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TA
E 1468 GPa ~ =114GPa
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s= 1337 MPa p = 1550 kgm3
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Y )~ ~ ~ ~L W)1i bull ~~ IIgt)IS
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140~ 0 5 If L~II cil 1( is u - J I)r-- 1 r- ~
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~fJ4 I - de Freitas M Silva A and Reis L (2000) Numerical evaluation of failure mechanisms on composite
specimens subjected to impact loading Composites Part B Engineering Vol 31 PP 199-207
2 - Mohammadi S (2003) Discontinuum Mechanics using Finite and Discrete Elements WITPress- UK
3 - Koh CG Owen D R J and Perie D (1995) Explicit dynamic analysis of elsto-plastic laminated
composite shells implementation of non-iterative stress update schemes for the Hoffinan yield criterion
Computational Mechanics Vol 16 PP 307-314
4 - Schellekens 1 C 1 (1992) Computational strategies for composite structures PhD thesis Technische
Universiteit Delft Holland
5 - Forouzan-sepehr S and Mohammadi S (2001) A contact based method for 3D delamination analysis of
composites subjected to impact loading in S ValliaPPan N Khalili (editors) Computational Mechanicsshy
New Frontiers for the New Millennium Proceedings of 1 Asian-Pactflc Congress on computational
Mechanics- PP 691-696
6 - Mohammadi S Forouzan-sepehr S and Asadollahi A (2002) Contact based delamination and fracture
analysis of composites Thin-Walled Structures Vol 40 No 7-8 PP 595-609
7 - Masters 1 E (1987) Basic failure modes of continuous fiber composites Engineering Materials
Handbook Vol 1 CompOSites ASM International USA
8 - Borovkov A Kiylo 0 Misnik Yu and Tripolnikov T (1999) Finite element stress and analysis of
multidirectional laminated composite structures 2 h-p- refinement and m- adaptive procedures
Zeitschrijiir Angewamte Mathematik undMechamle Vol 79 Suppl No2 PP S527-S528
9 - FEA (2000) LUSAS User Manual Ver 132 FEA Ltd
10 - Liu Sh (1994) Quasi-impact damage initiation and growth of thick-section and toughened composite
materials lnt J Solids andStructures Vol 31 No 22 PP 3079-3098
11 - Mi Y Crisfield M A (1996) Analytical derivation ofloaddisplacement relatiollShip for the DCB and
MMB andproofofthe FEA formulation IC-AERO Report 97-02 Dept Aeronautics Imperial College
London UK
12 - Mi Y Crisfield M A Davies G A O and Hellweg H B (1998) Progressive delamination using
interface elements J Composite Materials Vol 32 No 14 PP 1246-1272
13 - Grady J E Chamis C C and Aiello R A (1989) Dynamic delamination buckling in composite
laminates under impact loading computational simulation In Lagace PA (ed) Composite Materials
Fatigue and Fracture ASTM-STP 1012 PP 137-149
~ )) O)~ ~~ ~~ 0) 1 - Matrix Cracking 2 - Delamination 3 - Fibre Breakage 4 - Fragmentation 5 - Theory ofPlasticity 6 - Computational Contact Mechanics 7 - Solid Element 8 - Discrete Element Method (DEM) 9 - Generalised Hook Law 10 - Transversely Isotropic 11 - Anisotropic 12 - Associated Flow Rule 13 - Normal Gap 14 - Tangential Gap 15 - Penalty 16 - Remeshing 17 - Adapti vity
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l tl~fj ~jLo ~ S(K) y1 ~~jLo
middot~415 5r
lA~~ 1 S~I 1Sr~l1~ ISiWoM 1S1r 10
IS~) ~~il ~4 ~ laquo~~~ 1S1bgtgtgt )
bull 1 lL l ci ~ ts -LL LslSo- _ 15 Y) 15 bull V shy
Lo L)JS bull lAo ~ 6- t L bull bull - 1- t$Ir- - y r oJ)
~Ib middot~415 (y - r f) ISlA)l )l ~4-sI
bullli15 o~l ~4 ~Ir ~ rlAo ~I 1Sr)tse
~ jl ~s ~19 s- $-~~ ISIbgt ~ 6J 1S1r
~~)l )~ ~~ l1~ ~)~ ~(gNltO)
bull10 a r aN ~4 ~Ir yG1 4 oM~115
IS~ )br otIb ISIbgt olj ~l 1~ ~ ~I
)~ s- $-~~ )lr ISI~~I
(rv) (rr)
gN~O
gNgtO K~O
gNgtO KgtOSN(K)ltl (iO)
gNgtO
Er K~O
(l-Sr(KraquoEr K gt 0 Sr(K) lt 1 Oy(g) =
K gt 0 Sr(K) ~ 1 (Jr lt a r(l-)ar a-gr KgtO Sr(K)~l (Jr=a (if)
IA-)I ~ ll kl bull ~ IS- bull r ~gt
