )
33 1 ( 1)k k
k
k k
Compression
Biaxial tension
Tension
tension compression
14 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
How to define the accumulation of damage ? A comparison of model approaches
Investigation of failure criteria for the following case:
Plane stress:
Small elastic deformations:
Isochoric plasticity:
Proportional loading:
3 0
1 1 2 2p pand
2 1
2 1p p
a
b
3 3 1 2p p p
1 2
2
ba
b
2 21
2 21
2
41
3
1
1
3 1
p p
vm
vm
b b
a a
p a
a a
Damage or failure criteria
15 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
How to define the accumulation of damage ? A comparison of classical model approaches
Some typical loading paths
16 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
How to define the accumulation of damage ? A comparison of classical model approaches
Some typical loading paths
1 max 1 1 max
2max2 2
1 max 1 2
3max max3 1
2
1 max 2
4 31
3 4 1
2 1 2 1
2 11 2 2
p
p p p
pp p
p
b bb b
b b
b bb b b
Four criteria
Principal strain:
Equivalent plastic strain:
Thinning:
Diffuse necking:
17 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Failure models in the plane of principal strain
Failure strain under
uniaxial tension is
set the same in all
4 criteria.
Thinning and FLD predict
no failure under pure
shear loading.
18 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Failure models in the plane of major strain vs. b
19 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Failure models in the plane equivalent plastic strain vs. b
Calibrating different criteria
to a uniaxial tension test
can lead to considerably
different response in other
load cases.
20 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Failure models: equivalent plastic strain vs. triaxiality
2, 1, 1,
1, 2, 1,
0.5
2
p p p p
p p p p
For uniaxial and biaxial tension
different criteria lead to a factor
of 2:
21 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Johnson-Cook criterion (Hancock-McKenzie )
3
1 2
1
3
12
2 1
0
32
vm
pd
pf
f
d d e
d
d
d e
Johnson-Cook and
FLC are very close in
the neighborhood of
uniaxial tension.
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Parametrized for 3D stress space
23 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Lode-angle: Extension- and Compression test
I
III
II
0
II III
Iand
View parallel and on hydrostatic axis
(perpendicular to deviator plane)
Possible value for first
principle stress
I
III
II
Compression
0
II III
Iand
View not parallel to hydrostatic axis
Extension
30
30
Co
mp
ressio
n
24 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
1 01
1
1
0 0
10 04
10 0
4
1
1
0 0
0 0
0 0 0
1
1
0 0
10 02
0 0 0
1 0 0
0 0 0
0 0 0
1
1
0 0
0 0 0
0 0
1
0 0 0
0 0 0
0 0
1
1
1
0 0
0 0
10 0
2
3D-Stress state parameterised for volume elements
compression
extension
vm
p
F
25 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Parameter definition
1
3
m
vM vM
I
3
3
27
2 vM
J
3 1 2 3J s s smit
[Source: Wierzbicki et al.]
Stress domain in
sheet metal forming
Invariants in 3D stress space Failure criterion extd. for 3D solids
1 30or
0 0or
1 30or
26 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Deriving GISSMO from that…
27 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Forming simulation
Closing the process chain: UHS materials for press hardening
v. Mises or Gurson model
Strain rate dependency
Isotropic hardening (locally)
Damage evolution (locally)
Failure models
(mapping damage variable)
II
I
III
Hill based models
Ortho- or isotropic yield surface
Isotropic hardening
Feasibility by thinning or
damage (calibration?!)
Dependency on temperature
Microstructural evolution (#244)
II
IIII
II
I
III
Crash simulation
Mapping
28 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Different ways to realize a consistent modeling
One Material Model for Forming and
Crash Simulation
Requirements for Forming Simulations:
Anisotropy, Exact Description of Yield
Locus, Kinematic Hardening, etc.
Requirements for Crash Simulation:
Dynamic Material Behavior, Failure
Prediction, Energy Absorption, Robust
Formulation
Leads to very complex model
Modular Concept for the Description
of Plasticity & Failure
Plasticity and Failure Model are treated
separately
Existing Material Models are kept
unaltered
Consistent modeling through the use of
one damage model for forming and crash
simulation
*MAT_ADD….(damage)
29 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Produceability to Serviceability: Modular Concept
Damage model
Material model Material model 00, , tpl
pl ,
Mapping
tpl ,
D D Damage model
pl ,
Forming simulation Crash simulation
D D
Modular Concept:
Proven material models for both disciplines are retained
Use of one continuous damage model for both
30 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
GISSMO
Barlat Mises 00,0 ,, tpl
pl ,
Mapping
tpl ,,
Fo
rtra
n-P
rog
ram
D D
GISSMO
pl ,
Forming simulation Crash simulation
Ebelsheiser, Feucht & Neukamm [2008]
Neukamm, Feucht, DuBois & Haufe [2008-2010]
Produceability to Serviceability: Modular Concept Current status in 971R5
31 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Parameter definition
1
3
m
vM vM
I
3
3
27
2 vM
J
3 1 2 3J s s smit
[Source: Wierzbicki et al.]
