Ls-dyna Manual Vol II r7.0

7/26/2019 Ls-dyna Manual Vol II r7.0

1/1151

LS-DYNAKEYWORD USER'S MANUAL

VOLUME IIMaterial Models

Februar !"#$Versio% R&"

LIVERMORE SOF(WARE (E)*NOLO+Y )OR,ORA(ION LS().


2/1151

)or/orate AddressLivermore Software Technology CorporationP. O. Box 712Livermore, California !""1#$712

Su//ort Addresses

Livermore Software Technology Corporation7%7! La& Po&ita& 'oa(Livermore, California !""1Tel) 2"#!!#2"$$ * +ax) 2"#!!#2"$7E0ail1 sales2lst33o0Website1 444lst33o0

Livermore Software Technology Corporation17!$ e&t Big Beaver 'oa(S-ite 1$$Troy, ichigan !/$/!Tel) 2!/#0!#!72/ * +ax) 2!/#0!#0%2/

Dis3lai0erCopyright 12#2$1% Livermore Software Technology Corporation. ll 'ight& 'e&erve(.

LS#3456, LS#OPT6an( LS#PrePo&t6are regi&tere( tra(emar& of Livermore Software Tech#

nology Corporation in the 8nite( State&. ll other tra(emar&, pro(-ct name& an( 9ran( name&9elong to their re&pective owner&.

LSTC re&erve& the right to mo(ify the material containe( within thi& man-al witho-t prior notice.

The information an( example& incl-(e( herein are for ill-&trative p-rpo&e& only an( are not in#ten(e( to 9e exha-&tive or all#incl-&ive. LSTC a&&-me& no lia9ility or re&pon&i9ility what&oeverfor any (irect of in(irect (amage& or inacc-racie& of any type or nat-re that co-l( 9e (eeme( tohave re&-lte( from the -&e of thi& man-al.

ny repro(-ction, in whole or in part, of thi& man-al i& prohi9ite( witho-t the prior written ap#proval of LSTC. ll re:-e&t& to repro(-ce the content& hereof &ho-l( 9e &ent to &ale&;l&tc.com.

#####################################################################################################################9rg;gla(man.-.net?, orce&ter, 8@. ll right& re&erve(.LAC


3/1151

5(A6LE OF )ON(EN(S

LS-DYNA R&" $#1 TBL< O+ CO5T


4/1151

5(A6LE OF )ON(EN(S

$#2 TBL< O+ CO5T


5/1151

5(A6LE OF )ON(EN(S

LS-DYNA R&" $#% TBL< O+ CO5T


6/1151

5(A6LE OF )ON(EN(S

$#! TBL< O+ CO5T


7/1151

5(A6LE OF )ON(EN(S

LS-DYNA R&" $#" TBL< O+ CO5T


8/1151

5(A6LE OF )ON(EN(S

$#0 TBL< O+ CO5T


9/1151

5(A6LE OF )ON(EN(S

LS-DYNA R&" $#7 TBL< O+ CO5T


10/1151

5(A6LE OF )ON(EN(S

$#/ TBL< O+ CO5T


11/1151

5EOS

LS-DYNA R&" 1#


12/1151

5EOS

1#1$


13/1151

5EOS

LS-DYNA R&" 1#11


14/1151

5EOS

1#12


15/1151

5EOS

LS-DYNA R&" 1#1%


16/1151

5EOS 5EOS7LINEAR7,OLYNOMIAL

1#1!


17/1151

5EOS7LINEAR7,OLYNOMIAL 5EOS

LS-DYNA R&" 1#1" - > -88 > - > (-W > -X > -Y8) , Z

where term& -88 an(-[\are &et to Hero if ] + < = 1 < ^_` i& the

ratio of c-rrent (en&ity to reference (en&ity. "i& a nominal or reference (en&ity (efine(in the ITJ58LL car(.

The linear polynomial e:-ation of &tate may 9e -&e( to mo(el ga& with the gamma lawe:-ation of &tate. Thi& may 9e achieve( 9y &etting)

- = -= -8 = - = -Y = +an(

-W = -X= a 1where a = bcbdi& the ratio of &pecific heat&. Pre&&-re for a perfect ga& i& then given 9y)

e = (a 1) ,< ha& the -nit of pre&&-re where

"an(

"

2 hen - = -= -8 = - = -Y = +, it (oe& not nece&&arily mean that the initialpre&&-re i& Hero, ;+ * -+ The initial pre&&-re (epen(& the val-e& of all the coefficient&an( on %f=+an( ,%f=+. The pre&&-re in a material i& comp-te( from the whole e:-ationa9ove, ; = ;(g< ,). At i& alway& prefera9le to initialiHe the initial con(ition 9a&e( on%f=+an( ,%f=+. The -&e of - = -= -8 = - = -Y = +m-&t 9e (one with ca-#tion a& it may change the form an( 9ehavior of the material. The &afe&t way i& to -&e thewhole


18/1151

5EOS 5EOS78WL

1#10


19/1151

5EOS7SA)K7(UESDAY 5EOS

LS-DYNA R&" 1#17


20/1151

5EOS 5EOS7+RUNEISEN

1#1/


21/1151

5EOS7+RUNEISEN 5EOS

LS-DYNA R&" 1#1 (a> x ),Zan( for expan(e( material& a&

e = " - 8 > (a> x),Zwhere C i& the intercept of the vvpc-rve in velocity -nit&D S1, S2, an( S%are the -nitle&& co#efficient& of the &lope of the vvpc-rveD $i& the -nitle&& =r-nei&en gammaD a i& the -nitle&&,fir&t or(er vol-me correction to $Dan( = 1.


22/1151

5EOS 5EOS7RA(IO7OF7,OLYNOMIALS

1#2$


23/1151

5EOS7RA(IO7OF7,OLYNOMIALS 5EOS

LS-DYNA R&" 1#21


24/1151


1#22


25/1151

5EOS7RA(IO7OF7,OLYNOMIALS 5EOS

LS-DYNA R&" 1#2%


26/1151


1#2!


27/1151

5EOS7LINEAR7,OLYNOMIAL7WI(*7ENER+Y7LEAK 5EOS

LS-DYNA R&" 1#2"


28/1151

5EOS 5EOS7LINEAR7,OLYNOMIAL7WI(*7ENER+Y7LEAK

1#20


29/1151

5EOS7I+NI(ION7AND7+ROW(*7OF7REA)(ION7IN7*E 5EOS

LS-DYNA R&" 1#27


30/1151

5EOS 5EOS7I+NI(ION7AND7+ROW(*7OF7REA)(ION7IN7*E

1#2/


31/1151

5EOS7I+NI(ION7AND7+ROW(*7OF7REA)(ION7IN7*E 5EOS

LS-DYNA R&" 1#2 84Y#> ?## (= #)where e an( Te are the relative vol-me an( temperat-re, re&pectively, of the -nreacte( explo#&ive. nother KL e:-ation of &tate (efine& the pre&&-re in the reaction pro(-ct& a&

;= x 4 > 4 8 > ? = where p an( Tp are the relative vol-me an( temperat-re, re&pectively, of the reaction pro(-ct&.& the chemical reaction convert& -nreacte( explo&ive to reaction pro(-ct&, the&e KL e:-ation&of &tate are -&e( to calc-late the mixt-re of -nreacte( explo&ive an( reaction pro(-ct& (efine( 9ythe fraction reacte( ++O implie& no reaction, +1 implie& complete reaction. The tempera#t-re& an( pre&&-re& are a&&-me( to 9e e:-al /#= /,e#= e an( the relative vol-me& are a((i#tive, i.e.,

=(1 )#> The chemical reaction rate for conver&ion of -nreacte( explo&ive to reaction pro(-ct& con&i&t& ofthree phy&ically reali&tic term&) an ignition term in which a &mall amo-nt of explo&ive react&

&oon after the &hoc wave compre&&e& itD a &low growth of reaction a& thi& initial reaction&prea(&D an( a rapi( completion of reaction at high pre&&-re an( temperat-re. The form of thereaction rate e:-ation i&

{& = S4(1 )$#(4 1 f)##& Agnition>1(1 )#e# =rowth


32/1151

5EOS 5EOS7I+NI(ION7AND7+ROW(*7OF7REA)(ION7IN7*E

1#%$


33/1151

5EOS7(A6ULA(ED7)OM,A)(ION 5EOS

LS-DYNA R&" 1#%1


34/1151

5EOS 5EOS7(A6ULA(ED7)OM,A)(ION

1#%2


35/1151

5EOS7(A6ULA(ED 5EOS

LS-DYNA R&" 1#%%


36/1151

5EOS 5EOS7(A6ULA(ED

1#%!


37/1151

5EOS7,RO,ELLAN(7DEFLA+RA(ION 5EOS

LS-DYNA R&" 1#%"


38/1151

5EOS 5EOS7,RO,ELLAN(7DEFLA+RA(ION

1#%0


39/1151


LS-DYNA R&" 1#%7


40/1151

5EOS 5EOS7,RO,ELLAN(7DEFLA+RA(ION

1#%/ (1 )e

{P {

where$i& the fraction reacte( $ $ implie& no reaction, $ 1 i& complete reaction, ti& time,an( p i& pre&&-re in 9ar&, r,s,u,%,&,y, $

limit1 an( $

limit2 are con&tant& -&e( to (e&cri9e the

pre&&-re (epen(ence an( &-rface area (epen(ence of the reaction rate&. Two or more pre&&-re(epen(ant reaction rate& are incl-(e( in ca&e the propellant i& a mixt-re or exhi9ite( a &harpchange in reaction rate at &ome pre&&-re or temperat-re. B-rning &-rface area (epen(encie& can9e approximate( -&ing the '"(+y+x term&. Other form& of the reaction rate law, &-ch a& rrhe#ni-& temperat-re (epen(ent e()*!Ttype rate&, can 9e -&e(, 9-t the&e re:-ire very acc-rate tem#perat-re& calc-lation&. ltho-gh the theoretical G-&tification of pre&&-re (epen(ent 9-rn rate& atilo9ar type pre&&-re& i& not complete, a va&t amo-nt of experimental 9-rn rate ver&-& pre&&-re(ata (oe& (emon&trate thi& effect an( hy(ro(ynamic calc-lation& -&ing pre&&-re (epen(ent 9-rnacc-rately &im-late &-ch experiment&.

The (eflagration reactive flow mo(el i& activate( 9y any pre&&-re or particle velocity increa&e onone or more Hone 9o-n(arie& in the reactive material. S-ch an increa&e create& pre&&-re in tho&eHone& an( the (ecompo&ition 9egin&. Af the pre&&-re i& relieve(, the reaction rate (ecrea&e& an(can go to Hero. Thi& feat-re i& important for &hort (-ration, partial (ecompo&ition reaction&. Afthe pre&&-re i& maintaine(, the fraction reacte( event-ally reache& one an( the material i& com#pletely converte( to pro(-ct molec-le&. The (eflagration front rate& of a(vance thro-gh the pro#pellant calc-late( 9y thi& mo(el for &everal propellant& are :-ite clo&e to the experimentally o9#&erve( 9-rn rate ver&-& pre&&-re c-rve&.