is)iI)~ ~Ir - ~~ - )~~)I gt Jgt gNltO
~ltgt~gtIS- is-)l0~ S jy 0~ J ~j4 0lt -N-gN ltgmax
~ jI o~ 1~ iSlA-)I J ~j4 gt -NgN -gmax
Jgt)gtS 0~ J ~ jL9 )gt y 0lt -T-gT ltgmax IS-~- (gt gt
J gt)gtS jI ~ ~I jL9 )gt j-iJ gt-TgJ -gma
I J
I 8T
J
1i)J ~Ioo slt40-J sl) () ~ij slt40-J sl) (AlI)~ s~lt40-~) sl~lI~~ dMi ~I)V ~
(0 =jJ(-CFN)) J~ jli)J ~Ioo slt40-J sl) (-) J~
iSlA) ltIS JAJ 0-11 )0 jI)gt JIlIIgtI iS~4
ciy )gt I) ~j~1S iSlA~~ J))gt5 ~ IV II shy
jl bull is)lfjL bull - ~1)j4 0~ ~IAIj) 4j~
yly )) ~ ~41S o~ I~ iS~WI ~) 0~
iSl) is~ is)l) I~ iS~WI 4 ~ ) I~ ~I ) ~ yIb bull) 0-11 )) lIIgtgt1S ~ )4 0-11 -5 )) I~ 0W1 ~ ljoJb SIA-)I jl iSl~gt 4 IA-)I jI
~ iS~WI iSr)S 4 gtgt o~ ci fo It ~OJLIIIAltgt)ImiddotL middotmiddot(Ijl gtgt t~J r-- JY bull u U--) Y IS Igt 1)
(lb)i1S (~I ~ ~)) o~~ iSyJl
)l iSl-)l0~ ISL ~ ~ iSl) Jc)) Ij) jl ~I jL9 )l (if) ~I) jl J ~ jL9
~ )l 1 ~~~ )IS isr is
01)4 ltIS lIIgtgt1S t) ISISa is))))4 ~~l
~ ~Lj (If jl is)~ ~Lj (If s1gt -5
middot~4A~
JJ)gt S~ ~~J ~ ~lJS ~)
~I~--JUIto ~~ is~ ~lSo ~4 ) gt~ ~Ir- )
II sJ4 ) Lltmin ~~ lo~llS ~ ~4 o~ JrS O~ sr Mcr ~Ir ~t) rlS 1~
jl ~t) rlS ytgt ) Llt -)J ~ Y- 4 1
) ~ 1 yi sr min (1tcrMmin)
) -jJ ~4 i s1~4 ~ sl) bull) y-I
L~11 JrS rgt s1 Jt ~tj rlSytgt
IS~)S IS~) ~v (iJ1- toJ
~4 ) I) ~)yJ1 hrJ 01~oJII (Grady) sJ
1 Ali W ~ 1 1 I_~ d ~sts) 1Sr ~ - ~ ) shy
5 4 sl-J ~jrolS II sl ) u~J ISI~
JjJ )~ sl~rb s)lf)4 I ~ ~I s1~J01o
0Li (All - A) ~ ) y-I s)lf)4 -gtlgtJb
)1 )r- r s) IS)) ) 1 ol 01
sr-) syJI 4 TIOOI034-C ~~1-4IJ ~
) ol 01 0Li ~lo sVi-t [OO]lOs JLJl
middotl41S (y- A)~ J~
5 ci)l r~1 -J )~ ) 1 y-I sjLJlo
u-J ~ ~ 010 OmiddotA em ojl)j ~ s1~1
- A ~) )IS 010 jI I) uL 0)Q u ) Y
laquoAll
sur-AI) jl sr-0 - 4 ~Iio sl) uL y-I ~ (wI ~I ~ s~JA ~x 0l1 ) ol ltlJ1)
~ 4JJ )~ jl ~ ytgt u W y-14 )l1S r~1
1IS s~JA 0l1 ol ciJ ~ ) lr--o 0 W1
t I ciL KA bull (All-) 1(-u ))) -- ~ shy
lt) jS ol ISW) )~ 1= + see
5 o)j))) -J ) I)) ~Io 46A 1S~4-- )
) ol ltlJI) ) 4 u llb1S 0Li tj Jk ) ~I ~ lgt sl) I) ~ bA9 u (w] ~I --
1 ~Iio ~li 01 ltlJ1) rblgt ~ 0t) r)p
) sl-J010 )gt5 r-S ssJ1 () jS
sur-A) sr-)~ 4 0 jl ~ jI u llb1S Li
~~ u ~IA bull1 olol ~ ~~ y-I
1S~ts ) s14JJ01o )gt5 ~I~ l1S
)1 ) suy ~ s~rb s) )4 )) ~
JIS
jll~ ~Ir-I ) ~ s1~J0l-o ~)gt5 ~
bulls)~ )IS JgtI j sr-0 - 4 ~ Ir-I -~ ~~ tIla sl) ~4 ~4 jI)~
(V)
1 I TTJCOn TTftXt bull TIflntbull TIflnertia -1 ) lt)) ~) j cu
(A)
rgt ~ Iy-I ) 1 jS ~I sr-)~ 4 s1~J0l-o ss) ssJ1 i)W -4its s~)sJ1
15t jS ~ (fV) ~I ~I) ol )r
Mii + fint = fext + fcon
sur-i )) M rr- ~t1)u JISk~
sur-i )) felU ~t sur-i )) fint ~)
~11S ~)j ~I) jI fcon sl-Jl-o ISW
(fr)
fint = 1BTSan (ff )
fext = 1NTb an + 1NTtar I (10)
) u01 )I- ~ ~bo ~~ ~ 4 4 laquosrgt ~W ~r raquo )gt5 ~
p) y-I ) ~ ~ IS ciJ )~ )I)li ~tj s4-0lS
~r-1 ~) sr-i su)) ~I ) 4 ~ ) sr )) ~ ~tj rlS ) sl-J10
) ~ytgt ~11S~~s fl3 ~~4-- ))
Ojt)j ~)) o~ k~ )~~srgt ~W
s)~~li ~bullbull lgt Ssect )IS )~ ~t) rl3
bullbullbullbull
TA
E 1468 GPa ~ =114GPa
G2 = 6184 GPa G23 = 4380 GPa
v =03 ~ =1730MPa A =1380MPa
1= 665 MPa 1 = 268 MPa
s= 1337 MPa p = 1550 kgm3
~ M
190N
T
~~X
(y) (All)
T3001034-C ~~I-~I ISI~ ~lAo IS~) (~)~u ISI-~ ISJIJJ~ 4IJiA (ill) It ~
a bull-amp----~~g----~a (y) (All)
KiP Reoldon H~lot1 Plo I D bull 1 P 5
bull -1 n t -15 n
-L Z
-25
- -5
-
5
-5 11 u u u 5 u 7 U 1
- I I I
25
lIIS-altlCllr -
~ E -_ I ~ 125 ~_tM
- C -- -
~ bull ~~~ ~E 0bull f4u -
bull ii ~h -125
0 j -
~ -25 25 50_
~ position (em)
~ r-I---
- _ algorINa 0 -4 ~ I---(SOIIXJISOloolJUJfgto6MX
~ r--- -U
TIaa
~ jl OJo1 ~ ~Is~ o~JI)~J) tIJ ui~ 4laii IT-~~ Jb ~io ~
[-]~)A jl4iS~ ~middot-r~middotlsec 1S~loj J) 4iSt ~ ytNu
bull Q
Qbull amp
amp a bull
(y) (All)
bull bull
bull bull bull bull
bull bull
bull bull bull
bull bull abull a ia bullbull a () lt)
45~oi IIgt ~ 4iw 454)~~ IIgtJs ~J 45l11 ~
1=- sec ()t=~ sec (11)= sec ()=++ bullbull sec (All)
( bull IJoZ 1gt11gt ~~ j)~sJ ~ lo ~u ~JsJ ~s j~j 45-Slsj ~ 1A4) r~)
