ansys contact

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ANSYS, Inc. Proprietary© 2004 ANSYS, Inc.

Penalty vs. Lagrange

ANSYS contact- Penalty vs. Lagrange- How to make it converge

Erke Wang

CAD-FEM Gm!. Germany





Variety of algorithmsVariety of algorithms





Pena"ty mean# t$at any %io"ation o& t$e contact con'ition (i"" e p)ni#$e' yincrea#in* t$e tota" %irt)a" (or+

Pre !enalty metho"

( ) ( )[ ]dA g g T T T T N N N N ∫ Γ +++ gg δ ε λ δ ε λ A)*mente' a*ran*e met$o'

dA g g dV T T T N N N V

T

∫ ∫ Γ ++=Ψ )( gg δ ε δ ε δε σ δ

$e e/)ation can a"#o e (ritten in FE &orm

F uGG K T =+ )( ε

$i# i# t$e e/)ation )#e' in FEA &or t$e p)re pena"ty met$o' ($ere i# t$e contact

#ti&&ne##

ε

N ε

#

T ε N g

T g





Pre !enalty metho"

$e contact #prin* (i"" 'e&"ect an amo)nt ∆,

#)c$ t$at e/)i"iri)m i# #ati#&ie'

F uGG K T =+ )( ε

Some &inite amo)nt o& penetration, ∆ > 0, i# re/)ire' mat$ematica""y to maintain

e/)i"iri)m. !o(e%er, p$y#ica" contactin* o'ie# 'o not interpenetrate ∆ 1 0.

F =∆ε

$ere i# no o%ercon#trainin* pro"em

Iterati%e #o"%er# are app"ica"e 3 "ar*e mo'e"# are 'oa"e

$e con'ition o& t$e #ti&&ne## matri5 cr)cia""y 'epen'# on t$e contact #ti&&ne## it#e"&.

GG K K T ε +=

−

$ere i# no a''itiona" D6F. F uGG K T =+ )( ε

N

N ε

#

T ε N g

T g





Pre !enalty metho"

Some &inite amo)nt o& penetration, ∆ > 0, i# re/)ire' mat$ematica""y to maintaine/)i"iri)m. !o(e%er, p$y#ica" contactin* o'ie# 'o not interpenetrate ∆ 1 0.

$ifference in d:

0.281e-3/ 0.284e-7

=1e4

$ifference in stress:

(3525-3501)/ 3525

=0.7%

#%N&'

PENE

Stress

#%N&'e(

PENE

Stress

∆ i# t$e 7e#)"t &rom F8N an' t$e e/)i"iri)m ana"y#i#. Pre##)re1 ∆ 9 1: Stre## ε

;00-time# Di&&erence in F8N "ea'# to ;00-time# Di&&erence in ∆

)t "ea'# to on"y ao)t ;< Di&&erence in Contact pre##)re an' t$e re"ate' #tre##.





Pre !enalty metho"

Some &inite amo)nt o& penetration, ∆ > 0, i# re/)ire' mat$ematica""y to maintain

e/)i"iri)m. !o(e%er, p$y#ica" contactin* o'ie# 'o not interpenetrate ∆ 1 0.

)i!*

As long as the !enetration "oes not lea"s to the change of the contact

region+

)he !enetration will not inflence the contact !ressre an" Stress

n"erneath the contact element

,ation*

#or !re-tension !rolem+ se large #%N'+ /ecase the small !enetration

will strongly inflence the !re-tension force.


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Pre !enalty metho"


Iteration n

#

Iteration n+1

#

F,ontact

#

Iteration n+2

I& t$e contact #ti&&ne## i# too "ar*e, it (i"" ca)#e con%er*ence 'i&&ic)"tie#.

$e mo'e" can o#ci""ate, (it$ contactin* #)r&ace# o)ncin* o&& o& eac$ ot$er.

#%N&'

#%N&0.0'




Pre !enalty metho"


$i# pro"em i# a"mo#t #o"%e' #ince =.;, (it$

a)tomatic contact #ti&&ne## a'>)#tment.

