computational fracture mechanics with samcef€¦ · this document is the propertyof samtechs.a....

$: Computational fracture mechanics with SAMCEF€¦ · This document is the propertyof SAMTECHS.A. Computational fracture mechanics with SAMCEF New trends and illustration on an industrial$
This document is the property of SAMTECH S.A.

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


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



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


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 :


Methods available in SAMCEF

☺

☺

☺

☺

☺

☺

FEM without crack box

2D3D

FEM with crack box

XFEM


Outline




- Conclusions


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


Classic FE method: illustration

Crack propagation with bifurcation ( crack box )

a

ττττ

Modeling time


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


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


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


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


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


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


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


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


Outline




- Conclusions


XFEM application

σσσσ

L

b

β

Crack 1

R

2D Propagation (done in 2005 for )


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



a

ττττ Finite element mesh Crack (level-sets)

Example of a refinement in the XFEM domain

No remeshing during the crack propagation

XFEM application



FEM (crack box) XFEM (level-sets)

K1 K1

XFEM application



3D propagation

Bifurcation

XFEM application


Industrial test case

Centrifugal load

Imposed radial displacement

Location of the crack (1/4 of a circle)

Level-sets

XFEM application


Industrial test case

XFEM model FEM model

Contact In-plane crack propagation

Free crack propagation

XFEM application


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


Industrial test case: FEM and Barsoum elements

Elliptical cack propagation in a plane

Parameterized model with a crack box

XFEM application


Industrial test case: XFEM (initial crack of 1mm)

Free crack propagation, with bifurcation

XFEM application


Industrial test case: XFEM (initial crack of 3mm)

Free crack propagation, with bifurcation

XFEM application


Outline




- Conclusions


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


Thank youDr. Michael BruyneelProject [email protected]: +32.4.361.69.69

computational fracture mechanics with samcef€¦ · this document is the propertyof samtechs.a....

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