- abull a
bull bull a
( ) (uJl)
1= + sec () t= middot middot0 sec (All) 45~oj)1gt I~ 4i 4514)~~ JI)s ~J 45l1IT ~
( bull loJoZ 1)111gt ~~ I)~ sJ ~ lo ~u ~J sJ 4s j~l 45-Sl s1 41A4) ul~)
f) Ibull JI Ibull bullbullc
bullt bullI
2 -Ut
Ja
ua
-
ua
1
-~Jlitt8lmiddotmiddot1 I I -
Ii lop
1 ~
~ Lfi ~ of
~
) IIgt )) ~j-S iSUb~ ~~) JLgti o~)by
)3) ~I jI o)~ ))gt5 jl ~ ~ ~r
jAl w~ iSl~~wl-o ))gt5 jI ~ Ub~~
)) Ub~~ u-W bull5~ o~ 0)4) ))gtY
t~ I~middot ~ IS )) If 1middot 1 1_~ramp- is~) isr) ) IS )r- r-
-wLS )lJ) ~Iu ()fl iS~ ~) 1$JJt
~l~I JLgti o)jl Ih) j) y (wlo
)LgtI )) 511gt o~ rlS ~I jl I) is)g3)
I$)Y iSly middotw4~ )) IIgt)IS i --b ~~
ul) ~ iSUb)rJb1) iSr)~ 4 ) S1)s ~))
f4W 4S l ul) is)lJ SUb~ )4 ~I )) ol
middotl41S is)~ isUb)rJb1) ~
~I~)li
oSjb ~~ iSl) ~~ jl ~~~
Syen ~Igt ) FfI(lf(V o ek jI d o ~ (~) wr-1J iSjL~yen ~W- Srshy
bull))- IS ~1))gt9 frY -Ii - - -i
) 4i (y
1 wlA JLgti bullJi) is wl~
)4 ~I ~ lA ~ 4 bull )y~1S r~1 ~it wlA 4 is~ i ~r)) iSl~ )4 ol is~)4 issJI
~ ~ )) l wlA 4 iSl~ yo )4 ~ I) )gt
Y )~ ~ ~ ~L W)1i bull ~~ IIgt)IS
~ (H) lt - ) is~ ))IS wl-o jl
140~ 0 5 If L~II cil 1( is u - J I)r-- 1 r- ~
~)IS wli -1- sec -1- - Osec is~Lj )) I)
~ )) wIj -gt y ~l-o ~~~ )b
))gt5 ~I )) 1 0 1 (i)
)4 yj 41 5 ~r )) 0it~ Ub~ jI iSl~~wl-o
)-IS jul isI~ yo
iSjW iSly ISL is)lJ ) )4 ~I )) Jlgt )) laquoiSl-~wl-o ))gt5J ~ o~~ I$)Y
~ts ~Io ~p ~I--o jI iSr0 4 is~4J )) ) ~I l ul) ~~lS d~b I)W
~fJ4 I - de Freitas M Silva A and Reis L (2000) Numerical evaluation of failure mechanisms on composite
specimens subjected to impact loading Composites Part B Engineering Vol 31 PP 199-207
2 - Mohammadi S (2003) Discontinuum Mechanics using Finite and Discrete Elements WITPress- UK
3 - Koh CG Owen D R J and Perie D (1995) Explicit dynamic analysis of elsto-plastic laminated
composite shells implementation of non-iterative stress update schemes for the Hoffinan yield criterion
Computational Mechanics Vol 16 PP 307-314
4 - Schellekens 1 C 1 (1992) Computational strategies for composite structures PhD thesis Technische
Universiteit Delft Holland
5 - Forouzan-sepehr S and Mohammadi S (2001) A contact based method for 3D delamination analysis of
composites subjected to impact loading in S ValliaPPan N Khalili (editors) Computational Mechanicsshy
New Frontiers for the New Millennium Proceedings of 1 Asian-Pactflc Congress on computational
Mechanics- PP 691-696
6 - Mohammadi S Forouzan-sepehr S and Asadollahi A (2002) Contact based delamination and fracture
analysis of composites Thin-Walled Structures Vol 40 No 7-8 PP 595-609
7 - Masters 1 E (1987) Basic failure modes of continuous fiber composites Engineering Materials
Handbook Vol 1 CompOSites ASM International USA
8 - Borovkov A Kiylo 0 Misnik Yu and Tripolnikov T (1999) Finite element stress and analysis of
multidirectional laminated composite structures 2 h-p- refinement and m- adaptive procedures
Zeitschrijiir Angewamte Mathematik undMechamle Vol 79 Suppl No2 PP S527-S528
9 - FEA (2000) LUSAS User Manual Ver 132 FEA Ltd
10 - Liu Sh (1994) Quasi-impact damage initiation and growth of thick-section and toughened composite
materials lnt J Solids andStructures Vol 31 No 22 PP 3079-3098
11 - Mi Y Crisfield M A (1996) Analytical derivation ofloaddisplacement relatiollShip for the DCB and
MMB andproofofthe FEA formulation IC-AERO Report 97-02 Dept Aeronautics Imperial College
London UK
12 - Mi Y Crisfield M A Davies G A O and Hellweg H B (1998) Progressive delamination using
interface elements J Composite Materials Vol 32 No 14 PP 1246-1272
13 - Grady J E Chamis C C and Aiello R A (1989) Dynamic delamination buckling in composite
laminates under impact loading computational simulation In Lagace PA (ed) Composite Materials
Fatigue and Fracture ASTM-STP 1012 PP 137-149