Stress domain in
sheet metal forming
Xue
Hutchinson
Gurson std.
Xue
Hutchinson
Gurson std.
f
[Experimental data
by Wierzbicki et al.]
GISSMO Failure criterion extd. for 3D solids
32 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Gurson
Mises
Forming Crash
GISSMO
Damage evolution
Damage regularly
overestimated for linear
damage accumulation!!
Failure curve
Neukamm, Feucht, DuBois & Haufe [2008-2010]
GISSMO - a short description Ductile damage and failure
triaxiality
33 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Gurson
Mises
Forming
Crash
Material Instability
11
,
nv
v loc
nF F
Flachzugprobe DIN EN 12001
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0,45
0,50
0,00 0,05 0,10 0,15 0,20 0,25 0,30
Simulation
Versuch
Tensile test specimen DIN EN 12001
GISSMO – a short description Engineering approach for instability failure n
t
1
2
triaxiality
Neukamm, Feucht, DuBois & Haufe [2008-2010]
Instability evolution Instability curve definition
34 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
GISSMO – a short description
Inherent mesh-size dependency of results
in the post-critical region
Simulation (and calibration) of tensile test
specimen with different mesh sizes
Mesh size dependency: Simple regularisation Test program and calibration
35 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
DMGTYP: Flag for coupling (Lemaitre)
D 1*
DCRIT, FADEXP: Post-critical behavior
0
0
True Strain
Tru
e S
tre
ss
GISSMO dmgtyp2
MAT_024
0
0True Strain
Tru
e S
tre
ss
m=2
m=5
m=8
FADEXP
CRIT
CRIT
D
DD
11*
GISSMO – a short description for the uniaxial case Generalized Incremental Stress State dependent damage MOdel
36 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Failure strain depending on
Loading state
Load path and pre-damage
Accumulation of damage
)( fail
fail
eqm /
Failure
GISSMO Non-proportional loading influence on failure behavior
37 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Non-Proportional Loading
vm
p
f
0.577 0.333
Triaxiality is no longer constant
over the stress-strain path if
lateral constraint is imposed or
lifted.
Compare 4 load paths:
A uniaxial tension
B uniaxial tension with lateral confinement
C uniaxial tension with/without confinement
D uniaxial tension without/with confinement
A B C D
A B
C
D
38 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Non-proportional loading criterion without triaxiality
1 0.4
1
f
p
p ff
d
d dt
vm
p
f
0.577 0.333
39 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Non-proportional loading criterion with triaxiality
3 1.5
1 2 0.66
1
vm vm
vm
p pd
f
pcte
p
p ff
d d e e
d dt
vm
p
f
0.577 0.333
40 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Comparison: Uniaxial tension with/without confinement
vm
p
f
0.577 0.333
43 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Input of GISSMO
*MAT_PIECEWISE_LINEAR_PLASTICITY
$ mid ro e pr sigy etan fail tdel
100 7.8000E-9 2.1000E+5 0.300000
$ c p lcss lcsr vp
0.000 0.000 99 0 1.000
...
*MAT_ADD_EROSION
$ MID EXCL MXPRES MNEPS EFFEPS VOLEPS NUMFIP NCS
100
$ MNPRES SIGP1 SIGVM MXEPS EPSSH SIGTH IMPULSE FAILTM
$ IDAM DMGTYP LCSDG ECRIT DMGEXP DCRIT FADEXP LCREGD
1 0 11 0.3 2 0.2 2 12
$ SIZFLG REFSZ NAHSV
0 5 4
Standard material
Input (i.e. MAT_24)
Input definition in LS-DYNA (1/4)
Standard failure
parameters (optional)
GISSMO failure
parameters
If IDAMG=1 GISSMO is invoked.
Further parameters are expected.
DMGTYP=0: Damage is accumulated
But not coupled to stresses, no failure.
DMGTYP=1: Damage is accumulated
and coupled to flow stress if D>Dcrit.
Failure occurs if D=1.
44 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Input of GISSMO
*MAT_PIECEWISE_LINEAR_PLASTICITY
$ mid ro e pr sigy etan fail tdel
100 7.8000E-9 2.1000E+5 0.300000
$ c p lcss lcsr vp
0.000 0.000 99 0 1.000
...
*MAT_ADD_EROSION
$ MID EXCL MXPRES MNEPS EFFEPS VOLEPS NUMFIP NCS
100
$ MNPRES SIGP1 SIGVM MXEPS EPSSH SIGTH IMPULSE FAILTM
$ IDAM DMGTYP LCSDG ECRIT DMGEXP DCRIT FADEXP LCREGD
1 0 11 0.3 2 0.2 2 12
$ SIZFLG REFSZ NAHSV
0 5 4
Standard material
Input (i.e. MAT_24)
Input definition in LS-DYNA (2/4)
Standard failure
parameters (optional)
GISSMO failure
parameters
ID of curve defining equivalent plastic
strain at failure vs. triaxiality.
Damage will have values from 0 up to 1.0.
ECRIT: Equiv. plastic strain at instability onset.