8EY6P;012

%EY1P)2'03&0 %EY1P)2'03&4

405

iterations

6(

iterations

http://var/www/apps/conversion/tmp/scratch_7/C:%5CProgramme%5CAnsys%20Inc%5CANSYS61%5Cbin%5Cintel%5Canimate.exe%20d:%5Cusers%5Cerich%5Cpr%C3%A4sentation%5Cfkn.avi




Pre !enalty metho"


For en'in* 'ominant pro"em, yo) #$o)"' #ti"" )#e

t$e 0.0; &or t$e #tartin* F8N an' comine (it$

8EY6P;012

#%N&0.0'+ %EY2'03&0

#%N&'* %EY2'03&0 $ivergence

#%N&0.0'+ %EY2'03&4

407 iterations (7 iterations




Pre !enalty metho"


)i!*

Always se %EY1P)2'03&4#or en"ing !rolem se #%N&0.0' an" %EY1P)2'03&4

#or lky !rolem se #%N&' an" %EY1P)2'03&4

,ation*

#or !re-tension !rolem+ se large #%N'. /ecase the small !enetration

will strongly inflence the !re-tension force.




Pre !enalty metho"

$ere i# no a''itiona" D6F.

$ere i# no o%ercon#trainin* pro"em

Iterati%e #o"%er# are app"ica"e 3 "ar*e mo'e"# are 'oa"e

)i!*

Always se Penalty if*

? Symmetric contact or self-contact is se".

? 8lti!le !arts share the same contact 9one

? 7$ large mo"el2 700.000 $1#s3+ se P,: solver.




? Any %io"ation o& t$e contact con'ition (i"" e &)rni#$e' (it$ a a*ran*e m)"tip"ier.

Pre Lagrange mlti!liers metho"

dA g dV T N N V

T

∫ ∫ Γ ++=Ψ )( gλ Tδ δ λ δε σ δ

Contact con#traint con'ition

0

0

0

=

≤

≥

N N

N

N

g

g

λ

λ

En#)re no penetration

En#)re compre##i%e contact &orce@pre##)re

No contact , *ap i# non ero

Contact , contact &orce i# non ero0= N λ

0= N g

0

=0 g

F

λ

u

G

G K T

$e e/)ation i# "inear, in ca#e o& "inear e"a#tic an' No'e-to-No'e contact. 6t$er(i#e,

t$e e/)ation i# non"inear an' an iterati%e met$o' i# )#e' to #o"%e t$e e/)ation. B#)a""yt$e Ne(ton-Met$o' i# )#e'.

For "inear e"a#tic pro"em#





0

=0 g

F

λ

u

G

G K T

a*ran*e m)"tip"ier# are a''itiona" D6F# t$e FE mo'e" i# *ettin* "ar*e.

NG

ero main 'ia*ona"# in #y#tem matri5No iterati%e #o"%er i# app"ica"e.

For #ymmetric contact or a''itiona" CP@CE, an' o)n'ary con'ition#, t$e e/)ation

#y#tem mi*$t e o%er-con#traine'

Sen#iti%e to c$atterin* o& t$e %ariation o& contact #tat)#

No nee' to 'e&ine contact #ti&&ne##

Acc)racy - con#traint i# #ati#&ie' e5act"y, t$ere are no matri5 con'itionin* pro"em#





a*ran*e m)"tip"ier# are a''itiona" D6F# t$e FE mo'e" i# *ettin* "ar*e.

)i!*

Always se Lagrange mlti!lier metho" if*? )he mo"el is 4$.

? 7$ nonlinear material !rolem with ; '00.000 $ofs





)i!*

<f the Lagrange mlti!lier metho" is se"*

? Always se asymmetric contact.

? $o not se ,P=,E in on contact srfaces

? $o not "efine the mlti!le contacts+ which share the common

interfaces.

For #ymmetric contact or a''itiona" CP@CE, an' o)n'ary con'ition#, t$e e/)ation#y#tem i# o%er-con#traine'

Contact pair-;

Contact pair-;

Sin*"e contact pair





Penalty symmetric

Penetration

<terations* '>(

,P?* '00

Pressre

Lagrange symmetric

Penetration

<terations* @4

,P?* 50

Pressre





)i!*

?se Penalty is chattering occrs or

,hattering ,ontrol Parameters*

#)1LN an" )N1P

Sen#iti%e to c$atterin* o& t$e %ariation o& contact #tat)#

'&4-$elta

' 4#





Penalty

#%N&'

$EL)&0.'