~ )) O)~ ~~ ~~ 0) 1 - Matrix Cracking 2 - Delamination 3 - Fibre Breakage 4 - Fragmentation 5 - Theory ofPlasticity 6 - Computational Contact Mechanics 7 - Solid Element 8 - Discrete Element Method (DEM) 9 - Generalised Hook Law 10 - Transversely Isotropic 11 - Anisotropic 12 - Associated Flow Rule 13 - Normal Gap 14 - Tangential Gap 15 - Penalty 16 - Remeshing 17 - Adapti vity
Y
~IS QJ )iu )~ AE ~ )br s 4 s
~ ~ ~ ~ fl--i sjf)4 ft )~ oS
~ AEP 0L ~ Apound 0lS
~~JIS
(A)
0~ri w~ )~ -1 ~- 4 J6u jj) )~ middot~4 IS
-11) pound ~ )~r ~ oS ~ts -I~ ~L
4 olroJb s sjj) -1 bull)$IS k~ 0 ~ )~r
~j4 jjraquo )~ 0I~ ~41S jl lbgt 0-) )~ laquo0~1) -~ t1~t Jgt ol~ laquofi1
)~ ~ ~ )~r ot~ )~I )~ ~IS QJ
)~ pound_1 0_1 4 rlr ~ -1 fl--i s1)4 ft ju1
fi1 ~j4 jj) 4 J1lbo middot~4 pound 0 ft 0I10lt4
0lt4 ~ ~) ~ rogt s) -1 I) ~ )~r f~Ir oS
zb ~1gt [~] lA~1S ~j4 f1J
OJ =Oi-l +Aoj ( )
(H)
fl--j )~ )~ ~ J)lgt1 0 1r-o 4r1r Ao j 4ril)~ oS
Apound j (A) )~ () () ~I) s)~~ 4 middot~41S
middot1 W j J)lgt1 middot Il 11) ) - r
j b i -- bull ~gJlgt I La I vmiddotmiddot ) r ~ rr- ~)_ sr
41 rlr
0-=POmiddot+POcr
lt f)
(f)
Yoj )~ P )I~r P ~L 01)~ oS jj1S At~
jj IS At~
2(a +all) -2a -2all 0 0 o -2a 2(a12 +a) -2all 0 0 o -2a -2a 2(a +a) 0 0 op
0 0 0 0 o 0 0 0 0 o
6a 6a
0 0 0 0 0 6a
clt ~lA s~i -1 afJ -I~ ~I) 011 )~ oS
~I ~ sIr s)~ ~I) 0)1 1il~l
~ )~ 0l-o 011)~ oS 1 o~ -11)1 l ~~lA[j
0~ lA)~ j1s)~ 4- -IlA)~oijA s~~
-sl- slA)~ s~~ O~J i Qi~ JAgt )~ 011 ~I )1 ~)kl I) J~s--~lI bullsj~1
Q) )~ ~ slA)- jl s)~ )~ J~ I )~
~~ 011)~ d~ 0 1 r] ell 4i sl)-l) 1
~ ajro1S slAojl 0L )j) 1S)r sIr rgt 01)4 0 ~J )iu)~ 4 )~ 011)~ ~)IS )~ )~
)~)l9s )~ ~lgt 119s~ Xc X T
)~ ~ lgt ~l9 s~ Yc 1 J~I slI)
lgt ~r ~ J~I r ~ slI) )~ )l9 s jjISJro Yo] )~ afj -I~S ~
1 1 all =--shy
X] Xc 1 1
a l2 =a33 =--shy1 Yc
1 3a44 = 3ass =S
4 13a(6=----
YrYc XrXc 1
2al2 = 2a13 =--XrXc
2 12a23 =----
YrYc XrXc (V)
u~-uJ-S ~~-~ ~1(~
sjj) h~ lAo] 0L-0lS J6u sIr
I II ill
~I ~AIT ~
~~ I ~li gtj~ 9 ~
~ fftJ ~ 0~ y I ~li rJ f
-gt[ojL (r ~)~ 4 ~4y jl ~li 0 01~~ I ~ 0 15 -gt)9
-gt[OjL ~ ~ ~ S
[~J (51~ 0fi r fftJ f -gt[ ~j-S
[V] ~~5 ~
JSlJl ~~ y [~J (51~ ~ 1 ~
S ltlil5cI -gt[
-gtI (5[ U Gill Gil Gi 0 i 45 gt45
si1Y- ISj1 (5[ U GIIIC GIIC GIC ~~
IS~0M ~ r n m J )IlOo 0 ~ cI jl ~ y1b
(5[ U ~ y1b ~15 ~ ~~Iojl ~l I
jl -gt~ -gt~ ~ fftJ silY- s)1
~ ([ A] ltIi sl~) 1 0 ~ ~
r-ol~ xl ~ 1S1y ~Io) ~ 0s l ~ xl
r p IS~ o~ ci)l~ )lJl1 ~
(5[ U 1Sy1y 0~ oJ$oL (5~) ~ ~
lJlci)l~ f~1 [J fftJ f IS[ IY- s1
s[ ~ ~I s[r-ol~4 ~ ~ xl
~ [~J (51~ ISjLJlo ~ S f
fftJ f s[ -gt~Jb ~ ~ 4 ~ y1b bulllJJ5 xl si1Y- ISI ~[ U -gtyly Jgt) U-
s~ l r fftJ r-St is 015 []
~ sly Wt- ~~ 9~ 4 0 lS1 ~
OJ == D(I + LlAjDPfl
x (t_1 + Atj - LlAp) 00)
j(LlA) == 0
1(middot ~ql I (~ bull 1 ~ L)I ~ vr- -0-~ 1Sr W sr0M
~i5 ~
LlA~+1 == LlA~ - j() (W)
OLlAj ut
oj oj Ocrj--=--- OA)OLlAj 00j OLlAj 00 I _ == -D(I +LlAraquoPf OLlAj
lt )x [D(I + LlAjDPf1p(t_1
+At j - LlAp) +p]
0) OA) Of) ~I s)~~ ~ ~ x~
~15 ~ s)P lJ ~ jl LlAj)lAo (W)
cS1A~~ J~ cS~Ju~ JtSJ cS1A~1 ~ S~J~
~llt1lI~~ )ti) ~JJ (~ smiddot ltIi -~tt bullS sl5o --lIgtLio LIr r -- W y
S ~4 cI jl d ~ h5 I y
~ ~)IS ~~ g T 4 I) ub ~) (~I Jlgt 0-1 ))
~ ~ j19 9) )) ub 9) (SL tSl~101-0 )l9)
Jraquo 0-1 4 -~ 0-1 bull))JIS (S)Yo ~tsb1 j19
I bull S 11 At L 1 7 ) Gl 1gtlltWraquo (S (S - ~ 4gt IS
I )) 9 tSl~101-0 ~ ~) 01-0 ) ) u-
~11S )Po ))pS ) 0141 )Po tS~~t
- Lual lI laquo - () 1( )(Sj w- u - ) -r v bull shy
~tsb j19 )) (SL ~ iS~~ 4 tSl~l01-o ~4~ (-- - r) jS )) o~ 0)) 01 )b )~
(A)
i~) ~j~lS elL tSlj ~ )yo tS~~~
l c~ middot1 ) 1_ 1 l-gt I )1middotj Ur-- u u )-- Yo ) bull 0 tS ~
-
9) )) ~I) Yo)) I) lA~l ~ij iS~~ )
~) 0~ ~)ji ~ (~ j4) ub ~) 0~ o~ j19
)~ )~ 0-- ))J IS ()~) ub(S)Yo
~rU ~l ~) ~ij iS~~ 01-0 J)lgt1 01~ gN 1
~ ~j~lS ~~ ~)I ~l ~) iSI~ JgtI) o~
01 (f) jS )) ~ (i) jS )) 4-i1 ) j-i
(SL iS ~~ 0l--o J)lgt1 ~ -1 o~ 0)1)
(0)
(B)(C)
()bull
(D)
(E)
(c) J~ 1I)~ J) ~IT~~ ( IJ~~ IT~~ (y) 4Ow- dJ1 ~ (ill) ~ij ampSI~IJ~ JIa)f ~
middothJSt ~ ~ ) IJ~ tl)J (d IA~ ITI~ ()~))) ampSI~IJ~ J))gts jlif
