Computational fracture mechanics with SAMCEF€¦ · This document is the propertyof SAMTECHS.A....
Transcript of Computational fracture mechanics with SAMCEF€¦ · This document is the propertyof SAMTECHS.A....
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Computational fracture mechanics Computational fracture mechanics
with with SAMCEFSAMCEFNew trends and illustration on an industrial test caseNew trends and illustration on an industrial test case
C. HenrardC. Henrard11, M. Suptille, M. Suptille22, N Visseaux, N Visseaux22, , M. BruyneelM. Bruyneel11
11SAMTECH LiSAMTECH Lièège, Belgiumge, Belgium22SAMTECH Paris, FranceSAMTECH Paris, France
NAFEMS Nordic Regional Conference, "Trends and Future Needs in ENAFEMS Nordic Regional Conference, "Trends and Future Needs in Engineering ngineering Simulation", Gothenburg, Sweden, 26Simulation", Gothenburg, Sweden, 26--27 October, 201027 October, 2010
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Composite and aeronautics applications
Wind turbine modelling
Flexible systems dynamics and mechatronics
Bird impact on a slat
Courtesy of SONACA
Delamination in a composite structures
Few words about SAMTECH
SAMCEF Finite Element codeSAMCEF Finite Element code
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Few words about SAMTECH
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Few words about SAMTECH
Japan
India
USA
CanadaRussia
Korea
ChinaMalaysia
Singapore
Belgium (Headquarters, Liège)
Italy (Milan)France (Paris, Toulouse, Pau)
Spain (Barcelona)
United Kingdom (Bristol)
Germany (Reutlingen, Hamburg)
Bulgaria
Czech Republic
DistributorsSAMTECH offices
Argentina
Chile
World wide representation
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Outline
- Methods available in SAMCEF for fracture mechanics
- XFEM method in SAMCEF
- Applications of XFEM with SAMCEF
- Conclusions
……let me recall that SAMCEF has been used for more th an 25 let me recall that SAMCEF has been used for more th an 25 years by the largest aerospace companies in Europeyears by the largest aerospace companies in Europe
……SAMCEF is already selected for its XFEM solution by :SAMCEF is already selected for its XFEM solution by :
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Methods available in SAMCEF
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FEM without crack box
2D3D
FEM with crack box
XFEM
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Outline
- Methods available in SAMCEF for fracture mechanics
- XFEM method in SAMCEF
- Applications of XFEM with SAMCEF
- Conclusions
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Why XFEM method ?
Classic FE approach
• Difficulty to include a crack in an existing mesh
=> define new geometric items (crack lips) + define a crack box around the crack tip
• Difficulty to study a crack propagation
=> modification of the geometry
=> remeshing is required at each step
?
Crack lips
Crack box
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Classic FE method: illustration
Crack propagation with bifurcation ( crack box )
a
ττττ
Modeling time
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Advantages of XFEM method
XFEM approach : easier definition of a crack
• A crack can be easily defined in the structure
• The crack is defined on the mesh, and can cut the elements
• No more crack box (the stress singularity is included in the enrichment)
• A same mesh can be used to study different crack configurations
OR
Enriched FE
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XFEM approach : simplified crack propagation
• The crack is defined on the mesh, and can cut the elements
• No more crack box to move with the crack tip
• No more updating of the geometry (crack tips)
=> no remeshing (to some extent)
Advantages of XFEM method
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XFEM method features in SAMCEF
XFEM in SAMCEF
Enrichment (true XFEM method of Belytschko and Moes)
Specific integration scheme is adpoted
Implicit crack representation with level-sets
Stress Intensity Factors (SIF) computation
Automatic fatigue crack propagation
Research contacts and partnerships
- Prof. Nicolas Moës (Ecole Centrale de Nantes, France)
- CENAERO (Belgium): our key partner
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Classical dof Additional dof
Displacement field ∑ ∑∑∑∈ =∈∈
++=
1
4
1)()()()()()(
Ki l
lili
Liii
Niii cFNHNbNuu xxxxxx
Crack tip
• discontinuity of u(x) )2/sin()(1 θrF =x
)2/cos()(2 θrF =x
)sin()2/sin()(3 θθrF =x
)sin()2/cos()(4 θθrF =x
)2/sin()(1 θrF =x
• accuracy of the solution
crack tip
Displacement discontinuity
H(x,y) = 1
H(x,y) = -1
discontinuity
HN3 HN3
1
2
3
4
discontinuity
function H (+1,-1)
XFEM method: enrichment
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XFEM method: integration
Triangulation of the element for the integration
4 3
1 2 X
Y
u1
v1
u2
v2
u3
v3
u4
v4
b1
c1
b2
c2
b3
c3
b4
c4
4 3
1 2 X
Y
+
-
Discontinuous H function => integration on each side
Element cut by the crack
Integration ( 2D elements)
Integration ( 3D elements)
x
y
z
Crack plane
Division of the element for the integration
Element cut by the crack