=!re!>

et+'+'67

et+4+'B@

et+7+'>4++(++4

m!+eC+'+4e5

!cir+'@0+400-$EL)+-@0+@0

w!of+0+-"elt!cir+400+4'0+-@0+@0

w!of+0+"elt

esi9+5

Esha+4

ames+all

lsel+s+++'

nsll+s+'

eal+4

ty!e+7

esrf

lsel+s+++>

nsll+s+'

ty!e+4Esrf

=sol

Nsel+s+loc+C+0

$+all+C

lsel+s+++5

nsll+s+'

"+all+all

lsel+s+++7

nsll+s+'Dget+nn+no"e++cont

f+all+fy+400=nn

alls

Solv

?se Penalty is chattering occrs





Sy Pene

Pre Lagrange

<ter&'7

Sy Pene

Pre Penalty2#%N&'3

<ter&6

Pre Penalty2#%N&'e(3

<ter&7@

Sy Pene







Sy Pene

Pre Lagrange

<ter&'7

Sy Pene

Pre Penalty2#%N&'e(3

<ter&7@

Sy Pene

Agmente" Lagrange

#%N&'+ )1L&-7e->

<ter&'74>







eCam!le-'eCam!le-'Element* Plane'67Element* Plane'67

8aterial* Neo-Hookean8aterial* Neo-Hookean

,ontact*,ontact* Pre LagrangePre Lagrange

Loa"* $is!lacementLoa"* $is!lacement





=!re!> =!re!>

et+'+'67et+'+'67

et+4+'B@et+4+'B@

et+7+'>4++7++4et+7+'>4++7++4

t+hy!er+'+++neot+hy!er+'+++neo

t"ata+'+.7+0.00't"ata+'+.7+0.00'

m!+eC+4+4e5m!+eC+4+4e5

m!+"ens+4+>.6e-@m!+"ens+4+>.6e-@

r+4++++++5r+4++++++5r+7++++++5r+7++++++5

!cir+4+5!cir+4+5

agen+5+'+'++44agen+5+'+'++44

agen+4+'+'++''+-70agen+4+'+'++''+-70

agen+(+B+B++44agen+(+B+B++44

rect+-B+-5+-60+0rect+-B+-5+-60+0

rect+5+B+-70+0rect+5+B+-70+0

agen+@+''+''++''agen+@+''+''++''

!cir+5+B+0+'60!cir+5+B+0+'60

agen+5+40+40++44agen+5+40+40++44

w!of+''+-70w!of+''+-70

!cir+5+B+'60+7B0!cir+5+B+'60+7B0

agen+(+45+45++44agen+(+45+45++44

w!cs+-'w!cs+-'rect+-'B+-B+-'00+-60rect+-'B+-B+-'00+-60

rect+-B+-5+-'00+-60rect+-B+-5+-'00+-60

rect+-5+5+-'00+-60rect+-5+5+-'00+-60

asel+s+++'0+7'+'+'asel+s+++'0+7'+'+'

nmm+k!nmm+k!

esha+4esha+4

esi9+4esi9+4

ames+'+46ames+'+46eshaesha

allsalls

mat+4mat+4

ames+allames+all

lsel+s+++>(+'0B+6lsel+s+++>(+'0B+6

lsel+a+++60+''4+6lsel+a+++60+''4+6

lsel+a+++''5+'7'+(lsel+a+++''5+'7'+(

lsel+a+++'77+'(5+(lsel+a+++'77+'(5+(

nsll+s+'nsll+s+'

ty!e+4ty!e+4

real+4real+4

mat+7mat+7

esrf esrf

lsel+s+++'+(lsel+s+++'+(

lsel+a+++@+'4lsel+a+++@+'4

lsel+a+++'>+40lsel+a+++'>+40

lsel+a+++45+46lsel+a+++45+46

lsel+a+++77+7Blsel+a+++77+7B

cm+l'+linecm+l'+line

nsll+s+'nsll+s+'

ty!e+7ty!e+7

esrf esrf lsel+s+++>B+'06+6lsel+s+++>B+'06+6

lsel+a+++>6+'04+6lsel+a+++>6+'04+6

lsel+a+++''7+'4@+(lsel+a+++''7+'4@+(

lsel+a+++'75+'(>+(lsel+a+++'75+'(>+(

nsll+s+'nsll+s+'