E
o=o o=o
I I j I I ~ ~I I II
g~ltlgTIltg- () OltlgTIltg~ (~) IgTI=O (UJI)
o=o~
II ~~ J Ishy
(J) ()
jltl (0) J~J~ 01raquo00 () ~~J~ 01raquo00 (-l) =1 ~~ (ill) 1Slttll~1o JI08J C) ~
J~I jli JI u~~ () JIJsii
IgTIgtg- IgTI=g~1Ilt
-------4-8r
(~) (UJI)
J~ILi (-l) J~ jli (ill) IILoo ~I$l~~ ~ 1S1lttll~1o ~X~ ~Io ~IJ1 1S1uP ~
u1~ j~l )~ 14~u~ )ti) ~I ( J=bU s~ ~loj Ilf )gt gtjl- s-i )~ Jltgtb
t4~ ~19 olol ~ ~4 jgt ~ )gt gtgtIs ~
1S~4- [ 1 )$oo (Mi) Is sll ~~) Is sll jlsro 4~ tY~ bullgt alP J~
4)1 s1~)0l-o ~ )~ ~) gt ~ ~Irgt sl) J~ J) ~ jl3 sl) 01~
-s ~I gt ~ )gt bull)5 Jb )gt 41 sLAuJo ~jlgtjl jl IS--t LA~) ~ bulls)lb1 sxlt)A
gt=Is ogt) 4W ~41s ISL pS19 ~ 1S~4- sLA)gt)
0 Jl)
$-~ ~ lAl jl s Ib )l I) ~ 1S4d~~ 0illil
g r =1 gr I a r =1 G r 1j5 ~I )l llIll15 ~
-sI1gt -s ~1)4 lAl ~j 1 1S1r middot~4 15
)~ 1sAgt 15 ISJI )l K
_x-a x~a(x-a)shy
o xlta
() ~sLo ~I jllSr0M )l ~ l15 ~j4
$-~~ ~ ~ 1 p~ ~19 $-~~ l 1S1r
middotlpound1 Igt - ~ l (~~L) bullbull ( ) -sir Vr-) IS ) bull s-- ~
Jl ~I ~j 1 - ISI~~I tll)ySj
~I)l ci))tse ISI~~I 1S9) 1Jllao ~ ~4 ) lol jI )~ ~ oM~115 )~
Dc = diag(D(g) LJ(g) LJ(g)]
Sr(K) SN(K) tl~fj ISlA~I)4 ~tU 4
tll)gtSj jlpoundl ~ ISL s- $-~~ ojllil H -r
)~ g ISI~~I
-N S (I()=~ gmax
N 1 -N-N +1( gmax - go
(11)
(11)
D(g) ISL ~19 ~ ~Ir il s Ib
l115 1J rj ~I) jl LJ(g)
(n)
$-~~ ISI~~I IS~ 1 ~I) otIb
l )l sbgt l )~ $-~ ~ l Ib )l jt s-
)~ o~ ci )2i )l tl~fj lS Ollgtlto
j5 ~ lA~~ $-I~
tl~fj Ollgtlto)l lAl1 ~)lil bullll~tU
)~ Ie ~1)4 4 1(=
(rf)
ISlA4Iil- 4 ISI~~I IS~ 1 ~I) o~ ~
~115 1J ri ~I) il s- $-~~
00)
s- $-~~ OlW toi ISlA~I)4 01) ~I) )l
Dc (r0) ~I) )l )2i l) l Ao 4 jt
l tl~fj ~jLo ~ S(K) y1 ~~jLo
middot~415 5r
lA~~ 1 S~I 1Sr~l1~ ISiWoM 1S1r 10
IS~) ~~il ~4 ~ laquo~~~ 1S1bgtgtgt )
bull 1 lL l ci ~ ts -LL LslSo- _ 15 Y) 15 bull V shy
Lo L)JS bull lAo ~ 6- t L bull bull - 1- t$Ir- - y r oJ)
~Ib middot~415 (y - r f) ISlA)l )l ~4-sI
bullli15 o~l ~4 ~Ir ~ rlAo ~I 1Sr)tse
~ jl ~s ~19 s- $-~~ ISIbgt ~ 6J 1S1r
~~)l )~ ~~ l1~ ~)~ ~(gNltO)
bull10 a r aN ~4 ~Ir yG1 4 oM~115
IS~ )br otIb ISIbgt olj ~l 1~ ~ ~I
)~ s- $-~~ )lr ISI~~I
(rv) (rr)
gN~O
gNgtO K~O
gNgtO KgtOSN(K)ltl (iO)
gNgtO
Er K~O
(l-Sr(KraquoEr K gt 0 Sr(K) lt 1 Oy(g) =
K gt 0 Sr(K) ~ 1 (Jr lt a r(l-)ar a-gr KgtO Sr(K)~l (Jr=a (if)
IA-)I ~ ll kl bull ~ IS- bull r ~gt
is)iI)~ ~Ir - ~~ - )~~)I gt Jgt gNltO
~ltgt~gtIS- is-)l0~ S jy 0~ J ~j4 0lt -N-gN ltgmax
~ jI o~ 1~ iSlA-)I J ~j4 gt -NgN -gmax
Jgt)gtS 0~ J ~ jL9 )gt y 0lt -T-gT ltgmax IS-~- (gt gt
J gt)gtS jI ~ ~I jL9 )gt j-iJ gt-TgJ -gma
I J
I 8T
J
1i)J ~Ioo slt40-J sl) () ~ij slt40-J sl) (AlI)~ s~lt40-~) sl~lI~~ dMi ~I)V ~
(0 =jJ(-CFN)) J~ jli)J ~Ioo slt40-J sl) (-) J~
iSlA) ltIS JAJ 0-11 )0 jI)gt JIlIIgtI iS~4
ciy )gt I) ~j~1S iSlA~~ J))gt5 ~ IV II shy
jl bull is)lfjL bull - ~1)j4 0~ ~IAIj) 4j~
yly )) ~ ~41S o~ I~ iS~WI ~) 0~
iSl) is~ is)l) I~ iS~WI 4 ~ ) I~ ~I ) ~ yIb bull) 0-11 )) lIIgtgt1S ~ )4 0-11 -5 )) I~ 0W1 ~ ljoJb SIA-)I jl iSl~gt 4 IA-)I jI
~ iS~WI iSr)S 4 gtgt o~ ci fo It ~OJLIIIAltgt)ImiddotL middotmiddot(Ijl gtgt t~J r-- JY bull u U--) Y IS Igt 1)
(lb)i1S (~I ~ ~)) o~~ iSyJl
)l iSl-)l0~ ISL ~ ~ iSl) Jc)) Ij) jl ~I jL9 )l (if) ~I) jl J ~ jL9
~ )l 1 ~~~ )IS isr is
01)4 ltIS lIIgtgt1S t) ISISa is))))4 ~~l
~ ~Lj (If jl is)~ ~Lj (If s1gt -5
middot~4A~
JJ)gt S~ ~~J ~ ~lJS ~)
~I~--JUIto ~~ is~ ~lSo ~4 ) gt~ ~Ir- )
II sJ4 ) Lltmin ~~ lo~llS ~ ~4 o~ JrS O~ sr Mcr ~Ir ~t) rlS 1~
jl ~t) rlS ytgt ) Llt -)J ~ Y- 4 1
) ~ 1 yi sr min (1tcrMmin)
) -jJ ~4 i s1~4 ~ sl) bull) y-I
L~11 JrS rgt s1 Jt ~tj rlSytgt
IS~)S IS~) ~v (iJ1- toJ
~4 ) I) ~)yJ1 hrJ 01~oJII (Grady) sJ
1 Ali W ~ 1 1 I_~ d ~sts) 1Sr ~ - ~ ) shy
5 4 sl-J ~jrolS II sl ) u~J ISI~
JjJ )~ sl~rb s)lf)4 I ~ ~I s1~J01o
0Li (All - A) ~ ) y-I s)lf)4 -gtlgtJb
)1 )r- r s) IS)) ) 1 ol 01
sr-) syJI 4 TIOOI034-C ~~1-4IJ ~
) ol 01 0Li ~lo sVi-t [OO]lOs JLJl
middotl41S (y- A)~ J~