41/1151


LS-DYNA R&" 1#% \ 4 jY > j ? {jljwhere -an( T-are the relative vol-me an( temperat-re re&pectively of the -nreacte( propel#lant. The relative (en&ity i& o9vio-&ly the inver&e of the relative vol-me. The pre&&-rePpin thereaction pro(-ct& i& given 9y)

; = h 4Ac

> k 4A8c

>?

cbbj?

& the reaction procee(&, the -nreacte( an( pro(-ct pre&&-re& an( temperat-re& are a&&-me( to9e e:-ili9rate( Tu Tp T,pPuPp an( the relative vol-me& are a((itive)

= (1 ) > where Vi& the total relative vol-me. Other mixt-re a&&-mption& can an( have 9een -&e( in (if#ferent ver&ion& of 34523E%3. The reaction rate law ha& the form)

{

&='O1P ]+'


42/1151

5EOS 5EOS7(ENSOR7,ORE7)OLLA,SE

1#!$


43/1151

5EOS7(ENSOR7,ORE7)OLLA,SE 5EOS

LS-DYNA R&" 1#!1


44/1151

5EOS 5EOS7(ENSOR7,ORE7)OLLA,SE

1#!2


45/1151

5EOS7IDEAL7+AS 5EOS

LS-DYNA R&" 1#!%


46/1151

5EOS 5EOS7IDEAL7+AS

1#!!


47/1151

5EOS78WL6 5EOS

LS-DYNA R&" 1#!"


48/1151

5EOS 5EOS78WL6

1#!0


49/1151

5EOS78WL6 5EOS

LS-DYNA R&" 1#!7 l > - 1 i (iO) = (hE > kE)4j> XE' where i& the relative vol-me, < i& the energy per -nit initial vol-me, an( hE, E, hE, kE, E,-, an( are inp-t con&tant& (efine( a9ove.


50/1151

5EOS 5EOS78WL6

1#!/


51/1151

5EOS7+ASKE( 5EOS

LS-DYNA R&" 1#!


52/1151

5EOS 5EOS7+ASKE(

1#"$


53/1151

5EOS7+ASKE( 5EOS

LS-DYNA R&" 1#"1


54/1151

5EOS 5EOS7MIE7+RUNEISEN

1#"2


55/1151

5EOS7MIE7+RUNEISEN 5EOS

LS-DYNA R&" 1#"%


56/1151

5EOS 5EOS7USER7DEFINED

1#"!


57/1151

5EOS7USER7DEFINED 5EOS

LS-DYNA R&" 1#""


58/1151


59/1151

5MA(

LS-DYNA R&" 2#1 T

5MA(LS#345 ha& hi&torically reference( each material mo(el 9y a n-m9er. & &hown 9elow, a

three (igit n-merical (e&ignation can &till 9e -&e(, e.g., ITJ$$1, an( i& e:-ivalent to a corre#&pon(ing (e&criptive (e&ignation, e.g., ITJ


60/1151

5MA(

2#2 T LS-DYNA R&"

ITJ33JT


61/1151

5MA(

LS-DYNA R&" 2#% T

ITJ$") ITJCOPOSAT


62/1151

5MA(

2#! T LS-DYNA R&"

ITJ11$) ITJKO5SO5JOLR8ASTJC


63/1151

5MA(

LS-DYNA R&" 2#" T

ITJ10!) ITJB'A5JLA5


64/1151

5MA(

2#0 T LS-DYNA R&"

ITJ2!") ITJPLJNOPTAO5T'OPACJ


65/1151

5MA(

LS-DYNA R&" 2#7 T

ITJL


66/1151

5MA( 5MA(ERIAL MODEL REFEREN)E (A6LES

2#/ T LS-DYNA R&"

MA(ERIAL MODEL REFEREN)E (A6LES

The ta9le& provi(e( on the following page& li&t the material mo(el&, &ome of their attri9-te&, an(the general cla&&e& of phy&ical material& to which the n-merical mo(el& might 9e applie(.

Af a material mo(el, witho-t con&i(eration of ITJ33J


67/1151

5MA(ERIAL MODEL REFEREN)E (A6LES 5MA(

LS-DYNA R&" 2# T

Material Nu0ber a%d Des3ri/tio% SRA(E

FAIL

EOS

(*ERMAL

ANISO

DAM

(ENS

A//li3atio%s

# Elasti3 +NC FL

! Ortotro/i3 Elasti3 A%isotro/i3-solids. Y )MC M(

$ ,lasti3 Ki%e0ati3Isotro/i3 Y Y )MC M(C ,L

9 Elasti3 ,lasti3 (er0al Y M(C ,L

: Soil a%d Foa0 Y FMC SL

; Li%ear Vis3oelasti3 Y R6

& 6lat-Ko Rubber R6

< *i E/losiJe 6ur% Y *Y

= Null Material Y Y Y Y FLC *Y

#" Elasti3 ,lasti3 *drod%a0i3. Y Y Y *YC M(## Stei%ber1 (e0/ De/e%de%t Elasto/lasti3 Y Y Y Y Y *YC M(

#! Isotro/i3 Elasti3 ,lasti3 M(

#$ Isotro/i3 Elasti3 4it Failure Y Y M(

#9 Soil a%d Foa0 4it Failure Y Y FMC SL

#: 8o%so%)oo ,lasti3it Model Y Y Y Y Y Y *YC M(

#; ,seudo (e%sor +eoloi3al Model Y Y Y Y Y SL

#& Orie%ted )ra3 Elasto/lasti3 4 Fra3ture. Y Y Y Y *YC M(C ,LC )R

#< ,o4er La4 ,lasti3it Isotro/i3. Y M(C ,L

#= Strai% Rate De/e%de%t ,lasti3it Y Y M(C ,L

!" Riid

!# Ortotro/i3 (er0al Elasti3. Y Y +N

!! )o0/osite Da0ae Y Y Y )M

!$ (e0/erature De/e%de%t Ortotro/i3 Y Y )M

!9 ,ie3e4ise Li%ear ,lasti3it Isotro/i3. Y Y M(C ,L

!: I%Jis3id (4o I%Jaria%t +eoloi3 )a/ Y Y SL

!; *o%e3o0b Y Y Y Y )MC FMC SL

!& Moo%e-RiJli% Rubber Y R6

!< Resulta%t ,lasti3it M(

!= For3e Li0ited Resulta%t For0ulatio% Y$" Sa/e Me0or M(

$# Fraer-Nas Rubber Y R6

$! La0i%ated +lass )o0/osite. Y )MC +L

$$ 6arlat A%isotro/i3 ,lasti3it YLD=;. Y Y )RC M(

$9 Fabri3 Y Y Babri3

$: ,lasti3-+ree% Nadi Rate Y M(

$; (ree-,ara0eter 6arlat ,lasti3it Y Y Y M(


68/1151


2#1$ T LS-DYNA R&"


FAIL

EOS

(*ERMAL

ANISO

DAM

(ENS

A//li3atio%s

$& (ra%sJersel A%isotro/i3 Elasti3 ,lasti3 Y M($< 6lat-Ko Foa0 FMC ,L

$= FLD (ra%sJersel A%isotro/i3 Y M(

9" No%li%ear Ortotro/i3 Y Y Y Y )M

9#-:" User DeBi%ed Materials Y Y Y Y Y Y Y +N

:# 6a00a% (e0/Rate De/e%de%t ,lasti3it. Y Y +N

:! 6a00a% Da0ae Y Y Y Y M(

:$ )losed 3ell Boa0 Lo4 de%sit /olureta%e. FM

:9 )o0/osite Da0ae 4it )a% Failure Y Y Y Y )M

:: )o0/osite Da0ae 4it (sai-Wu Failure Y Y Y Y )M

:& Lo4 De%sit Ureta%e Foa0 Y Y Y FM

:< La0i%ated )o0/osite Fabri3 Y Y Y Y )MC Babri3

:= )o0/osite Failure ,lasti3it 6ased. Y Y Y )MC )R

;" Elasti3 4it Vis3osit Vis3ous +lass. Y Y +L

;# KelJi%-Ma4ell Vis3oelasti3 Y FM

;! Vis3ous Foa0 )ras du00 Foa0. Y FM

;$ Isotro/i3 )rusable Foa0 Y FM

;9 Rate Se%sitiJe ,o4erla4 ,lasti3it Y M(

;: erilli-Ar0stro% Rate(e0/ ,lasti3it. Y Y Y Y M(

;; Li%ear Elasti3 Dis3rete 6ea0 Y Y;& No%li%ear Elasti3 Dis3rete 6ea0 Y Y Y

;< No%li%ear ,lasti3 Dis3rete 6ea0 Y Y Y

;= SID Da0/er Dis3rete 6ea0 Y

&" *drauli3 +as Da0/er Dis3rete 6ea0 Y

)able Dis3rete 6ea0 Elasti3. Y 3able

&! )o%3rete Da0ae i%3l Release III. Y Y Y Y Y SL

&$ Lo4 De%sit Vis3ous Foa0 Y Y Y FM

&9 Elasti3 S/ri% Dis3rete 6ea0 Y Y Y

&: 6iluDubois Foa0 Y FM

&; +e%eral Vis3oelasti3 Ma4ell Model. Y Y Y R6

&& */erelasti3 a%d Ode% Rubber Y Y R6

&< Soil )o%3rete Y Y Y SL

&= *stereti3 Soil Elasto-,erBe3tl ,lasti3. Y Y SL


69/1151


LS-DYNA R&" 2#11 T


FAIL

EOS

(*ERMAL

ANISO

DAM

(ENS

A//li3atio%s


70/1151


2#12 T LS-DYNA R&"


FAIL

EOS

(*ERMAL

ANISO

DAM

(ENS

A//li3atio%s

#!# +e%eral No%li%ear #DOF Dis3rete 6ea0 Y Y Y#!! *ill $R) Y M(

#!$ ModiBied ,ie3e4ise Li%ear ,lasti3it Y Y M(C ,L

#!9 ,lasti3it )o0/ressio% (e%sio% Y Y Y M(C ,L

#!: Ki%e0ati3 *arde%i% (ra%sJersel A%iso Y M(

#!; ModiBied *o%e3o0b Y Y Y Y Y )MC FMC SL

#!& Arruda 6o3e Rubber Y R6

#!< *eart (issue Y Y 6IO

#!= Lu% (issue Y Y 6IO

#$" S/e3ial Ortotro/i3 Y

#$# Isotro/i3 S0eared )ra3 Y Y Y M(C )M

#$! Ortotro/i3 S0eared )ra3 Y Y Y M(C )M

#$$ 6arlat YLD!""" Y Y Y M(

#$9 Vis3oelasti3 Fabri3

#$: Wea a%d Stro% (eture Model Y Y Y M(

#$; )orus Veter Y M(

#$< )oesiJe Mied Mode Y Y Y Y AD

#$= ModiBied For3e Li0ited Y Y

#9" Va3uu0

#9# Rate Se%sitJe ,ol0er Y ,L#9! (ra%sJersel A%isotro/i3 )rusable Foa0 Y Y FM

#9$ Wood Y Y Y Y Y 4ood.