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Implicit representation with level-sets ( 3D)
LSN = 0
LSN <0
LST = 0
Crack surface
θ
r
LST = 0
LST < 0
LST > 0 e1
e3
XFEM method: crack representation
Implicit representation with level-sets ( 2D)
LST = 0
LST = 0
LST < 0
LST > 0
LSN < 0
LSN > 0
LSN = 0
θ r
e1
e2
22 LSTLSNr +=
LST
LSNtg 1−=θ
Level-sets => nodal values
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XFEM method: SIF computation
Computation of the Stress Intensity Factors K 1 and K 2 (2D)
Interaction integral(variant of the J integral on an
equivalent domain)
( ))2()1()2()1(2
)2,1( )1(2IIIIII KKKK
EI +−= ν
)2,1()2()1( IJJJ ++= (1) Present state(2) Auxiliary state
∫ −−−=A
miijmiijmjklkljm dAuuI )( )1(,
)2()2(,
1)2()1(,
)2,1( σσδεσθ
=> KI for KI(2)=1 and KII
(2)=0
=> KII for KI(2)=0 and KII
(2)=1
∫ −−−=A
mlljmlljmjklkljmi dVuuI )( )1(,
)2()2(,
1)2()1(,
)2,1( σσδεσθ
∫Γ
=i
dsGI ii θ)2,1()2,1(
Computation of the Stress Intensity Factors K1, K2 and K 3 (3D)
Interaction integral(variant of the J integral on an
equivalent domain)
( ) )2()1()2()1()2()1(2
)2,1( 1)1(2IIIIIIIIIIII KKKKKK
EG
µν ++−=
Crack front
location i
Set of elements
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For 2D problems (available since 2005 in SAMCEF)
- Not automatic
- Iterative process managed by the user
- Possibility to use BOSS quattro, with a parameterized BACON bank file
- Level-sets completely re-initialized at each iteration
XFEM method: crack propagation
- Automatic
- Based on the update of the level-sets (∆a, θp)
- Criterion = maximum principal stress
- Fatigue based on the Paris/Nasgro law
+±=
II
IIIIp
K
KKK
4
8arctan2
22
θ
( )meffIKC
dN
da ∆=m
effax
effI
K
Kaa
∆∆∆=∆
Im
max
( )materialKKKfctK pIIIIII
effI ,,,, θ∆∆∆=∆
Bifurcation angle
Propagation / fatigue
For 3D problems
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Outline
- Methods available in SAMCEF for fracture mechanics
- XFEM method in SAMCEF
- Applications of XFEM with SAMCEF
- Conclusions
This document is the property of SAMTECH S.A.
XFEM application
σσσσ
L
b
β
Crack 1
R
2D Propagation (done in 2005 for )
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Classical benchmark (3D)
a
ττττ
∑∈
=Ni
iiNuu )()( xx
Initial finite element mesh
XFEM domain
FEM domains
∑ ∑∑∑∈ =∈∈
++=
1
4
1)()()()()()(
Ki l
lili
Liii
Niii cFNHNbNuu xxxxxx
XFEM application
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Classical benchmark (3D)
a
ττττ Finite element mesh Crack (level-sets)
Example of a refinement in the XFEM domain
No remeshing during the crack propagation
XFEM application
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Classical benchmark (3D)
FEM (crack box) XFEM (level-sets)
K1 K1
XFEM application
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Classical benchmark (3D)
3D propagation
Bifurcation
XFEM application
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Industrial test case
Centrifugal load
Imposed radial displacement
Location of the crack (1/4 of a circle)
Level-sets
XFEM application
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Industrial test case
XFEM model FEM model
Contact In-plane crack propagation
Free crack propagation
XFEM application
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Industrial test case: comparaison of SIF
-5000
50010001500200025003000350040004500
0 0.5 1 1.5 2
XFEM - K2 FEM - K2
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
XFEM - K3 FEM - K3
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
XFEM - K1 FEM - K1Initial crack (1/4 circle)
K1
K2 K3
XFEM
FEM (Barsoum)
0
1000
2000
3000
4000
5000
6000
0 0.5 1 1.5 2 2.5 3 3.5
XFEM - K1 FEM - K1
-1000
0
1000
2000
3000
4000
5000
6000
0 0.5 1 1.5 2 2.5 3 3.5
XFEM - K2 FEM - K2
-1000
0
1000
2000
3000
4000
5000
6000
0 0.5 1 1.5 2 2.5 3 3.5
XFEM - K3 FEM - K3
K1
K2 K3
After a 1mm propagation
XFEM application
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Industrial test case: FEM and Barsoum elements
Elliptical cack propagation in a plane
Parameterized model with a crack box
XFEM application
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Industrial test case: XFEM (initial crack of 1mm)
Free crack propagation, with bifurcation
XFEM application
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Industrial test case: XFEM (initial crack of 3mm)
Free crack propagation, with bifurcation
XFEM application
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Outline
- Methods available in SAMCEF for fracture mechanics
- XFEM method in SAMCEF
- Applications of XFEM with SAMCEF
- Conclusions
This document is the property of SAMTECH S.A.
Conclusions
� XFEM available in SAMCEF for 2D and 3D fracture mechanics problems
• Crack modelled in a very simple way
• Automatic crack propagation (3D problems)
� XFEM is a powerful method for fracture mechanics
� XFEM simplifies the life of the analyst for fracture mechanics problems
� XFEM in SAMCEF is still under improvements for/with our industrial partners
� XFEM is a easy, ready and the best solution for fracture mechanics
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Thank youDr. Michael BruyneelProject [email protected]: +32.4.361.69.69