5 ci)l r~1 -J )~ ) 1 y-I sjLJlo
u-J ~ ~ 010 OmiddotA em ojl)j ~ s1~1
- A ~) )IS 010 jI I) uL 0)Q u ) Y
laquoAll
sur-AI) jl sr-0 - 4 ~Iio sl) uL y-I ~ (wI ~I ~ s~JA ~x 0l1 ) ol ltlJ1)
~ 4JJ )~ jl ~ ytgt u W y-14 )l1S r~1
1IS s~JA 0l1 ol ciJ ~ ) lr--o 0 W1
t I ciL KA bull (All-) 1(-u ))) -- ~ shy
lt) jS ol ISW) )~ 1= + see
5 o)j))) -J ) I)) ~Io 46A 1S~4-- )
) ol ltlJI) ) 4 u llb1S 0Li tj Jk ) ~I ~ lgt sl) I) ~ bA9 u (w] ~I --
1 ~Iio ~li 01 ltlJ1) rblgt ~ 0t) r)p
) sl-J010 )gt5 r-S ssJ1 () jS
sur-A) sr-)~ 4 0 jl ~ jI u llb1S Li
~~ u ~IA bull1 olol ~ ~~ y-I
1S~ts ) s14JJ01o )gt5 ~I~ l1S
)1 ) suy ~ s~rb s) )4 )) ~
JIS
jll~ ~Ir-I ) ~ s1~J0l-o ~)gt5 ~
bulls)~ )IS JgtI j sr-0 - 4 ~ Ir-I -~ ~~ tIla sl) ~4 ~4 jI)~
(V)
1 I TTJCOn TTftXt bull TIflntbull TIflnertia -1 ) lt)) ~) j cu
(A)
rgt ~ Iy-I ) 1 jS ~I sr-)~ 4 s1~J0l-o ss) ssJ1 i)W -4its s~)sJ1
15t jS ~ (fV) ~I ~I) ol )r
Mii + fint = fext + fcon
sur-i )) M rr- ~t1)u JISk~
sur-i )) felU ~t sur-i )) fint ~)
~11S ~)j ~I) jI fcon sl-Jl-o ISW
(fr)
fint = 1BTSan (ff )
fext = 1NTb an + 1NTtar I (10)
) u01 )I- ~ ~bo ~~ ~ 4 4 laquosrgt ~W ~r raquo )gt5 ~
p) y-I ) ~ ~ IS ciJ )~ )I)li ~tj s4-0lS
~r-1 ~) sr-i su)) ~I ) 4 ~ ) sr )) ~ ~tj rlS ) sl-J10
) ~ytgt ~11S~~s fl3 ~~4-- ))
Ojt)j ~)) o~ k~ )~~srgt ~W
s)~~li ~bullbull lgt Ssect )IS )~ ~t) rl3
bullbullbullbull
TA
E 1468 GPa ~ =114GPa
G2 = 6184 GPa G23 = 4380 GPa
v =03 ~ =1730MPa A =1380MPa
1= 665 MPa 1 = 268 MPa
s= 1337 MPa p = 1550 kgm3
~ M
190N
T
~~X
(y) (All)
T3001034-C ~~I-~I ISI~ ~lAo IS~) (~)~u ISI-~ ISJIJJ~ 4IJiA (ill) It ~
a bull-amp----~~g----~a (y) (All)
KiP Reoldon H~lot1 Plo I D bull 1 P 5
bull -1 n t -15 n
-L Z
-25
- -5
-
5
-5 11 u u u 5 u 7 U 1
- I I I
25
lIIS-altlCllr -
~ E -_ I ~ 125 ~_tM
- C -- -
~ bull ~~~ ~E 0bull f4u -
bull ii ~h -125
0 j -
~ -25 25 50_
~ position (em)
~ r-I---
- _ algorINa 0 -4 ~ I---(SOIIXJISOloolJUJfgto6MX
~ r--- -U
TIaa
~ jl OJo1 ~ ~Is~ o~JI)~J) tIJ ui~ 4laii IT-~~ Jb ~io ~
[-]~)A jl4iS~ ~middot-r~middotlsec 1S~loj J) 4iSt ~ ytNu
bull Q
Qbull amp
amp a bull
(y) (All)
bull bull
bull bull bull bull
bull bull
bull bull bull
bull bull abull a ia bullbull a () lt)
45~oi IIgt ~ 4iw 454)~~ IIgtJs ~J 45l11 ~
1=- sec ()t=~ sec (11)= sec ()=++ bullbull sec (All)
( bull IJoZ 1gt11gt ~~ j)~sJ ~ lo ~u ~JsJ ~s j~j 45-Slsj ~ 1A4) r~)
- abull a
bull bull a
( ) (uJl)
1= + sec () t= middot middot0 sec (All) 45~oj)1gt I~ 4i 4514)~~ JI)s ~J 45l1IT ~
( bull loJoZ 1)111gt ~~ I)~ sJ ~ lo ~u ~J sJ 4s j~l 45-Sl s1 41A4) ul~)
f) Ibull JI Ibull bullbullc
bullt bullI
2 -Ut
Ja
ua
-
ua
1
-~Jlitt8lmiddotmiddot1 I I -
Ii lop
1 ~
~ Lfi ~ of
~
) IIgt )) ~j-S iSUb~ ~~) JLgti o~)by
)3) ~I jI o)~ ))gt5 jl ~ ~ ~r
jAl w~ iSl~~wl-o ))gt5 jI ~ Ub~~
)) Ub~~ u-W bull5~ o~ 0)4) ))gtY
t~ I~middot ~ IS )) If 1middot 1 1_~ramp- is~) isr) ) IS )r- r-
-wLS )lJ) ~Iu ()fl iS~ ~) 1$JJt
~l~I JLgti o)jl Ih) j) y (wlo
)LgtI )) 511gt o~ rlS ~I jl I) is)g3)
I$)Y iSly middotw4~ )) IIgt)IS i --b ~~
ul) ~ iSUb)rJb1) iSr)~ 4 ) S1)s ~))
f4W 4S l ul) is)lJ SUb~ )4 ~I )) ol
middotl41S is)~ isUb)rJb1) ~
~I~)li
oSjb ~~ iSl) ~~ jl ~~~
Syen ~Igt ) FfI(lf(V o ek jI d o ~ (~) wr-1J iSjL~yen ~W- Srshy
bull))- IS ~1))gt9 frY -Ii - - -i
) 4i (y
1 wlA JLgti bullJi) is wl~
)4 ~I ~ lA ~ 4 bull )y~1S r~1 ~it wlA 4 is~ i ~r)) iSl~ )4 ol is~)4 issJI
~ ~ )) l wlA 4 iSl~ yo )4 ~ I) )gt
Y )~ ~ ~ ~L W)1i bull ~~ IIgt)IS
~ (H) lt - ) is~ ))IS wl-o jl
140~ 0 5 If L~II cil 1( is u - J I)r-- 1 r- ~
~)IS wli -1- sec -1- - Osec is~Lj )) I)
~ )) wIj -gt y ~l-o ~~~ )b
))gt5 ~I )) 1 0 1 (i)
)4 yj 41 5 ~r )) 0it~ Ub~ jI iSl~~wl-o
)-IS jul isI~ yo
iSjW iSly ISL is)lJ ) )4 ~I )) Jlgt )) laquoiSl-~wl-o ))gt5J ~ o~~ I$)Y
~ts ~Io ~p ~I--o jI iSr0 4 is~4J )) ) ~I l ul) ~~lS d~b I)W
~fJ4 I - de Freitas M Silva A and Reis L (2000) Numerical evaluation of failure mechanisms on composite
specimens subjected to impact loading Composites Part B Engineering Vol 31 PP 199-207