#99 ,iter )rusable Foa0 Y Y FM

#9: S34er Murra )a/ Model Y Y Y Y SL

#9; #DOF +e%eralied S/ri% Y

#9& FW*A Soil Y Y Y SL

#9&N F*WA Soil Nebrasa Y Y Y SL

#9< +as Miture Y FL

#:# EJolJi% Mi3rostru3tural Model oB I%elast Y Y Y Y Y M(

#:$ Da0ae $ Y Y Y M(C ,L

#:9 Des/a%de Fle3 Foa0 Y FM

#:: ,lasti3it )o0/ressio% (e%sio% EOS Y Y Y Y i3e.

#:; Mus3le Y Y 6IO

#:& A%isotro/i3 Elasti3 ,lasti3 Y M(C )M

#:< Rate-Se%sitiJe )o0/osite Fabri3 Y Y Y Y Y )M

#:= )S)M Y Y Y Y SL

#;"ALE i%3o0/ressible FL


71/1151


LS-DYNA R&" 2#1% T


FAIL

EOS

(*ERMAL

ANISO

DAM

(ENS

A//li3atio%s

#;#C#;! )o0/osite MS) Y Y Y Y Y )M#;$ ModiBied )rusable Foa0 Y Y FM

#;9 6rai% Li%ear Vis3oelasti3 Y 6IO

#;: ,lasti3 No%li%ear Ki%e0ati3 Y M(

#;; Mo0e%t )urJature 6ea0 Y Y Y )IV

#;& M3)or0i3 Y M(

#;< ,ol0er Y Y ,L

#;= Aru/ AdesiJe Y Y Y Y AD

#&" Resulta%t A%isotro/i3 Y ,L

# Steel )o%3e%tri3 6ra3e Y Y )IV

#&! )o%3rete E)! Y Y Y SLC M(

#&$ Mor )oulo0b Y Y SL

#&9 R) 6ea0 Y Y SL

#&: Vis3oelasti3 (er0al Y Y Y R6

#&; @uasili%ear Vis3oelasti3 Y Y Y Y 6IO

#&& *ill Foa0 Y FM

#&< Vis3oelasti3 *ill Foa0 Orto. Y Y FM

#&= Lo4 De%sit S%teti3 Foa0 Y Y Y Y Y FM

#


72/1151


2#1! T LS-DYNA R&"


FAIL

EOS

(*ERMAL

ANISO

DAM

(ENS

A//li3atio%s

!#= )ODAM! Y Y Y Y )M!!" Riid Dis3rete

!!# Ortotro/i3 Si0/liBied Da0ae Y Y Y Y )M

!!9 (abulated 8o%so% )oo Y Y Y Y Y Y *YC M(C ,L

!!: Vis3o/lasti3 Mied *arde%i% Y Y M(C ,L

!!; Ki%e0ati3 arde%i% 6arlat


73/1151


LS-DYNA R&" 2#1" T


FAIL

EOS

(*ERMAL

ANISO

DAM

(ENS

A//li3atio%s

A": ALE I%3o0/ressible FLA"; ALE *ers3el Y Y FL

S# S/ri% Elasti3 Li%ear.

S! Da0/er Vis3ous Li%ear. Y

S$ S/ri% Elasto/lasti3 Isotro/i3.

S9 S/ri% No%li%ear Elasti3 Y Y

S: Da0/er No%li%ear Vis3ous Y Y

S; S/ri% +e%eral No%li%ear Y

S& S/ri% Ma4ell $-,ara0eter Vis3oelasti3. Y

S< S/ri% I%elasti3 (e%sio% or )o0/ressio%. Y

S#$ S/ri% (rili%ear Deradi% Y Y )IV

S#9 S/ri% Suat Sear4all Y )IV

S#: S/ri% Mus3le Y Y 6IO

6# Seatbelt Y

("# (er0al Isotro/i3 Y *eat tra%sBer

("! (er0al Ortotro/i3 Y Y *eat tra%sBer

("$ (er0al Isotro/i3 (e0/ De/e%de%t. Y *eat tra%sBer

("9 (er0al Ortotro/i3 (e0/ De/e%de%t. Y Y *eat tra%sBer

(": (er0al Dis3rete 6ea0 Y *eat tra%sBer

("& (er0al )WM Weldi%. Y *eat tra%sBer("< (er0al Ortotro/i3(e0/ de/-load 3urJe. Y Y *eat tra%sBer

("= (er0al Isotro/i3 ,ase )a%e.. Y *eat tra%sBer

(#" (er0al Isotro/i3 (e0/ de/-load 3urJe. Y *eat tra%sBer

(## (er0al User DeBi%ed Y *eat tra%sBer

Ta9le 2.1


74/1151

5MA( 5MA(7ADD7AIR6A+7,OROSI(Y7LEAKA+E

2#10 T LS-DYNA R&"

5MA(7ADD7AIR6A+7,OROSI(Y7LEAKA+E

Thi& comman( allow& -&er& to mo(el poro&ity leaage thro-gh non#fa9ric material when &-chmaterial i& -&e( a& part of control vol-me, air9ag. At applie& to 9oth IA'B=J4B'A3 an(IA'B=J5=J5


75/1151

5MA(7ADD7AIR6A+7,OROSI(Y7LEAKA+E 5MA(

LS-DYNA R&" 2#17 T

VARIA6LE DES)RI,(ION


76/1151

5MA( 5MA(7ADD7EROSION

2#1/ T LS-DYNA R&"

5MA(7ADD7EROSIONany of the con&tit-tive mo(el& in LS#345 (o not allow fail-re an( ero&ion. The33J


77/1151

5MA(7ADD7EROSION 5MA(

LS-DYNA R&" 2#1 T

IB IDAM+(" deBi%e te Bollo4i% 3ard1

Car( ! 1 2 % ! " 0 7 /

aria9le SAQ+L= '


78/1151


2#2$ T LS-DYNA R&"

O/tio%al 3ard 9 IDAM". or : IDAMP". or 9Q!5IDAM IDAM".1

Car( !E"E... 1 2 % ! " 0 7 /

aria9le LC+L3


79/1151


LS-DYNA R&" 2#21 T


58+AP 5-m9er of faile( integration point& prior to element (eletion. The (e#fa-lt i& -nity.

LT.$.$ A3$) 58+AP i& percentage of integration point&which m-&t excee( the fail-re criterion 9efore el#ement fail&) Only for &hell&.

LT.$.$ A31) 58+AP i& percentage of layer& which m-&t fail9efore element fail&) Only for &hell&. +or &hellform-lation& with ! integration point& per layer,the layer i& con&i(ere( faile( if any of the integra#tion point& in the layer fail&.

5CS 5-m9er of fail-re con(ition& to &ati&fy 9efore fail-re occ-r&. +or exam#ple, if SA=P1 an( SA= are (efine( an( if 5CS2, 9oth fail-re criteria

m-&t 9e met 9efore element (eletion can occ-r. The (efa-lt i& &et to -ni#ty.

5P'


80/1151


2#22 T LS-DYNA R&"


3=T4P +or =ASSO (amage type the following applie&.


81/1151


LS-DYNA R&" 2#2% T


SAQ+L= +lag for metho( of element &iHe (etermination.


82/1151


2#2! T LS-DYNA R&"


P2 3amage initiation parameter

3AT4P.


83/1151


LS-DYNA R&" 2#2" T

%. ; ;,whereP i& the pre&&-re po&itive in compre&&ion, an( ;i& the min#im-m pre&&-re at fail-re.

! ,whereDi& the maxim-m principal &tre&&, an( Di& the maxim-mprincipal &tre&& at fail-re.

". 8 DEFDEF D, where DEF are the (eviatoric &tre&& component&, an( Di& thee:-ivalent &tre&& at fail-re.

0. Q Q, where Q i& the maxim-m principal &train, an( Q i& the maxim-mprincipal &train at fail-re.

7. a a, where ai& the maxim-m &hear &train (Q Q)\, an( ai& the&hear &train at fail-re.

/. The T-ler#B-tcher criterion,

9^(+


84/1151


2#20 T LS-DYNA R&"

with

3) 3amage val-e (+ 1). +or n-merical rea&on&, 3 i& initialiHe( to a val-e of1.


85/1151


LS-DYNA R&" 2#27 T

any infl-ence. Thi& option can 9e -&e( to calc-late pre#(amage in m-lti#&tage (eformation&witho-t infl-encing the &im-lation re&-lt&.

+or 3=T4P.


86/1151


2#2/ T LS-DYNA R&"

Thi& inp-t allow& for the -&e of extreme val-e& al&o for example, 3C'AT.


87/1151


LS-DYNA R&" 2#2 T

can 9e of maxim-m, , or m-ltiplicative, , type, thi& i& (efine( 9y the 3CT4Pparameter. The glo9al (amage varia9le i& (efine( a&

= ^(< )where

= ^EE= 1 ( 1 E)E The (amage varia9le relate& the macro&copic (amage( an( micro&copic tr-e &tre&& accor(ingto

D = (1)D.Once the (amage ha& reache( the level of $. 9y (efa-lt the &tre&& i& &et to Hero an(the integration point i& a&&-me( faile(, th-& not proce&&e( after that. hen 58+AP integration

point& have faile( the element i& ero(e( an( remove( from the finite element mo(el.5ow to the evol-tion of the in(ivi(-al (amage initiation an( evol-tion hi&tory varia9le&, an( forthe &ae of clarity we &ip the &-per&cript i from now on.

The varia9le& govern& the on&et of (amage an( evolve& in(epen(ently of each other an( ac#cor(ing to the following.

uctile 'IT5P-)6-7/8

+or the (-ctile initiation option a f-nction Q= Q(!


88/1151


2#%$ T LS-DYNA R&"

Antro(-ce( here i& al&o the pre&&-re infl-ence parameter SP2. Optionally thi& can 9e (efine(a& a ta9le with the &econ( (epen(ency 9eing on the effective pla&tic &train rate Q. The (amageinitiation hi&tory varia9le evolve& accor(ing to

= Rc

RcRc

.

;:$


89/1151


LS-DYNA R&" 2#%1 T

+or the evol-tion of the a&&ociate( (amage varia9le we intro(-ce the pla&tic (i&placement 2Awhich evolve& accor(ing to

2 = + ] 1

3Q

1

with l9eing a characteri&tic length of the element. +ract-re energy i& relate( to pla&tic (i&place#ment a& follow&

S= D2Se+ 2 ewith y9eing the yiel( &tre&&. The following (efine& the evol-tion of the (amage varia9le.


90/1151

5MA( 5MA(7ADD7,ERMEA6ILI(Y

2#%2 T LS-DYNA R&"

5MA(7ADD7,ERMEA6ILI(Y

+or con&oli(ation calc-lation&.

Car( 1 1 2 % ! " 0 7 /

aria9le A3 P


91/1151

5MA(7ADD7,ORE7AIR 5MA(

LS-DYNA R&" 2#%% T

5MA(7ADD7,ORE7AIR

+or pore air pre&&-re calc-lation&.