ty!e+4ty!e+4

real+7real+7

esrf esrf

lsel+s+++('+((lsel+s+++('+((

lsel+a+++(@+54lsel+a+++(@+54

lsel+a+++5>+B0lsel+a+++5>+B0

lsel+a+++B5+B6lsel+a+++B5+B6

cm+l4+linecm+l4+line

nsll+s+'nsll+s+'

ty!e+7ty!e+7esrf esrf

=sol =sol

nlgeo+onnlgeo+on

acel++@6'0acel++@6'0

asel+s+++'+@+'+'asel+s+++'+@+'+'

cmsel++l'cmsel++l'

cmsel++l4cmsel++l4

nsll+s+'nsll+s+'

"+all+all"+all+all

asel+s+++4@+7'+'asel+s+++4@+7'+'nsla+s+'nsla+s+'

"+all+C"+all+C

ns+5+'5+'ns+5+'5+'

lsel+s+++'0@+++'lsel+s+++'0@+++'

"+all+C"+all+C

"+all+y+0"+all+y+0

allsalls

cnvt+f++.0'cnvt+f++.0'ns+'00+'0000+'ns+'00+'0000+'

solvsolv

lsel+s+++'0@+++'lsel+s+++'0@+++'

"+all+y+-50"+all+y+-50

ns+'00+'0000+'ns+'00+'0000+'

otres+all+allotres+all+all

allsallssolvsolv

)i!*)i!*

#or large sli"ing#or large sli"ing

!rolem+!rolem+

?se Lagrange metho"+?se Lagrange metho"+

the convergencethe convergenceehavior is very goo"ehavior is very goo"

an" stalean" stale






Lagrange*Lagrange*

''0 <terations''0 <terations

,P?*,P?*

'( Sec.'( Sec.

Penalty*Penalty*

4'6 <terations4'6 <terations

,P?*,P?*

4( Sec.4( Sec.






/en"ing stress/en"ing stress

,ontact !enetration,ontact !enetration

/en"ing eCam!le/en"ing eCam!le Lagrange*

'0 <terations

4 Sec.

Penalty %ey2'03&'*5( <terations

'4 Sec.






=!re!>

et+'+'67+++'et+4+'67+++'+++'

et+7+'B@

et+(+'>4++(++4

m!+eC+'+4e5

t+hy!er+4+'+4+moon

t"ata+'+'+.4+4e-7

8!+m+4+0.7

rect+'+5+0+7

rect+4+5+'.5+(

asa+'+4

rect+4.'+5+4.5+7.5

w!of+7+4

!cir+.50'

esi9+.7

ames+'+7+4

esi9+.'

ty!e+4mat+4

ames+4

lsel+s+++4

nsll+s+'ty!e+7

real+7

esrf

lsel+s+++6+'4+(

nsll+s+'

ty!e+(

esrf

lsel+s+++5

nsll+s+'ty!e+7

real+(

esrf

lsel+s+++'7+'(+'

nsll+s+'

ty!e+(

esrf

=sol

nlgeo+on

solcon++++'e-4

nsel+s+loc+y+0

"+all+y

nsel+s+loc+y+7.5

sf+all+!res+4

alls

ns+'0+'00+'

solv

er eCam!leer eCam!le

Element* Plane'67Element* Plane'67

8aterial* 8ooney8aterial* 8ooney

,ontact*,ontact* Pre Lagrange#rictionPre Lagrange#riction

Loa"* PressreLoa"* Pressre

Lagrange*

74 <terations

'7 Sec.

Penalty %ey2'03&4*

B7 <terations40 Sec.





Let s talk aot convergence





6ne rea#on &or con%er*ence 'i&&ic)"tie# co)"' e t$e &o""o(in*

? #E 8o"el is not mo"ele" correctly in a !hysical sense

; I& yo) )#e a point "oa' to 'o a p"a#tic ana"y#i#, yo) (i"" ne%er *et t$e con%er*e' #o")tion.

eca)#e o& t$e #in*)"arity at t$e no'e, on ($ic$ t$e concentrate' &orce i# app"ie', t$e