2 - Mohammadi S (2003) Discontinuum Mechanics using Finite and Discrete Elements WITPress- UK
3 - Koh CG Owen D R J and Perie D (1995) Explicit dynamic analysis of elsto-plastic laminated
composite shells implementation of non-iterative stress update schemes for the Hoffinan yield criterion
Computational Mechanics Vol 16 PP 307-314
4 - Schellekens 1 C 1 (1992) Computational strategies for composite structures PhD thesis Technische
Universiteit Delft Holland
5 - Forouzan-sepehr S and Mohammadi S (2001) A contact based method for 3D delamination analysis of
composites subjected to impact loading in S ValliaPPan N Khalili (editors) Computational Mechanicsshy
New Frontiers for the New Millennium Proceedings of 1 Asian-Pactflc Congress on computational
Mechanics- PP 691-696
6 - Mohammadi S Forouzan-sepehr S and Asadollahi A (2002) Contact based delamination and fracture
analysis of composites Thin-Walled Structures Vol 40 No 7-8 PP 595-609
7 - Masters 1 E (1987) Basic failure modes of continuous fiber composites Engineering Materials
Handbook Vol 1 CompOSites ASM International USA
8 - Borovkov A Kiylo 0 Misnik Yu and Tripolnikov T (1999) Finite element stress and analysis of
multidirectional laminated composite structures 2 h-p- refinement and m- adaptive procedures
Zeitschrijiir Angewamte Mathematik undMechamle Vol 79 Suppl No2 PP S527-S528
9 - FEA (2000) LUSAS User Manual Ver 132 FEA Ltd
10 - Liu Sh (1994) Quasi-impact damage initiation and growth of thick-section and toughened composite
materials lnt J Solids andStructures Vol 31 No 22 PP 3079-3098
11 - Mi Y Crisfield M A (1996) Analytical derivation ofloaddisplacement relatiollShip for the DCB and
MMB andproofofthe FEA formulation IC-AERO Report 97-02 Dept Aeronautics Imperial College
London UK
12 - Mi Y Crisfield M A Davies G A O and Hellweg H B (1998) Progressive delamination using
interface elements J Composite Materials Vol 32 No 14 PP 1246-1272
13 - Grady J E Chamis C C and Aiello R A (1989) Dynamic delamination buckling in composite
laminates under impact loading computational simulation In Lagace PA (ed) Composite Materials
Fatigue and Fracture ASTM-STP 1012 PP 137-149
~ )) O)~ ~~ ~~ 0) 1 - Matrix Cracking 2 - Delamination 3 - Fibre Breakage 4 - Fragmentation 5 - Theory ofPlasticity 6 - Computational Contact Mechanics 7 - Solid Element 8 - Discrete Element Method (DEM) 9 - Generalised Hook Law 10 - Transversely Isotropic 11 - Anisotropic 12 - Associated Flow Rule 13 - Normal Gap 14 - Tangential Gap 15 - Penalty 16 - Remeshing 17 - Adapti vity
I II ill
~I ~AIT ~
~~ I ~li gtj~ 9 ~
~ fftJ ~ 0~ y I ~li rJ f
-gt[ojL (r ~)~ 4 ~4y jl ~li 0 01~~ I ~ 0 15 -gt)9
-gt[OjL ~ ~ ~ S
[~J (51~ 0fi r fftJ f -gt[ ~j-S
[V] ~~5 ~
JSlJl ~~ y [~J (51~ ~ 1 ~
S ltlil5cI -gt[
-gtI (5[ U Gill Gil Gi 0 i 45 gt45
si1Y- ISj1 (5[ U GIIIC GIIC GIC ~~
IS~0M ~ r n m J )IlOo 0 ~ cI jl ~ y1b
(5[ U ~ y1b ~15 ~ ~~Iojl ~l I
jl -gt~ -gt~ ~ fftJ silY- s)1
~ ([ A] ltIi sl~) 1 0 ~ ~
r-ol~ xl ~ 1S1y ~Io) ~ 0s l ~ xl
r p IS~ o~ ci)l~ )lJl1 ~
(5[ U 1Sy1y 0~ oJ$oL (5~) ~ ~
lJlci)l~ f~1 [J fftJ f IS[ IY- s1
s[ ~ ~I s[r-ol~4 ~ ~ xl
~ [~J (51~ ISjLJlo ~ S f
fftJ f s[ -gt~Jb ~ ~ 4 ~ y1b bulllJJ5 xl si1Y- ISI ~[ U -gtyly Jgt) U-
s~ l r fftJ r-St is 015 []
~ sly Wt- ~~ 9~ 4 0 lS1 ~
OJ == D(I + LlAjDPfl
x (t_1 + Atj - LlAp) 00)
j(LlA) == 0
1(middot ~ql I (~ bull 1 ~ L)I ~ vr- -0-~ 1Sr W sr0M
~i5 ~
LlA~+1 == LlA~ - j() (W)
OLlAj ut
oj oj Ocrj--=--- OA)OLlAj 00j OLlAj 00 I _ == -D(I +LlAraquoPf OLlAj
lt )x [D(I + LlAjDPf1p(t_1
+At j - LlAp) +p]
0) OA) Of) ~I s)~~ ~ ~ x~
~15 ~ s)P lJ ~ jl LlAj)lAo (W)
cS1A~~ J~ cS~Ju~ JtSJ cS1A~1 ~ S~J~
~llt1lI~~ )ti) ~JJ (~ smiddot ltIi -~tt bullS sl5o --lIgtLio LIr r -- W y
S ~4 cI jl d ~ h5 I y
~ ~)IS ~~ g T 4 I) ub ~) (~I Jlgt 0-1 ))
~ ~ j19 9) )) ub 9) (SL tSl~101-0 )l9)
Jraquo 0-1 4 -~ 0-1 bull))JIS (S)Yo ~tsb1 j19