Car( 1 1 2 % ! " 0 7 /

aria9le A3 PJ'O PJP'< PO' 38) (8> 8) (38> 83)\383 \8 \8 (38> 38) (8> 8) (83> 38)\33 \ \ (3> 3) (> ) (3> 3)

3E, E, Eare the (irection co&ine&GE= 3E> E8> ES = 1


186/1151

5MA(7"!$ 5MA(7(EM,ERA(URE7DE,ENDEN(7OR(*O(RO,I)

2#12/ T LS-DYNA R&"

which incl-(e the local thermal &train& which are integrate( in time)

QO= Q > y /ONP 9/O /:

Q!!O

= Q!!

> y! /ONP

9/O

/

:QO= Q > y /ONP 9/O /:

fter comp-ting EFwe then o9tain the Ca-chy &tre&&)DEF= "" NENH NFNH

Thi& mo(el will pre(ict reali&tic 9ehavior for finite (i&placement an( rotation& a& long a& the&train& are &mall.

+or &hell element&, the &tre&&e& are integrate( in time an( are -p(ate( in the corotational coor(i#nate &y&tem. An thi& proce(-re the local material axe& are a&&-me( to remain orthogonal in the(eforme( config-ration. Thi& a&&-mption i& vali( if the &train& remain &mall.


187/1151

5MA(7,IE)EWISE7LINEAR7,LAS(I)I(Y 5MA(7"!9

LS-DYNA R&" 2#12 T

5MA(7,IE)EWISE7LINEAR7,LAS(I)I(Y7NOPTION

vaila9le option& incl-(e)

6LANKP

*A

S(O)*AS(I)

Thi& i&aterial Type 2!. n ela&to#pla&tic material with an ar9itrary &tre&& ver&-& &train c-rvean( ar9itrary &train rate (epen(ency can 9e (efine(. See al&o 'emar 9elow. l&o, fail-re 9a&e(on a pla&tic &train or a minim-m time &tep &iHe can 9e (efine(. +or another mo(el with a morecomprehen&ive fail-re criteria &ee TJO3A+A


188/1151

5MA(7"!9 5MA(7,IE)EWISE7LINEAR7,LAS(I)I(Y

2#1%$ T LS-DYNA R&"

Car( 2 1 2 % ! " 0 7 /

aria9le C P LCSS LCS' P LC+

Type + + + + + +

3efa-lt $ $ $ $ $ $

Car( % 1 2 % ! " 0 7 /

aria9le


189/1151


LS-DYNA R&" 2#1%1 T



190/1151


2#1%2 T LS-DYNA R&"


LCS' Loa( c-rve A3 (efining &train rate &caling effect on yiel( &tre&&. Af LCS'i& negative, the loa( c-rve i& eval-ate( -&ing a 9inary &earch for the cor#rect interval for the &train rate. The 9inary &earch i& &lower than the (e#fa-lt incremental &earch, 9-t in ca&e& where large change& in the &trainrate may occ-r over a &ingle time &tep, it i& more ro9-&t. Thi& option i&not nece&&ary for the vi&copla&tic form-lation. +or the Q option, thec-rve may optionally 9e &pecifie( 9y a ta9le, maing the &train rate &cal#ing a f-nction of the (i&tance from the clo&e&t &potwel(.

P +orm-lation for rate effect&)


191/1151


LS-DYNA R&" 2#1%% T

1 > Rb' where Qi& the &train rate. Q =QQEFQEF. Af P#1. The (eviatoric &train rate& are -&e( in&tea(.Af the vi&copla&tic option i& active, P1.$, an( if SA=4 i& ? $ then the (ynamic yiel( &tre&& i&comp-te( from the &-m of the &tatic &tre&&, DQ#$$ , which i& typically given 9y a loa( c-rveA3, an( the initial yiel( &tre&&, SA=4, m-ltiplie( 9y the Cowper#Symon(& rate term a& follow&)

DQ#$$ < Q#$$ = DQ#$$ > @ Q#$$- '

where the pla&tic &train rate i& -&e(. ith thi& latter approach &imilar re&-lt& can 9e o9taine( 9e#tween thi& mo(el an( material mo(el) ITJ5ASOT'OPACJASCOPLSTAC. Af SA=4$,the following e:-ation i& -&e( in&tea( where the &tatic &tre&&,

D

Q#$$

, m-&t 9e (efine( 9y a

loa( c-rve)

DQ#$$ < Q#$$ = DQ#$$ R1 > Q#$$- ' S

Thi& latter e:-ation i& alway& -&e( if the vi&copla&tic option i& off.

AA. +or complete generality a loa( c-rve LCS' to &cale the yiel( &tre&& may 9e inp-t in&tea(.An thi& c-rve the &cale factor ver&-& &train rate i& (efine(.

AAA. Af (ifferent &tre&& ver&-& &train c-rve& can 9e provi(e( for vario-& &train rate&, the option-&ing the reference to a ta9le LCSS can 9e -&e(. Then the ta9le inp-t in I3


192/1151


2#1%! T LS-DYNA R&"

+ig-re 2#1$. 'ate effect& may 9e acco-nte( for 9y (efining a ta9le of c-rve&. Af a ta9leA3 i& &pecifie( a c-rve A3 i& given for each &train rate, &ee I3


193/1151

5MA(7+EOLO+I)7)A,7MODEL 5MA(7"!:

LS-DYNA R&" 2#1%" T

5MA(7+EOLO+I)7)A,7MODEL

Thi& i& aterial Type 2". Thi& i& an invi&ci( two invariant geologic cap mo(el. Thi& materialmo(el can 9e -&e( for geomechanical pro9lem& or for material& a& concrete, &ee reference& cite(9elow.

Car( 1 1 2 % ! " 0 7 /

aria9le A3 'O B8L@ = LP T


194/1151

5MA(7"!: 5MA(7+EOLO+I)7)A,7MODEL

2#1%0 T LS-DYNA R&"


= +ail-re envelope exponential coefficient, .

B


195/1151


LS-DYNA R&" 2#1%7 T

Re0ars1

The implementation of an exten(e( two invariant cap mo(el, &-gge&te( 9y StoGo W1$X, i&9a&e( on the form-lation& of Simo, et al. W1//, 1$X an( San(ler an( '-9in W17X. An thi&mo(el, the two invariant cap theory i& exten(e( to incl-(e nonlinear inematic har(ening a& &-g#ge&te( 9y A&en9erg, a-ghan, an( San(ler W17/X. 9rief (i&c-&&ion of the exten(e( cap mo(elan( it& parameter& i& given 9elow.

The cap mo(el i& form-late( in term& of the invariant& of the &tre&& ten&or. The &:-are root ofthe &econ( invariant of the (eviatoric &tre&& ten&or, Q08i& fo-n( from the (eviatoric &tre&&e& sa&

Q08T8 EFEFan( i& the o9Gective &calar mea&-re of the (i&tortional or &hearing &tre&&. The fir&t invariant of the&tre&&, K1, i& the trace of the &tre&& ten&or.

The cap mo(el con&i&t& of three &-rface& in Q08 0&pace, a& &hown in +ig-re2#11 +ir&t, therei& a fail-re envelope &-rface, (enote( f1in the +ig-re2#11. The f-nctional form of f1i&S=Q08 _(#(0)< /E#),

where +ei& given 9y

#(0)Ty a(z0) > 0

+ig-re 2#11. The yiel( &-rface of the two#invariant cap mo(el in pre&&-reQ08 0&pace. S-rface f1 i& the fail-re envelope, f2 i& the cap &-rface, an( f% i& the ten&ion c-t#

off.


196/1151


2#1%/ T LS-DYNA R&"

an( /E#T%(U) (U)%. Thi& fail-re envelop &-rface i& fixe( in Q08 0 &pace, an(therefore (oe& not har(en -nle&& inematic har(ening i& pre&ent. 5ext, there i& a cap &-rface,(enote( f2in the fig-re, with f2given 9y

S8=Q08 (0< )

where +ci& (efine( 9y

(0< U)T jQ9(U) (U):8 90 (U):8,(U)i& the inter&ection of the cap &-rface with the K1axi&

(U)=U> #(U),an(

(U

)i& (efine( 9y(U)T VU U ++ U +

The har(ening parameter i& relate( to the pla&tic vol-me change Q.thro-gh the har(ening lawQ.=1 9((U) ):

=eometrically, i& &een in the fig-re a& the K1coor(inate of the inter&ection of the cap &-rfacean( the fail-re &-rface. +inally, there i& the ten&ion c-toff &-rface, (enote( f%in the +ig-re2#11.The f-nction f%i& given 9y

T W Xwhere T i& the inp-t material parameter which &pecifie& the maxim-m hy(ro&tatic ten&ion &-taina9le 9y the material. The ela&tic (omain in Q08 0&pace i& then 9o-n(e( 9y the fail-reenvelope &-rface a9ove, the ten&ion c-toff &-rface on the left, an( the cap &-rface on the right.

n a((itive (ecompo&ition of the &train into ela&tic an( pla&tic part& i& a&&-me()

e] p,

where e i& the ela&tic &train an( p i& the pla&tic &train. Stre&& i& fo-n( from the ela&tic &train

-&ing ooe\& law, )# p,

where i& the &tre&& an( )i& the ela&tic con&tit-tive ten&or.

The yiel( con(ition may 9e written

S() +


197/1151


LS-DYNA R&" 2#1% T

S8(< U) +S() +

an( the pla&tic con&i&tency con(ition re:-ire& that

HSH= + = 1


198/1151


2#1!$ T LS-DYNA R&"

yiel( &-rface an( a limiting fail-re envelope &-rface. Th-&, the &hape of the yiel( &-rface& (e#&cri9e( a9ove remain& -nchange(, 9-t they may tran&late in a plane orthogonal to the K axi&,

Tran&lation of the yiel( &-rface& i& permitte( thro-gh the intro(-ction of a U9ac &tre&&V ten&or, The form-lation incl-(ing inematic har(ening i& o9taine( 9y replacing the &tre&& with the

tran&late( &tre&& ten&or !TD yin all of the a9ove e:-ation. The hi&tory ten&or i& a&&-me((eviatoric, an( therefore ha& only " -ni:-e component&. The evol-tion of the 9ac &tre&& ten&ori& governe( 9y the nonlinear har(ening lawy = 9(D< y)4

where 9 i& a con&tant, i& a &calar f-nction of an( an( 4i& the rate of (eviatoric pla&tic&train. The con&tant may 9e e&timate( from the &lope of the &hear &tre&& # pla&tic &hear &trainc-rve at low level& of &hear &tre&&.

The f-nction i& (efine( a&T^ +


199/1151

5MA(7*ONEY)OM6 5MA(7"!;

LS-DYNA R&" 2#1!1 T

5MA(7*ONEY)OM6

Thi& i&aterial Type 20. The maGor -&e of thi& material mo(el i& for honeycom9 an( foam ma#terial& with real ani&otropic 9ehavior. nonlinear ela&topla&tic material 9ehavior can 9e (efine(&eparately for all normal an( &hear &tre&&e&. The&e are con&i(ere( to 9e f-lly -nco-ple(. See

note& 9elow.