#tre## i# in&inite. $e "oca" #in*)"arity can 'e#troy t$e ($o"e #y#tem con%er*ence

e$a%ior. $e #ame t$in* $o"'# &or t$e contact ana"y#i#. I& yo) #imp"i&y t$e *eometry or)#e a too coar#e me#$ (it$ t$e con#e/)ence t$at t$e contact re*ion i# >)#t a point contact

in#tea' o& an area contact yo) mo#t "i+e"y (i"" en' )p (it$ #ome pro"em# in

con%er*ence.point "oa'

ε

σ

p"a#tic ana"y#i# contact ana"y#i#

Geometry Me#$

Sggestion





Sggestion

%EY1P)253&'

%EY1P)253&0

? #E 8o"el is not mo"ele" correctly in a nmerical sense

2 A po##i"e ri*i' o'y motion i# /)ite o&ten t$e rea#on ($ic$ ca)#e# 'i%er*ence in a

contact ana"y#i#. $i# co)"' e t$e re#)"t o& t$e &o""o(in* e a"(ay# e"ie%e, t$at i& (e

mo'e" t$e *ap #ie a# ero &rom *eometry, it #$o)"' a"#o e ero in t$e FE mo'e". )t ')e

to t$e mat$ematica" appro5imation an' 'i#cretiation, it 'oe# not $a%e nece##ari"y to e

ero anymore. E5act"y, t$i# can +i"" t$e con%er*ence. I& po##i"e, )#e 8EY6P to c"o#et$e *ap. Yo) can a"#o )#e 8EY6PH1; to i*nore ;< penetration, i& it i# mo'e"e'.






Sggestion

,ation*? <f the ga! !hysically eCists+ yo shol" not se %EY1P253&' to close it+instea"+ yo

shol" se" the weak s!ring metho". $EL)&0.'

=!re!>

et+'+'67

et+4+'B@

et+7+'>4

m!+eC+'+4e5

!cir+'+4-$EL)+-@0+@0

!cir+4+7+-@0+@0

rect+0+'+->+-4.5

aa""+4+7

esi9+.7

ames+all

Ps!rng+(6+tran+'+0+0.5

lsel+s+++'

nsll+s+'

eal+4

ty!e+7

esrf

lsel+s+++>

nsll+s+'ty!e+4

Esrf

+4++++++-'

=sol

Nsel+s+loc+C+0

$+all+Cnsel+s+loc+y+->

"+all+all

Alls

#+(4+fy+0.''

Solv

#+(4+fy+4000

Solv#"el+all+all

#+(6+fy+-.''

Solv

#+(6+fy+-7000

solv

81;, DE10.;

F189B

o c"o#e t$e *ap

F;1;90.;0.;10.;;

LS'* #'&0.''

LS4* #'&7000





Sggestion

? N)merica""y a" con"itione" #E 8o"el

4 ANSYS )#e# t$e pena"ty met$o' a# a a#i# to #o"%e t$e contact pro"em an' t$e

con%er*ence e$a%ior "ar*e"y 'epen'# on t$e pena"ty #ti&&ne## it#e"&. A #emi-'e&a)"t

%a")e

&or t$e pena"ty #ti&&ne## i# )#e', ($ic$ )#)a""y (or+# &ine &or a )"+y mo'e", )t mi*$t not e

#)ita"e &or a en'in* 'ominate' pro"em or a #"i'in* pro"em. A #i*n &or a' con'itionin*i# t$at t$e con%er*ence c)r%e r)n# para""e" to t$e t$e con%er*ence norm. C$oo#in* a #ma""er

%a")e &or F8N a"(ay# ma+e# t$e pro"em ea#ier to con%er*e. I& t$e ana"y#i# i# not

con%er*in*, eca)#e o& t$e too m)c$ penetration, t)rn o&& t$e a*ran*e m)"tip"ier.

$e re#)"t i# )#)a""y not a# a' a# yo) (o)"' e"ie%e.

