an open source abaqus/uel implementation of the phase...

AnopensourceABAQUS/UELimplementationofthephase‐fieldmethodtosimulatebrittlefracture

Gergely Molnár andAnthonyGravouil

ContentIntroductiontophase‐fields

1. Phase-field concept2. Strain energy degradation3. Staggered scheme

Parameters1. Finite element mesh2. Time step3. Length-scale parameter

ABAQUS/UELimplementationConclusion

IntroductionWhatisdiffusedamage?

Solvingfracturemechanics problemwithPartialDifferentialEquations(PDEs)

theoretical crack (d = 1)

damaged zone (0 < d < 1)

undamaged zone (0 = d)

IntroductionWhatisdiffusedamage?

Solvingfracturemechanics problemwithPartialDifferentialEquations(PDEs)

IntroductionHowdoweapproximateitwithaphase‐field?

2.Minimizationproblem

1.Brittlefracture Griffith,1921cga

, cE d g d

u u

Mumford& Shah,1989Francfort &Marigo,1998

221,2 2

c

cc

ld dl

E d g dg d d

u u

3.Crackenergydensity

Ambrosio &Tortorelli,1990Bourdin etal.,2000Amoretal.,2009

Miehe etal.,2010a

0 converges

0cl

d

crackenergydensity‐ γ

Phase‐fieldmethodStaggeredscheme

Prof.Dr.‐Ing.ChristianMiehe(1956– †2016)

Miehe etal.,2010b

0 1 0

,

,

if

u

dn

n n

E d

E d H

H H

u

u

Robustness!!!Efficiency?

Phase‐fieldmethod

Molnár&Gravouil,2017

Staggeredscheme

Phase‐fieldmethodSingleelementsolution

222

222

y

cy

c

cd g c

l

2221y yd c

22 - (2,2) element of the stiffness matrixc

Molnár&Gravouil,2017

Phase‐fieldmethodSingleelementsolution

analytic

analyticy y

y

Molnár&Gravouil,2017

ParametersHowfineshouldthemeshbe?

0.5

l d

theoretical

Miehe etal.,2010a

/ 2h l

ParametersDoublenotchedspecimenundertension

Molnár&Gravouil,2017

EffectofFEmesh

ParametersDoublenotchedspecimenundertension

Molnár&Gravouil,2017

Effectoftimestepsize

ParametersSinglenotchedspecimenundertension

Molnár&Gravouil,2017

Effectoflength‐scale

ExamplesCrackbranching

Molnár&Gravouil,2017

OptionsPositiveandnegativeenergydegradation

Molnár&Gravouil,2017

0 0g d

20

2 22 2

1 1 2

+2 1

E tr

E

ε

OpensourceimplementationABAQUS/UELoption(ABAQUS+FORTRANcompiler)

stiffnessmatrix +residuevector foreveryelement

FORTRANandABAQUSfilesareavailableinboth2D and3D

Visualization

Molnár&Gravouil,2017

OpensourceimplementationExamplesandtutorials:www.molnar‐research.com

FORTRAN filesINPUT filesTutorials

Molnár&Gravouil,2017

Conclusion

Advantagesanddisadvantages

Versatilitydynamics,shells,nonlinearelasticity,largestrains,coupledproblems,plasticity,anisotropy,etc…

XFEM/GFEMCohesiveZones

• crackinitiation,propagation• branching,merging• fixedmesh• fully3D

Phase‐field Predefinedcrack

• finemesh• finitecracksize• efficiency/robustness

ReferencesL.Ambrosio,V.M.Tortorelli,Comm.PureAppl.Math.43(1990)999‐1036.H.Amora,J.‐J.Marigo,C.Maurini,J.oftheMech.andPhys.ofSolids,57(8)(2009)1209‐

1229.B.Bourdin,G.A.Francfort,J.‐J.Marigo,J.oftheMech.andPhys.ofSolids,48(4)(2000)

797‐826.G.A.Francfort,J.‐J.Marigo,J.oftheMech.andPhys.ofSolids,46(8)(1998)1319‐1342.A.A.Griffith,Phil.Trans.oftheRoyalSoc.ofLondon.SeriesA,221(1921),163‐198.C.Miehe,F.Welschinger,M.Hofacker,Int.J.Numer.MethodsEng.,83(10)(2010a)

1273–1311.C.Miehe,M.Hofacker,F.Welschinger,Comput.MethodsAppl.Mech.Eng.,199(45–48)

(2010b)2765–2778.G.Molnár,A.Gravouil,Finite Element in Analysis andDesign130(2017)27‐38.D.B.Mumford,J.Shah.,Comm.PureAppl.Math.42(5)(1989)577‐685.

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www.molnar-research.comgmolnar.work@gmail.com