Car( 1 1 2 % ! " 0 7 /

aria9le A3 'O < P' SA=4 + 8 B8L@

Type / + + + + + + +

3efa-lt none none none none none none .$" $.$

Car( 2 1 2 % ! " 0 7 /

aria9le LC LCB LCC LCS LCB LCBC LCC LCS'

Type + + + + + + + +

3efa-lt none LC LC LC LCS LCS LCS optional

Car( % 1 2 % ! " 0 7 /

aria9le


200/1151

5MA(7"!; 5MA(7*ONEY)OM6

2#1!2 T LS-DYNA R&"

Car( " 1 2 % ! " 0 7 /

aria9le 31 32 3% TS


201/1151


LS-DYNA R&" 2#1!% T


tive vol-me or vol-metric &train. 3efa-lt LCBCLCS. See note& 9e#low.

LCC Loa( c-rve A3, &ee I3


202/1151


2#1!! T LS-DYNA R&"


O'3A5T


203/1151


LS-DYNA R&" 2#1!" T

where

z = ^s_5 ,Q

D!Or

= D!

> \!Q!

D!Or= D! > \!Q!DOr= D > \Q


204/1151


2#1!0 T LS-DYNA R&"

then

DEFO= DEF() LK5vNrZLK5vNrZOn Car( 2 iG i& (efine( 9y LC for the aa &tre&& component, LCB for the 99component,

LCC for the cc component, an( LCS for the a9, 9c, ca&hear &tre&& component&. The parameter i& either -nity or a val-e taen from the loa( c-rve n-m9er, LCS', that (efine& a& a f-nction of&train#rate. Strain#rate i& (efine( here a& the \QEF#.5vNP' where the (eviatoric &train increment i& (efine( a&

QEF#.= QEF QHHJEF5ow a chec i& ma(e to &ee if the yiel( &tre&& for the f-lly compacte( material i& excee(e( 9ycomparing

#$$&E = 8 EF&EEF&E8' the effective trial &tre&& to the (efine( yiel( &tre&&, SA=4. Af the effective trial &tre&& excee(& theyiel( &tre&& the &tre&& component& are &imply &cale( 9ac to the yiel( &-rface

EFO= L1r EF&E .5ow the pre&&-re i& -p(ate( -&ing the ela&tic 9-l mo(-l-&, @

eO= e QHHO8' = l(8.) to o9tain the final val-e for the Ca-chy &tre&&

DEFO= EFO eOJEFfter completing the &tre&& -p(ate tran&form the &tre&&e& 9ac to the glo9al config-ration.


205/1151


LS-DYNA R&" 2#1!7 T

+ig-re 2#12. Stre&& :-antity ver&-& vol-metric &train. 5ote that the Uyiel( &tre&&V at avol-metric &train of Hero i& non#Hero. An the loa( c-rve (efinition, &eeI3


206/1151

5MA(7"!& 5MA(7MOONEY-RIVLIN7RU66ER

2#1!/ T LS-DYNA R&"

5MA(7MOONEY-RIVLIN7RU66ER

Thi& i&aterial Type 27. two#parametric material mo(el for r-99er can 9e (efine(.

Car( 1 1 2 % ! " 0 7 /

aria9le A3 'O P' B '


207/1151

5MA(7MOONEY-RIVLIN7RU66ER 5MA(7"!&

LS-DYNA R&" 2#1! T


ST Specimen thicne&&, &ee +ig-re2#1%.

LCA3 Loa( c-rve A3, &ee I3


208/1151

5MA(7"!& 5MA(7MOONEY-RIVLIN7RU66ER

2#1"$ T LS-DYNA R&"

.

+ig-re 2#1%. 8niaxial &pecimen for experimental (ata

+ig-re 2#1! The &tre&& ver&-& &train c-rve can -&e( in&tea( of the force ver&-& thechange in the ga-ge length 9y &etting the ga-ge length, thicne&&, an( wi(th to -nity1.$ an( (efining the engineering &train in place of the change in ga-ge length an( thenominal engineering &tre&& in place of the force. ITJ$77JO i& a 9etter alternativefor fitting (ata re&em9ling the c-rve a9ove. ITJ$27 will provi(e a poor fit to ac-rve that exhi9it& an &trong -pt-rn in &lope a& &train& 9ecome large


209/1151

5MA(7RESUL(AN(7,LAS(I)I(Y 5MA(7"!


210/1151

5MA(7"!= 5MA(7FOR)E7LIMI(ED

2#1"2 T LS-DYNA R&"

5MA(7FOR)E7LIMI(ED

Thi& i&aterial Type 2. ith thi& material mo(el, for the Belyt&cho#Schwer 9eam only, platic hinge forming at the en(& of a 9eam can 9e mo(ele( -&ing c-rve (efinition&. Optionally, col#lap&e can al&o 9e mo(ele(. See al&o ITJ1%.

3e&cription) +O'C< LAAT


211/1151

5MA(7FOR)E7LIMI(ED 5MA(7"!=

LS-DYNA R&" 2#1"% T

Car( ! 1 2 % ! " 0 7 /

aria9le LPS1 S+S1 LPS2 S+S2 4S1 4S2

Type + + + + + +

3efa-lt $ 1.$ LPS1 1.$ 1.$


212/1151


2#1"! T LS-DYNA R&"


OPT xial loa( c-rve option)


213/1151


LS-DYNA R&" 2#1"" T


&ft1 Scale factor for pla&tic moment ver&-& rotation c-rve a9o-t t#axi& atno(e 1. 3efa-lt 1.$.

lpt2 Loa( c-rve A3 for pla&tic moment ver&-& rotation a9o-t t#axi& at no(e 2.3efa-lt) i& the &ame a& at no(e 1.

&ft2 Scale factor for pla&tic moment ver&-& rotation c-rve a9o-t t#axi& atno(e 2. 3efa-lt) i& the &ame a& at no(e 1.

4T1 4iel( moment a9o-t t#axi& at no(e 1 for interaction calc-lation& (efa-lt&et to 1.$


214/1151


2#1"0 T LS-DYNA R&"

= 80[i where i& the (amping factor at the reference fre:-ency in ra(ian& per &econ(. +or exampleif 1b (amping at 2H i& re:-ire(

= 80Z8\08 = +Z++1G]\Af (amping i& -&e(, a &mall time&tep may 9e re:-ire(. LS#345 (oe& not chec thi& &o to avoi(in&ta9ility it may 9e nece&&ary to control the time&tep via a loa( c-rve. & a g-i(e, the time&tepre:-ire( for any given element i& m-ltiplie( 9y $.%Lcwhen (amping i& pre&ent L elementlength, c &o-n( &pee(.

Mo0e%t I%tera3tio%1Pla&tic hinge& can form (-e to the com9ine( action of moment& a9o-t the three axe&. Thi& facili#ty i& activate( only when yiel( moment& are (efine( in the material inp-t. hinge form& whenthe following con(ition i& fir&t &ati&fie(.

5 1^68> 5 __1^68> 5 1^68 1where,

r, &, t c-rrent moment

ryiel(, &yiel(, tyiel( yiel( moment

5ote that &cale factor& for hinge 9ehavior (efine( in the inp-t will al&o 9e applie( to the yiel(moment&) for example, &yiel(in the a9ove form-la i& given 9y the inp-t yiel( moment a9o-tthe local axi& time& the inp-t &cale factor for the local & axi&. +or &train#&oftening characteri&tic&,

the yiel( moment &ho-l( generally 9e &et e:-al to the initial pea of the moment#rotation loa(c-rve.

On forming a hinge, -pper limit moment& are &et. The&e are given 9y

cc= h 5 < 1^8 6an( &imilar for &an( t.

Thereafter the pla&tic moment& will 9e given 9y

rp, min r-pper, rc-rve an( &imilar for & an( twhere

rp c-rrent pla&tic moment

rc-rve moment taen from loa( c-rve at the c-rrent rotation &cale( accor(ing to the&cale factor.

The effect of thi& i& to provi(e an -pper limit to the moment that can 9e generate(D it repre&ent&the &oftening effect of local 9-cling at a hinge &ite. Th-& if a mem9er i& 9ent a9o-t i& local axi& it will then 9e weaer in tor&ion an( a9o-t it& local t#axi&. +or moment&oftening c-rve&,


215/1151


LS-DYNA R&" 2#1"7 T

At i& not po&&i9le to mae the pla&tic moment vary with axial loa(.

axialforce

&train& or change in length &ee OPT

1

2

!

/

%

"

0

7

+ig-re 2#1". The force magnit-(e i& limite( 9y the applie( en( moment. +or an in#terme(iate val-e of the en( moment LS#345 interpolate& 9etween the c-rve& to (e#termine the allowa9le force val-e the effect i& to trim off the initial pea altho-gh ithe c-rve& &-9&e:-ently har(en, the final har(ening will al&o 9e trimme( off


216/1151

5MA(7"$" 5MA(7S*A,E7MEMORY

2#1"/ T LS-DYNA R&"

5MA(7S*A,E7MEMORY

Thi& i& material type %$. Thi& material mo(el (e&cri9e& the &-perela&tic re&pon&e pre&ent in&hape#memory alloy& S, that i& the pec-liar material a9ility to -n(ergo large (eformation&with a f-ll recovery in loa(ing#-nloa(ing cycle& See +ig-re2#10. The material re&pon&e i& al#

way& characteriHe( 9y a hy&tere&i& loop. See the reference& 9y -ricchio, Taylor an( L-9linerW17X an( -ricchio an( Taylor W17X. Thi& mo(el i& availa9le for &hell an( &oli( element&.+or -gheLi- 9eam element& it i& availa9le &tarting in 'elea&e % of ver&ion 71.

Car( 1 1 2 % ! " 0 7 /

aria9le A3 'O < P'

Type / + + +

3efa-lt none none none none

Car( 2 1 2 % ! " 0 7 /

aria9le SA=JSS SA=JS+ SA=JSS SA=JS+


217/1151

5MA(7S*A,E7MEMORY 5MA(7"$"

LS-DYNA R&" 2#1" T


SA=JS+ +inal val-e for the forwar( pha&e tran&formation conver&ion of a-&ten#ite into marten&ite in the ca&e of a -niaxial ten&ile &tate of &tre&&.SA=JS+a& a f-nction of temperat-re i& &pecifie( 9y -&ing the negativeof the loa( c-rve A3n-m9er.

SA=JSS Starting val-e for the rever&e pha&e tran&formation conver&ion of mar#ten&ite into a-&tenite in the ca&e of a -niaxial ten&ile &tate of &tre&&.SA=JSSa& a f-nction of temperat-re i& &pecifie( 9y -&ing the negativeof the loa( c-rve A3n-m9er.

SA=JS+ +inal val-e for the rever&e pha&e tran&formation conver&ion of marten#&ite into a-&tenite in the ca&e of a -niaxial ten&ile &tate of &tre&&.SA=JS+a& a f-nction of temperat-re i& &pecifie( 9y -&ing the negativeof the loa( c-rve A3n-m9er.


218/1151

5MA(7"$" 5MA(7S*A,E7MEMORY

2#10$ T LS-DYNA R&"

An the following, the re&-lt& o9taine( from a &imple te&t pro9lem i& reporte(. The material prop#

ertie& are &et a&)

< 0$$$$ Pa

5- $.%

&igJSJ& "2$ Pa

&igJSJf 0$$ Pa

&igJSJ& %$$ Pa

&igJSJf 2$$ Pa

ep&L $.$7

alpha $.12

ymrt "$$$$ Pa

AXf

ASs

SAs

SAf

L

+ig-re 2#10. S-perela&tic Behavior for a Shape emory aterial


219/1151

5MA(7S*A,E7MEMORY 5MA(7"$"

LS-DYNA R&" 2#101 T

The inve&tigate( pro9lem i& the complete loa(ing#-nloa(ing te&t in ten&ion an( compre&&ion.The -niaxial Ca-chy &tre&& ver&-& the logarithmic &train i& plotte( in +ig-re2#17.