If negative a curve is expected that defines
ECRIT vs. traiaxiality.
If ECRIT=0 the ordinate value Dcrit is used.
Exponent for nonlinear damage
accumulation:
45 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Input of GISSMO
*MAT_PIECEWISE_LINEAR_PLASTICITY
$ mid ro e pr sigy etan fail tdel
100 7.8000E-9 2.1000E+5 0.300000
$ c p lcss lcsr vp
0.000 0.000 99 0 1.000
...
*MAT_ADD_EROSION
$ MID EXCL MXPRES MNEPS EFFEPS VOLEPS NUMFIP NCS
100
$ MNPRES SIGP1 SIGVM MXEPS EPSSH SIGTH IMPULSE FAILTM
$ IDAM DMGTYP LCSDG ECRIT DMGEXP DCRIT FADEXP LCREGD
1 0 11 0.3 2 0.2 2 12
$ SIZFLG REFSZ NAHSV
0 5 4
Standard material
Input (i.e. MAT_24)
Input definition in LS-DYNA (3/4)
Standard failure
parameters (optional)
GISSMO failure
parameters
Fading exponent as defined in:
SIZFLG=0 (default) Characteristic element is
computed with respect to initial configuration.
SIZFLG=1 Characteristic element updated in each
increment (actual configuration, not recommended)
Load curve defining element size dependent
regularization factors vs. equiv. plastic strain to
failure.
FADEXP
CRIT
CRIT
D
DD
11*
46 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Input of GISSMO
*MAT_PIECEWISE_LINEAR_PLASTICITY
$ mid ro e pr sigy etan fail tdel
100 7.8000E-9 2.1000E+5 0.300000
$ c p lcss lcsr vp
0.000 0.000 99 0 1.000
...
*MAT_ADD_EROSION
$ MID EXCL MXPRES MNEPS EFFEPS VOLEPS NUMFIP NCS
100
$ MNPRES SIGP1 SIGVM MXEPS EPSSH SIGTH IMPULSE FAILTM
$ IDAM DMGTYP LCSDG ECRIT DMGEXP DCRIT FADEXP LCREGD
1 0 11 0.3 2 0.2 2 12
$ SIZFLG REFSZ NAHSV
0 5 4
Standard material
Input (i.e. MAT_24)
Input definition in LS-DYNA (4/4)
Standard failure
parameters (optional)
GISSMO failure
parameters
Reference element size for which the failure
parameters were calibrated. This may be used
when mapping of failure parameters from finer
to coarser meshes is necessary.
Number of additional history variables written to d3plot-
database. Please keep in mind, that this additional.
history variable are added to the standard variables of
the corresponding material model. I.e. the sum of both
history variable sets needs to be defined in
*DATABASE_EXTEND_BINARY. The number of the
history variables used in the material model (i.e.
MAT_24 in this example) is written to d3hsp-file.
47 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Flachzugproben DIN EN 10002
0,00
0,10
0,20
0,30
0,40
0,50
0,60
0,00 0,10 0,20 0,30 0,40
Mini-Flachzugproben ungekerbt
0,00
0,10
0,20
0,30
0,40
0,50
0,60
0,0 0,2 0,4 0,6 0,8
Mini-Flachzugproben Kerbradius 1mm
0,0
0,1
0,2
0,3
0,4
0,5
0,6
-0,10 0,10 0,30 0,50
Arcan
0
2
4
6
8
10
12
0,0 0,5 1,0 1,5
Scherzugproben Kerbradius 1mm, 0°
0,00
0,10
0,20
0,30
0,40
0,50
0,60
0,00 0,05 0,10 0,15 0,20
Scherzugproben Kerbradius 1mm, 15°
0,00
0,10
0,20
0,30
0,40
0,50
0,00 0,05 0,10 0,15 0,20
Scherzugproben Kerbradius 1mm, 15°
0,00
0,10
0,20
0,30
0,40
0,50
0,00 0,05 0,10 0,15 0,20
eps_technisch
Sig
ma_
tech
nis
ch [
GP
a]
Versuch
GISSMO
Gurson
constant (v. Mises)
Small tensile test specimen Notched tensile specimen, notch radius 1mm Shear test, inclined 15
Tensile specimen DIN EN 12001 Shear test, straight
GISSMO vs. Gurson vs. MAT_24/81 Comparison of experiments and simulations
48 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
GISSMO
Failure Strain constant
Fracture energy constant
Identification of Damage Parameters
is more straight-forward
Gurson
Resultant Failure Strain constant
Failure energy depending on el. size
Identification of damage parameters
is difficult
Gurson vs. GISSMO – “regularized” Regularization of element size dependency
49 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Summary
Use of existing material models and respective parameters
Constitutive model and damage formulation are treated separately
Allows for the calculation of pre-damage for forming and
crashworthiness simulations
Characterization of materials requires a variety of tests
Offers features for a comprehensive treatment of damage
in forming simulations and allows simply carrying aver to crash
analysis
50 LS-Dyna Developer Forum 2011 – DYNAmore – Stuttgart – A. Haufe
Thank you for your attention!
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