#%N&' #%N&0.0'


P l L





Sggestion


#%N&0.0'+ %EY2'03&0

#%N&'* %EY2'03&0 $ivergence

#%N&0.0'+ %EY2'03&'

#%N&'* %EY2'03&'

P lt L





Sggestion

? )a'# in#tea' o& tria'# Error in e"ement &orm)"ation or e"ement i# t)rne' in#i'e o)t

J I& #ome e"ement# are "oca""y 'i#torte' yo) mi*$t *et an error in t$e e"ement &orm)"ation or

t$e e"ement i# e%en t)rne' in#i'e o)t. ry to )#e a coar#er me#$ in t$i# re*ion to a%oi'

t$o#e pro"em#. Yo) can a"#o )#e NCNK,0 to contin)e t$e ana"y#i# an' i*nore t$o#e "oca"

pro"em# i& t$ey 'o not e&&ect t$e *"oa" e/)i"iri)m. In *enera", try to )#e trian*)"ar,

tetra$e'ra" or $e5a$e'ra" e"ement# "inear. Do not )#e /)a'ratic $e5a$e'ra" e"ement#.

inear /)a'# Mi'-#i'e tria'#

Error in e"ement &orm)"ation


P lt L





Sggestion

? $e part# $a%e no )ni/)e minim)m potentia" ener*y po#ition.

L I& t$e ma5. D6F increment i# not *ettin* #ma""er an' t$e &orce con%er*ence norm +eep#

a"mo#t con#tant, proa"y #ome part# in t$e mo'e" are o#ci""atin*. !ere, intro')cin* a #ma""

&riction coe&&icient i# )#)a""y etter t$an )#in* a (ea+ #prin*, not +no(in* e5act"y ($ere to

p"ace it. Friction can e app"ie' to a"" contact e"ement# try MB10.0; or 0.;

8?&0.'8?&0


P lt L





Sggestion

)arget

)arget

,ontact

,ontact

Some time#, i& yo) 'e&ine t$e contact an' tar*et proper"y, t$e ana"y#i# con%er*ence#

m)c$ &a#ter, an' t$e re#)"t i# a"#o etter.

,ontact

)arget ,ontact

)arget

##

P lt L





Sggestion

? Bnrea#ona"e 'e&ine' p"a#tic materia"

;; It i# not a"(ay# a *oo' i'ea to 'e&ine t$e tan*entia" #ti&&ne## to e ero )#in* a p"a#tic

materia" "a(. I& t$e yie"' #tre## i# reac$e' a"" o%er t$e ($o"e cro## #ection, t$ere i# no

materia" re#i#tance anymore to carry t$e "oa'. $ere (i"" e a p"a#tic $in*e an' #o t$e

#o")tion (i"" ne%er con%er*e. In t$i# ca#e, inp)t t$e correct tan*entia" #ti&&ne##.

P"a#tic #train Stre## #train c)r%e (it$

tan*entia" #"ope ero


P lt L





Sggestion

? Bnrea#ona"e 'e&ine' p"a#tic materia"

P"a#tic #train

Stre## #train c)r%e (it$

tan*entia" #"ope ;0000

Stre## 'i#tri)tion

Contact re*ion


P lt L





Sggestion

? $e &ine me#$ an' #imi"ar me#$ are a"(ay# *oo' &or t$e contact #im)"ationGoo' me#$ (i"" *enera""y ma+e pro"em ea#ier to con%er*e.

:eometry:eometry S!here inflenceS!here inflence 8esh8esh

Normal stressNormal stress

,ontact Pressre,ontact Pressre

P lt L





Sggestion

? $e &ine me#$ an' #imi"ar are a"(ay# *oo' t$e contact #im)"ationGoo' me#$ (i"" *enera""y ma+e pro"em ea#ier to con%er*e.

:eometry:eometry

,ontact mesh,ontact mesh

,ontact region,ontact region

P lt L





Sggestion

? $e &ine me#$ an' #imi"ar are a"(ay# *oo' t$e contact #im)"ationGoo' me#$ (i"" *enera""y ma+e pro"em ea#ier to con%er*e.

Normal stressNormal stress

,ontact !ressre,ontact !ressre

Penalty vs Lagrange





How can < make the !rolem convergeF

? )rst yorself* <Gm ale to make it converge? ,onsi"er the !rolem as i"eali9e" real worl" !rolem*

40I- 8echanics eC!ertise+ 40I- Engineer eC!ertise

70I- #EA eC!ertise+ 70I- Software eC!ertise

? ?se the magic %EY1P)<1NS

%EY1P)253&'* )o eliminate the rigi" o"y motion

%EY1P)2@3&'* )o eliminate the geometric noise

%EY1P)2'03&4* )o make ANSYS think

Penalty vs Lagrange




)hanks)hanks

ansys contact

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