+ig-re 2#17 Complete loa(ing#-nloa(ing te&t in ten&ion an( compre&&ion.


220/1151

5MA(7"$# 5MA(7FRAER7NAS*7RU66ER7MODEL

2#102 T LS-DYNA R&"

5MA(7FRAER7NAS*7RU66ER7MODEL

Thi& i&aterial Type %1. Thi& mo(el (efine& r-99er from -niaxial te&t (ata. At i& a mo(ifie(form of the hyperela&tic con&tit-tive law fir&t (e&cri9e( in @enchington W1//X. See al&o thenote& 9elow.

Car( 1 1 2 % ! " 0 7 /

aria9le A3 'O P' C1$$ C2$$ C%$$ C!$$

Type / + + + + + +

Car( 2 1 2 % ! " 0 7 /

aria9le C11$ C21$ C$1$ C$2$


221/1151

5MA(7FRAER7NAS*7RU66ER7MODEL 5MA(7"$#

LS-DYNA R&" 2#10% T


C!$$ C!$$


222/1151

5MA(7"$# 5MA(7FRAER7NAS*7RU66ER7MODEL

2#10! T LS-DYNA R&"

`= -> -88> -> -WW> -8>-888> -8> -888> S(0) where the invariant& can 9e expre&&e( in term& of the (eformation gra(ient matrix, $i>, an( the=reen#St. enant &train ten&or,)i>)

0 = UEFU= ,EE8= 1\a JbEF,E,bF

The (erivative of 8 with re&pect to a component of &train give& the corre&pon(ing component of&tre&&

EF= clK

here, SiG,i& the &econ( Piola#@irchhoff &tre&& ten&or.

The loa( c-rve (efinition that provi(e& the -niaxial (ata &ho-l( give the change in ga-ge length,L, an( the corre&pon(ing force. An compre&&ion 9oth the force an( the change in ga-ge lengthm-&t 9e &pecifie( a& negative val-e&. An ten&ion the force an( change in ga-ge length &ho-l( 9einp-t a& po&itive val-e&. The principal &tretch ratio in the -niaxial (irection, 1, i& then given 9y

= O@ lternatively, the &tre&& ver&-& &train c-rve can al&o 9e inp-t 9y &etting the ga-ge length, thic#

ne&&, an( wi(th to -nity an( (efining the engineering &train in place of the change in ga-gelength an( the nominal engineering &tre&& in place of the force, &ee +ig-re 2#1! The lea&t&:-are fit to the experimental (ata i& performe( (-ring the initialiHation pha&e an( i& a compari#&on 9etween the fit an( the act-al inp-t i& provi(e( in the printe( file. At i& a goo( i(ea to vi&-al#ly chec the fit to mae &-re it i& accepta9le. The coefficient& C1$$# C$2$ are al&o printe( in theo-tp-t file.


223/1151

5MA(7LAMINA(ED7+LASS 5MA(7"$!

LS-DYNA R&" 2#10" T

5MA(7LAMINA(ED7+LASS

Thi& i&aterial Type %2. ith thi& material mo(el, a layere( gla&& incl-(ing polymeric layer&can 9e mo(ele(. +ail-re of the gla&& part i& po&&i9le. See note& 9elow.

Car( 1 1 2 % ! " 0 7 /

aria9le A3 'O


224/1151

5MA(7"$! 5MA(7LAMINA(ED7+LASS

2#100 T LS-DYNA R&"



225/1151

5MA(76ARLA(7ANISO(RO,I)7,LAS(I)I(Y 5MA(7"$$

LS-DYNA R&" 2#107 T

5MA(76ARLA(7ANISO(RO,I)7,LAS(I)I(Y

Thi& i& aterial Type %%. Thi& mo(el wa& (evelope( 9y Barlat, Lege, an( Brem W11X formo(eling ani&otropic material 9ehavior in forming proce&&e&. The finite element implementationof thi& mo(el i& (e&cri9e( in (etail 9y Ch-ng an( Shah W12X an( i& -&e( here. At i& 9a&e( on a

&ix parameter mo(el, which i& i(eally &-ite( for %3 contin--m pro9lem&, &ee note& 9elow. +or&heet forming pro9lem&, material %0 9a&e( on a %#parameter mo(el i& recommen(e(.

Car( 1 1 2 % ! " 0 7 /

aria9le A3 'O < P' @


226/1151

5MA(7"$$ 5MA(76ARLA(7ANISO(RO,I)7,LAS(I)I(Y

2#10/ T LS-DYNA R&"

Car( " 1 2 % ! " 0 7 /

aria9le 1 2 % 31 32 3%

Type + + + + + +


A3 aterial i(entification. -ni:-e n-m9er or la9el not excee(ing / char#acter& m-&t 9e &pecifie(.

'O a&& (en&ity.

< 4o-ng\& mo(-l-&,


227/1151

5MA(76ARLA(7ANISO(RO,I)7,LAS(I)I(Y 5MA(7"$$

LS-DYNA R&" 2#10 T


OPT aterial axe& option)


228/1151

5MA(7"$$ 5MA(76ARLA(7ANISO(RO,I)7,LAS(I)I(Y

2#17$ T LS-DYNA R&"

ff=e(Dff D) xD Dffg I

f= SDff= Df

=;DThe material con&tant& a, 1, c, f, g an( 0 repre&ent ani&otropic propertie&. hen x = = =S = =;= 1, the material i& i&otropic an( the yiel( &-rface re(-ce& to the Tre&ca yiel( &-rfacefor m21 an( von i&e& yiel( &-rface for m22 or !.

+or face centere( c-9ic +CC material& m2/ i& recommen(e( an( for 9o(y centere( c-9icBCC material& m20is-&e(. The yiel( &trength of the material i&

D= (Q> Q)

where Qi& the &train corre&pon(ing to the initial yiel( &tre&& an( Qi& the pla&tic &train.


229/1151

5MA(76ARLA(7YLD=; 5MA(7"$$7=;

LS-DYNA R&" 2#171 T

5MA(76ARLA(7YLD=;

Thi& i& aterial Type %%. Thi& mo(el wa& (evelope( 9y Barlat, ae(a, Ch-ng, 4anagawa,Brem, aya&hi(a, Lege, at&-i, -rtha, attori, Becer, an( ao&ey W17X for mo(eling ani#&otropic material 9ehavior in forming proce&&e& in partic-lar for al-min-m alloy&. Thi& mo(el i&

availa9le for &hell element& only.

Car( 1 1 2 % ! " 0 7 /

aria9le A3 'O < P' @

Type / + + + +

Car( 2 1 2 % ! " 0 7 /

aria9le


230/1151

5MA(7"$$7=; 5MA(76ARLA(7YLD=;

2#172 T LS-DYNA R&"

Car( " 1 2 % ! " 0 7 /

aria9le 1 2 %

Type + + +

Car( 0 1 2 % ! " 0 7 /

aria9le 1 2 % 31 32 3%

Type + + + + + +



'O a&& (en&ity.

< 4o-ng\& mo(-l-&,


231/1151

5MA(76ARLA(7YLD=; 5MA(7"$$7=;

LS-DYNA R&" 2#17% T


C2 c2, &ee e:-ation& 9elow.

C% c%, &ee e:-ation& 9elow.

C! c!, &ee e:-ation& 9elow.

M ax, &ee e:-ation& 9elow.

4 ay, &ee e:-ation& 9elow.

Q$ aH$, &ee e:-ation& 9elow.

Q1 aH1, &ee e:-ation& 9elow.

OPT aterial axe& option)


232/1151

5MA(7"$$7=; 5MA(76ARLA(7YLD=;

2#17! T LS-DYNA R&"

The &econ(, the oce e:-ation, i& (efine( a&)

D= x 4Rcan( the thir( option i& to give a loa( c-rve A3 that (efine& the yiel( &tre&& a& a f-nction of effec#

tive pla&tic &train. The yiel( f-nctiondi& (efine( a&)d= y% 8%> y8%8 %> y% %= \Dwhere E i& a principle component of the (eviatoric &tre&& ten&or where in vector notation)

=Dan( i& given a&

=8>

I

I 8

I +I > I I +8I I > 8I ++ + + W

coor(inate tran&formation relate& the material frame to the principle (irection& of i& -&e( too9tain the yHcoefficient& con&i&tent with the rotate( principle axe&)

yH = yeH8 > ye8H8 > yfeH8 yf= yfh8\z > yfh_8\zwhere eEF are component& of the tran&formation matrix. The angle z(efine& a mea&-re of the

rotation 9etween the frame of the principal val-e of an( the principal ani&otropy axe&.


233/1151

5MA(7FA6RI) 5MA(7"$9

LS-DYNA R&" 2#17" T

5MA(7FA6RI)

Thi& i&aterial Type %!. Thi& material i& e&pecially (evelope( for air9ag material&. The fa9ricmo(el i& a variation on the layere( orthotropic compo&ite mo(el of material 22 an( i& vali( for %an( ! no(e mem9rane element& only. An a((ition to 9eing a con&tit-tive mo(el, thi& mo(el al&o

invoe& a &pecial mem9rane element form-lation which i& more &-ite( to the (eformation expe#rience( 9y fa9ric& -n(er large (eformation. +or thin fa9ric&, 9-cling can re&-lt in an ina9ility to&-pport compre&&ive &tre&&e&D th-& a flag i& incl-(e( for thi& option. linearly ela&tic liner i&al&o incl-(e( which can 9e -&e( to re(-ce the ten(ency for the&e element& to 9e cr-&he( whenthe no#compre&&ion option i& invoe(. An LS#345 ver&ion& after %1 the i&otropic ela&tic op#tion i& availa9le.

Car( 1 1 2 % ! " 0 7 /

aria9le A3 'O


234/1151

5MA(7"$9 5MA(7FA6RI)

2#170 T LS-DYNA R&"

Car( ! 1 2 % ! " 0 7 /

aria9le 1 2 % M$ M1

Type + + + + +

Car( " 1 2 % ! " 0 7 /

aria9le 1 2 % 31 32 3% B


235/1151


LS-DYNA R&" 2#177 T



236/1151


2#17/ T LS-DYNA R&"


OPT aterial axe& option &ee T7OPTION T'OPACJ


237/1151


LS-DYNA R&" 2#17 T


L5'C +lag to t-rn off compre&&ion in liner -ntil the reference geometry i& reache(,i.e., the fa9ric element 9ecome& ten&ile.


238/1151


2#1/$ T LS-DYNA R&"


M$,M1 Coefficient& of nagonye an( ang W1X poro&ity e:-ation for the leaagearea) h#H = h> > 8>

1 2 % Component& of vector Jfor OPT %.

31 32 3% Component& of vector dfor OPT 2.

B


239/1151


LS-DYNA R&" 2#1/1 T


LC Loa( c-rve or ta9le A3. Loa( c-rve A3 (efine& the &tre&& along the a#axi& fi9erver&-& 9iaxial &train. Ta9le A3 (efine& for each (irectional &train rate a loa(c-rve repre&enting &tre&& along the a#axi& fi9er ver&-& 9iaxial &train. vaila9lefor +O'1! only, if Hero, LC i& -&e(.

LCBB Loa( c-rve or ta9le A3. Loa( c-rve A3 (efine& the &tre&& along the 9#axi& fi9erver&-& 9iaxial &train. Ta9le A3 (efine& for each (irectional &train rate a loa(c-rve repre&enting &tre&& along the 9#axi& fi9er ver&-& 9iaxial &train. vaila9lefor +O'1! only, if Hero, LCB i& -&e(.

5ormaliHe( hy&tere&i& parameter 9etween $ an( 1.

3T Strain rate averaging option.


240/1151


2#1/2 T LS-DYNA R&"

IA'B=J'


241/1151


LS-DYNA R&" 2#1/% T

etry that re&-lt& in initial &train&. To prevent &-ch &train& from premat-rely opening an air#9ag, the&e &train& are eliminate( 9y (efa-lt. &i(e effect of thi& 9ehavior i& that air9ag&that -&e a reference geometry an( that are initially &tretche( will never achieve the correct&hape. The TS'+C factor i& -&e( to re&tore the ten&ile &train& over time &-ch that the cor#rect geometry i& achieve(. At i& recommen(e( that a loa( c-rve 9e -&e( to (efine TS'+Ca& f-nction of time. Anitially the loa( c-rve or(inate val-e &ho-l( 9e $.$ which will allow

the 9ag to remain -n&tre&&e(. t a time when the 9ag i& partially open, the val-e of TS'#+C &ho-l( ramp -p to a &mall n-m9er of a9o-t $.$$$1. h8)

1!. At i& po&&i9le to mo(el coating of the fa9ric -&ing a &heet of ela&tic#i(ealpla&tic materialwhere the 4o-ng\& mo(-l-&, yiel( &tre&& an( thicne&& i& &pecifie( for the coat material.Thi& will a(( rotational re&i&tance to the fa9ric for a more reali&tic 9ehavior of coate( fa9#ric&. To rea( in the&e three parameter& yo- nee( to p-t +O'#1! which rea(& the extra

line incl-(ing the la&t three parameter&


242/1151


2#1/! T LS-DYNA R&"

+ig-re 2#1/.

1

2

;D\

8=kD

;D

\ 8

> e8

8

Af PB$, the ani&otropic material con&tant& a, c, h, an( p are o9taine( thro-gh '$$, '!",an( '$)

x = \ \ jOj jlOjl = \ x;=k

1 >

1 >


251/1151

5MA(7$-,ARAME(ER76ARLA( 5MA(7"$;

LS-DYNA R&" 2#1% T

which give& the ela&tic &train at yiel( a&)

Q= 5,6B C

Af SA=4 yiel( i& nonHero an( greater than $.$2 then)Q= DBCThe other availa9le har(ening mo(el& incl-(e the oce e:-ation given 9yDn(Q) = x 4Rc,the =o&h e:-ation given 9y Dn(Q) = (Q> Q) e,an( finally the ocet#Sher9y e:-ation given 9y

Dn(Q) = x 4Rc5.+or the =o&h har(ening law, the interpretation of the varia9le SPA i& the &ame, i.e., if &etto Hero the &train at yiel( i& (etermine( implicitly from the inter&ection of the &train har(#ening e:-ation with the linear ela&tic e:-ation.

To incl-(e &train rate effect& in the mo(el we m-ltiply the yiel( &tre&& 9y a factor (epen(#ing on the effective pla&tic &train rate. e -&e the Cowper#Symon(&\ mo(el, hence theyiel( &tre&& can 9e written

Dn(Q < Q) = Dn(Q) o1 > 5Q- 6pwhere Dn(enote& the &tatic yiel( &tre&&, -an( eare material parameter&, Q i& the effec#tive pla&tic &train rate.

". inematic har(ening mo(el i& implemente( following the wor& of Cha9oche an('o-&&ilier. 9ac &tre&& Zi& intro(-ce( &-ch that the effective &tre&& i& comp-te( a&

D= D(D \y y88< D88 \y88 y< D8 y8)

The 9ac &tre&& i& the &-m of -p to fo-r term& accor(ing to

yEF= yEFHWH' an( the evol-tion of each 9ac &tre&& component i& a& follow&JyEFH = -H 5xH EFD yEFH 6 JQ


252/1151

5MA(7"$; 5MA(7$-,ARAME(ER76ARLA(

2#1! T LS-DYNA R&"

where -Han( xHare material parameter&,EFi& the (eviatoric &tre&& ten&or, Di& the ef#fective &tre&& an( Qi& the effective pla&tic &train.

0. hen the option J5LP i& -&e(, a necing fail-re criterion i& activate( to acco-nt for thenon#linear &train path effect in &heet metal forming. Ba&e( on the tra(itional +orming

Limit 3iagram +L3 for the linear &train path, the +orma9ility An(ex +.A. i& calc-late(for every element in the mo(el thro-gho-t the &im-lation (-ration an( the entire hi&toryi& &tore( in hi&tory varia9le ^ in 3%PLOT file&, acce&&i9le from Post*@istorymen- inLS#PrePo&t v%.1. The time hi&tory of the in(ex can 9e plotte( for each element -n(er themen-. At i& therefore nece&&ary to &et 5


253/1151


LS-DYNA R&" 2#1" T

$ FLD Definition

*DEFINE_CURVE

211

-0.2 0.325

-0.1054 0.2955

-0.0513 0.2585

0.0000 0.2054

0.0488 0.2240

0.0953 0.23960.1398 0.2523

0.1823 0.2622

...

The following +L3 pre(iction of non#linear &train path& on a &ingle element wa& (one-&ing thi& new option, for an l-min-m alloy with r$$$./, r!"$.0, r$$."", an( yiel( at1%$.$ Pa. An each ca&e, the element i& f-rther &traine( in three (ifferent path& -niaxial #8.., plane &train # P.S., an( e:-i#9iaxial


254/1151

5MA(7"$; 5MA(7$-,ARAME(ER76ARLA(

2#10 T LS-DYNA R&"

Typically, to a&&e&& &heet forma9ility, +.A. conto-r of the entire part &ho-l( 9e plotte(.Ba&e( on the conto-r plot, non#linear &train path an( the +.A. time hi&tory of a few ele#

ment& in the area of concern can 9e plotte( for f-rther &t-(y. The&e plot& are &imilar totho&e &hown in man-al page& of ITJ$%7.

At i& note( that the option J5LP i& implemente( for


255/1151


LS-DYNA R&" 2#17 T

IA5T


256/1151

5MA(7"$& 5MA(7(RANSVERSELY7ANISO(RO,I)7ELAS(I)7,LAS(I)

2#1/ T LS-DYNA R&"

5MA(7(RANSVERSELY7ANISO(RO,I)7ELAS(I)7,LAS(I)7NOPTAO5

vaila9le option allow& the change of 4o-ng\& o(-l-& (-ring the &im-lation)

6LANKP

E)*AN+E

new option i& availa9le to allow for the calc-lation of the +orma9ility An(ex +.A. which ac#co-nt& for &heet metal forming pro9lem& with non#linear &train path)

NL,7FAILURE

Thi& i&aterial Type %7. Thi& mo(el i& for &im-lating &heet forming proce&&e& with ani&otropicmaterial. Only tran&ver&e ani&otropy can 9e con&i(ere(. Optionally an ar9itrary (epen(ency of&tre&& an( effective pla&tic &train can 9e (efine( via a loa( c-rve. Thi& pla&ticity mo(el i& f-llyiterative an( i& availa9le only for &hell element&. l&o &ee the note& 9elow.

Car( 1 1 2 % ! " 0 7 /

aria9le A3 'O < P' SA=4


257/1151

5MA(7(RANSVERSELY7ANISO(RO,I)7ELAS(I)7,LAS(I) 5MA(7"$&

LS-DYNA R&" 2#1 T


SA=4 4iel( &tre&&.

(D D)8> i(D D88)8> \D88 >\D8 >\7D88 1 = +where D, D8, an( D, are the ten&ile yiel( &tre&&e& an( D8, D8, an( Dare the &hear yiel(&tre&&e&. The con&tant& +, = , L, , an( 5 are relate( to the yiel( &tre&& 9y

\= 1D88 \ = 1D8 \7 = 1D88


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2#2$$ T LS-DYNA R&"

\ = 1D88 > 1D8 1D8

\ = 1D8 >

1D8

1D88\i= 1D8 > 1D88 1D8 Z

The i&otropic ca&e of von i&e& pla&ticity can 9e recovere( 9y &etting

= =i= 1\D8n(

= = 7 = I\D8

+or the partic-lar ca&e of tran&ver&e ani&otropy, where propertie& (o not vary in the x1#x2plane,the following relation& hol()

\ = \ = 1D8\i= \D8 1D8

7 = \D8 1\ 1D8

where it ha& 9een a&&-me( that D= D8= D.Letting = L1L1, the yiel( criteria can 9e written(D)= D#= D,where

(D)T eD8 > D888 > 8D8 8D(D> D88) (\ 8)DD88>\D8(D88 > D8) > \ \ 8 8 D88C

8'

The rate of pla&tic &train i& a&&-me( to 9e normal to the yiel( &-rface &o QEF i& fo-n( fromQEF = NNDEF Z

5ow con&i(er the ca&e of plane &tre&&, where %% $. l&o, (efine the ani&otropy inp-t parame#ter, ', a& the ratio of the in#plane pla&tic &train rate to the o-t#of#plane pla&tic &train rate,


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LS-DYNA R&" 2#2$1 T

=Q 88Q ZAt then follow& that

= \8 1Z8&ing the plane &tre&& a&&-mption an( the (efinition of ', the yiel( f-nction may now 9e written

(D)= sD8 > D888 \ > 1 DD88> \ \ > 1 > 1 D88w8' Z

5ote that there are &everal (ifference& 9etween thi& mo(el an( other pla&ticity mo(el& for &hellelement& &-ch a& the mo(el, TJPA


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2#2$2 T LS-DYNA R&"

Loa( c-rve inp-t for +L3 AC+L3 follow& eywor( format in I3


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LS-DYNA R&" 2#2$% T

At i& &-gge&te( that varia9le MA5T\ in I3TBS


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2#2$! T LS-DYNA R&"

*DEFINE_CURVE

200

0.000,395.000

0.001,425.200

0.003,440.300

0.004,452.000

0.005,462.400

0.006,472.100

& &hown in +ig-re2#2!,typically, +.A conto-r can 9e plotte( in $CO;P*;isc, in LS#PrePo&t.Strain path& of an in(ivi(-al element, or element& in an area can 9e plotte( -&ing the U TracerVfeat-re in the$


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LS-DYNA R&" 2#2$" T

+ig-re 2#2! +.A. conto-r plot min AP val-e, non#average(

+ig-re 2#2". Thinning conto-r compari&on

it0 negative !(value it0 positive !(value


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2#2$0 T LS-DYNA R&"

Li&toryaria9le^1

,AP^.in

Time &ec

+ig-re 2#20. + A time hi&tory plot


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5MA(76LA(-KO7FOAM 5MA(7"$ 5stttttttt6 -EFwwhere CiGi& the right Ca-chy#=reen &train ten&or. Thi& &tre&& mea&-re i& tran&forme( to the Ca-#chy &tre&&, iG,accor(ing to the relation&hip

DEF=ttt8' EHFHwhere +iGi& the (eformation gra(ient ten&or.


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5MA(7"$= 5MA(7FLD7(RANSVERSELY7ANISO(RO,I)

2#2$/ T LS-DYNA R&"

5MA(7FLD7(RANSVERSELY7ANISO(RO,I)

Thi& i&aterial Type %. Thi& mo(el i& for &im-lating &heet forming proce&&e& with ani&otropicmaterial. Only tran&ver&e ani&otropy can 9e con&i(ere(. Optionally, an ar9itrary (epen(ency of&tre&& an( effective pla&tic &train can 9e (efine( via a loa( c-rve. +orming Limit 3iagram

+L3 can 9e (efine( -&ing a c-rve an( i& -&e( to comp-te the maxim-m &train ratio which can9e plotte( in LS#PrePo&t. Thi& pla&ticity mo(el i& f-lly iterative an( i& availa9le only for &hellelement&. l&o &ee the note& 9elow.

Car( 1 1 2 % ! " 0 7 /

aria9le A3 'O < P' SA=4


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5MA(7FLD7(RANSVERSELY7ANISO(RO,I) 5MA(7"$=

LS-DYNA R&" 2#2$ T


LCA3+L3 Loa( c-rve A3 (efining the +orming Limit 3iagram. inor &train& inpercent are (efine( a& a9&ci&&a val-e& an( aGor &train& in percent are(efine( a& or(inate val-e&. The forming limit (iagram i& &hown in +ig#-re 2#27. An (efining the c-rve li&t pair& of minor an( maGor &train&&tarting with the left mo&t point an( en(ing with the right mo&t point, &eeI3


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5MA(7"$= 5MA(7FLD7(RANSVERSELY7ANISO(RO,I)

2#21$ T LS-DYNA R&"

.

+ig-re 2#27. +orming limit (iagram.


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5MA(7NONLINEAR7OR(*O(RO,I) 5MA(7"9"

LS-DYNA R&" 2#211 T

5MA(7NONLINEAR7OR(*O(RO,I)

Thi& i&aterial Type !$. Thi& mo(el allow& the (efinition of an orthotropic nonlinear ela&ticmaterial 9a&e( on a finite &train form-lation with the initial geometry a& the reference. +ail-re i&optional with two fail-re criteria availa9le. Optionally, &tiffne&& proportional (amping can 9e (e#

fine(. An the &tre&& initialiHation pha&e, temperat-re& can 9e varie( to impo&e the initial &tre&&e&.Thi& mo(el i& only availa9le for &hell an( &oli( element&. e (o not recommen( -&ing thi&mo(el at thi& time &ince it can 9e -n&ta9le e&pecially if the &tre&&train c-rve& increa&e in &tiff#ne&& with increa&ing &train.

Car( 1 1 2 % ! " 0 7 /

aria9le A3 'O


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5MA(7"9" 5MA(7NONLINEAR7OR(*O(RO,I)

2#212 T LS-DYNA R&"

Car( ! 1 2 % ! " 0 7 /

aria9le MP 4P QP 1 2 %

Type + + + + + +

Car( " 1 2 % ! " 0 7 /

aria9le 1 2 % 31 32 3% B


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5MA(7NONLINEAR7OR(*O(RO,I) 5MA(7"9"

LS-DYNA R&" 2#21% T


P'CB c9, Poi&&on\& ratio c9.

=B =a9, &hear mo(-l-& a9.

=BC =9c, &hear mo(-l-& 9c.

=C =ca, &hear mo(-l-& ca.

3T Temperat-re increment for i&otropic &tre&& initialiHation. Thi& option can9e -&e( (-ring (ynamic relaxation.

T'P Time to ramp -p to the final temperat-re.

LP Thermal expan&ion coefficient.

LCA3 Optional loa( c-rve A3 (efining the nominal &tre&& ver&-& &train alonga#axi&. Strain i& (efine( a& a#1 where ai& the &tretch ratio along the aaxi&.

LCA3B Optional loa( c-rve A3 (efining the nominal &tre&& ver&-& &train along9#axi&. Strain i& (efine( a& 9#1 where 9i& the &tretch ratio along the 9axi&.


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5MA(7"9" 5MA(7NONLINEAR7OR(*O(RO,I)

2#21! T LS-DYNA R&"


the fir&t fo-r no(e& an( the la&t fo-r no(e& of the connectivity of theelement, re&pectively.


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5MA(7USER7DEFINED7MA(ERIAL7MODELS 5MA(7"9#-":"

LS-DYNA R&" 2#21" T

5MA(7USER7DEFINED7MA(ERIAL7MODELS

The&e areaterial Type& !1#"$. The -&er m-&t provi(e a material &-9ro-tine. See al&o ppen(ix. Thi& eywor( inp-t i& -&e( to (efine material propertie& for the &-9ro-tine. A&otopic, ani&o#tropic, thermal, an( hyperela&tic material mo(el& with fail-re can 9e han(le(.

Car( 1 1 2 % ! " 0 7 /

aria9le A3 'O T LC 5 AO'TOEASPOT

AB8L@ A=

Type / + A A A A A A

Car( 2 1 2 % ! " 0 7 /

aria9le A


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5MA(7"9#-":" 5MA(7USER7DEFINED7MA(ERIAL7MODELS

2#210 T LS-DYNA R&"

DeBi%e LM)0aterial /ara0eters usi% < /ara0eters /er 3ard

Car( 1 2 % ! " 0 7 /

aria9le P1 P2 P% P! P" P0 P7 P/

Type + + + + + + + +

DeBi%e LM)A0aterial /ara0eters usi% < /ara0eters /er 3ard

Car( 1 2 % ! " 0 7 /

aria9le P1 P2 P% P! P" P0 P7 P/

Type + + + + + + + +



'O a&& (en&ity.

T8&er material type !1#"$ incl-&ive. n-m9er 9etween !1 an( "$ ha&to 9e cho&en. Af T>$, &-9ro-tine rw-mat in (yn21.f i& calle(, wherethe material parameter rea(ing can 9e mo(ifie(.

LC Length of material con&tant array which i& e:-al to the n-m9er of mate#rial con&tant& to 9e inp-t. &ee remar !

5 5-m9er of hi&tory varia9le& to 9e &tore(, &ee ppen(ix . hen themo(el i& to 9e -&e( with an e:-ation of &tate, 5 m-&t 9e increa&e( 9y! to allocate the &torage re:-ire( 9y the e:-ation of &tate.

AO'TOEASPOT


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LS-DYNA R&" 2#217 T


A+AL +ail-re flag.


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5MA(7"9#-":" 5MA(7USER7DEFINED7MA(ERIAL7MODELS

2#21/ T LS-DYNA R&"


MP 4P QP Coor(inate& of point /for OPT 1 an( !.

1 2 % Component& of vector afor OPT 2.

1 2 % Component& of vector Jfor OPT % an( !.

31 32 3% Component& of vector dfor OPT 2.

B


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LS-DYNA R&" 2#21 T

!. Af AO'TO$, LC m-&t 9e [ !/. Af AO'TO1, LC m-&t 9e [ !$. Af more materialcon&tant& are nee(e(, LC may 9e -&e( to create an a((itional material con&tant array.There i& no limit on the &iHe of LC.

". Af the -&er#(efine( material i& -&e( for 9eam or 9ric element &pot wel(& that are tie( to

&hell element&, an( SPOTA5?$ on ICO5T'OLJCO5TCT, then &pot wel( thinningwill 9e (one for tho&e &hell& if ASPOT2. Otherwi&e, it will not 9e (one.

0. A


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5MA(7":# 5MA(76AMMAN

2#22$ T LS-DYNA R&"

5MA(76AMMAN

Thi& i&aterial Type "1. At allow& the mo(eling of temperat-re an( rate (epen(ent pla&ticitywith a fairly complex mo(el that ha& many inp-t parameter& WBamman 1/X.

Car( 1 1 2 % ! " 0 7 /

aria9le A3 'O < P' T C

Type / + + + + +

Car( 2 1 2 % ! " 0 7 /

aria9le C1 C2 C% C! C" C0 C7 C/

Type + + + + + + + +

Car( % 1 2 % ! " 0 7 /

aria9le C C1$ C11 C12 C1% C1! C1" C10

Type + + + + + + + +

Car( ! 1 2 % ! " 0 7 /

aria9le C17 C1/ 1 2 ! " 0 @PP

Type + + + + + + + +



'O a&& (en&ity.


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5MA(76AMMAN 5MA(7":#

LS-DYNA R&" 2#221 T


< 4o-ng\& mo(-l-& p&i

P' Poi&&on\& ratio

T Anitial temperat-re o'

C eat generation coefficient o'Ep&i

C1 P&i

C2 o'

C% P&i

C! o'C" 1E&

C0 o'

C7 1Ep&i

C/ o'

C P&i

C1$ o'

C11 1Ep&i#&

C12 o'

C1% 1Ep&i

C1! o'

C1" p&i

C10 o'

C17 1Ep&i#&

C1/ o'

1 1, initial val-e of internal &tate varia9le 1


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5MA(7":# 5MA(76AMMAN

2#222 T LS-DYNA R&"


2 2, initial val-e of internal &tate varia9le 2. 5ote) % #1]2

% !, initial val-e of internal &tate varia9le %

! ", initial val-e of internal &tate varia9le !

" 0, initial val-e of internal &tate varia9le "

@PP , initial val-e of internal &tate varia9le 0

&ec#p&i#o' &ec#Pa#o' &ec#P#o@C1 I11!" I11!"C2 q I"

C% I11!" I11!"C! q I"C" q qC0 q I"EC7 I1!" I1!"C/ q I"C I11!" I11!"C1$ q I"C11 I1!" I1!"C12 q I"

C1% I1!" I1!"C1! q I"C1" I11!" I11!"C10 q I"C17 I1!" I1!"C1/ q I"

C$C I1!" I1!"I"< I11!" I11!" q qT q I"

Re0ars1

The inematic& a&&ociate( with the mo(el are (i&c-&&e( in reference& Will 1!/, Bammann an(ifanti& 1/7, Bammann 1/X. The (e&cription 9elow i& taen nearly ver9atim from BammannW1/X.

ith the a&&-mption of linear ela&ticity we can write,


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5MA(76AMMAN 5MA(7":#

LS-DYNA R&" 2#22% T

D = (#)1 > \ #where the Ca-chy &tre&& i& convecte( with the ela&tic &pin#a&,

D

= D #D > D#

Thi& i& e:-ivalent to writing the con&tit-tive mo(el with re&pect to a &et of (irector& who&e (irec#tion i& (efine( 9y the pl

Ls-dyna Manual Vol II r7.0

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