I bull S 11 At L 1 7 ) Gl 1gtlltWraquo (S (S - ~ 4gt IS
I )) 9 tSl~101-0 ~ ~) 01-0 ) ) u-
~11S )Po ))pS ) 0141 )Po tS~~t
- Lual lI laquo - () 1( )(Sj w- u - ) -r v bull shy
~tsb j19 )) (SL ~ iS~~ 4 tSl~l01-o ~4~ (-- - r) jS )) o~ 0)) 01 )b )~
(A)
i~) ~j~lS elL tSlj ~ )yo tS~~~
l c~ middot1 ) 1_ 1 l-gt I )1middotj Ur-- u u )-- Yo ) bull 0 tS ~
-
9) )) ~I) Yo)) I) lA~l ~ij iS~~ )
~) 0~ ~)ji ~ (~ j4) ub ~) 0~ o~ j19
)~ )~ 0-- ))J IS ()~) ub(S)Yo
~rU ~l ~) ~ij iS~~ 01-0 J)lgt1 01~ gN 1
~ ~j~lS ~~ ~)I ~l ~) iSI~ JgtI) o~
01 (f) jS )) ~ (i) jS )) 4-i1 ) j-i
(SL iS ~~ 0l--o J)lgt1 ~ -1 o~ 0)1)
(0)
(B)(C)
()bull
(D)
(E)
(c) J~ 1I)~ J) ~IT~~ ( IJ~~ IT~~ (y) 4Ow- dJ1 ~ (ill) ~ij ampSI~IJ~ JIa)f ~
middothJSt ~ ~ ) IJ~ tl)J (d IA~ ITI~ ()~))) ampSI~IJ~ J))gts jlif
E
o=o o=o
I I j I I ~ ~I I II
g~ltlgTIltg- () OltlgTIltg~ (~) IgTI=O (UJI)
o=o~
II ~~ J Ishy
(J) ()
jltl (0) J~J~ 01raquo00 () ~~J~ 01raquo00 (-l) =1 ~~ (ill) 1Slttll~1o JI08J C) ~
J~I jli JI u~~ () JIJsii
IgTIgtg- IgTI=g~1Ilt
-------4-8r
(~) (UJI)
J~ILi (-l) J~ jli (ill) IILoo ~I$l~~ ~ 1S1lttll~1o ~X~ ~Io ~IJ1 1S1uP ~
u1~ j~l )~ 14~u~ )ti) ~I ( J=bU s~ ~loj Ilf )gt gtjl- s-i )~ Jltgtb
t4~ ~19 olol ~ ~4 jgt ~ )gt gtgtIs ~
1S~4- [ 1 )$oo (Mi) Is sll ~~) Is sll jlsro 4~ tY~ bullgt alP J~
4)1 s1~)0l-o ~ )~ ~) gt ~ ~Irgt sl) J~ J) ~ jl3 sl) 01~
-s ~I gt ~ )gt bull)5 Jb )gt 41 sLAuJo ~jlgtjl jl IS--t LA~) ~ bulls)lb1 sxlt)A
gt=Is ogt) 4W ~41s ISL pS19 ~ 1S~4- sLA)gt)
0 Jl)
$-~ ~ lAl jl s Ib )l I) ~ 1S4d~~ 0illil
g r =1 gr I a r =1 G r 1j5 ~I )l llIll15 ~
-sI1gt -s ~1)4 lAl ~j 1 1S1r middot~4 15
)~ 1sAgt 15 ISJI )l K
_x-a x~a(x-a)shy
o xlta
() ~sLo ~I jllSr0M )l ~ l15 ~j4
$-~~ ~ ~ 1 p~ ~19 $-~~ l 1S1r
middotlpound1 Igt - ~ l (~~L) bullbull ( ) -sir Vr-) IS ) bull s-- ~
Jl ~I ~j 1 - ISI~~I tll)ySj
~I)l ci))tse ISI~~I 1S9) 1Jllao ~ ~4 ) lol jI )~ ~ oM~115 )~
Dc = diag(D(g) LJ(g) LJ(g)]
Sr(K) SN(K) tl~fj ISlA~I)4 ~tU 4
tll)gtSj jlpoundl ~ ISL s- $-~~ ojllil H -r
)~ g ISI~~I
-N S (I()=~ gmax
N 1 -N-N +1( gmax - go
(11)
(11)
D(g) ISL ~19 ~ ~Ir il s Ib
l115 1J rj ~I) jl LJ(g)
(n)
$-~~ ISI~~I IS~ 1 ~I) otIb
l )l sbgt l )~ $-~ ~ l Ib )l jt s-
)~ o~ ci )2i )l tl~fj lS Ollgtlto
j5 ~ lA~~ $-I~
tl~fj Ollgtlto)l lAl1 ~)lil bullll~tU
)~ Ie ~1)4 4 1(=
(rf)
ISlA4Iil- 4 ISI~~I IS~ 1 ~I) o~ ~
~115 1J ri ~I) il s- $-~~
00)
s- $-~~ OlW toi ISlA~I)4 01) ~I) )l
Dc (r0) ~I) )l )2i l) l Ao 4 jt
l tl~fj ~jLo ~ S(K) y1 ~~jLo
middot~415 5r
lA~~ 1 S~I 1Sr~l1~ ISiWoM 1S1r 10
IS~) ~~il ~4 ~ laquo~~~ 1S1bgtgtgt )
bull 1 lL l ci ~ ts -LL LslSo- _ 15 Y) 15 bull V shy
Lo L)JS bull lAo ~ 6- t L bull bull - 1- t$Ir- - y r oJ)
~Ib middot~415 (y - r f) ISlA)l )l ~4-sI
bullli15 o~l ~4 ~Ir ~ rlAo ~I 1Sr)tse
~ jl ~s ~19 s- $-~~ ISIbgt ~ 6J 1S1r
~~)l )~ ~~ l1~ ~)~ ~(gNltO)
bull10 a r aN ~4 ~Ir yG1 4 oM~115
IS~ )br otIb ISIbgt olj ~l 1~ ~ ~I
)~ s- $-~~ )lr ISI~~I
(rv) (rr)
gN~O
gNgtO K~O
gNgtO KgtOSN(K)ltl (iO)
gNgtO
Er K~O
(l-Sr(KraquoEr K gt 0 Sr(K) lt 1 Oy(g) =
K gt 0 Sr(K) ~ 1 (Jr lt a r(l-)ar a-gr KgtO Sr(K)~l (Jr=a (if)
IA-)I ~ ll kl bull ~ IS- bull r ~gt
is)iI)~ ~Ir - ~~ - )~~)I gt Jgt gNltO
~ltgt~gtIS- is-)l0~ S jy 0~ J ~j4 0lt -N-gN ltgmax
~ jI o~ 1~ iSlA-)I J ~j4 gt -NgN -gmax
Jgt)gtS 0~ J ~ jL9 )gt y 0lt -T-gT ltgmax IS-~- (gt gt
J gt)gtS jI ~ ~I jL9 )gt j-iJ gt-TgJ -gma
I J
I 8T
J
1i)J ~Ioo slt40-J sl) () ~ij slt40-J sl) (AlI)~ s~lt40-~) sl~lI~~ dMi ~I)V ~
(0 =jJ(-CFN)) J~ jli)J ~Ioo slt40-J sl) (-) J~
iSlA) ltIS JAJ 0-11 )0 jI)gt JIlIIgtI iS~4
ciy )gt I) ~j~1S iSlA~~ J))gt5 ~ IV II shy
jl bull is)lfjL bull - ~1)j4 0~ ~IAIj) 4j~
yly )) ~ ~41S o~ I~ iS~WI ~) 0~
iSl) is~ is)l) I~ iS~WI 4 ~ ) I~ ~I ) ~ yIb bull) 0-11 )) lIIgtgt1S ~ )4 0-11 -5 )) I~ 0W1 ~ ljoJb SIA-)I jl iSl~gt 4 IA-)I jI
~ iS~WI iSr)S 4 gtgt o~ ci fo It ~OJLIIIAltgt)ImiddotL middotmiddot(Ijl gtgt t~J r-- JY bull u U--) Y IS Igt 1)
(lb)i1S (~I ~ ~)) o~~ iSyJl
)l iSl-)l0~ ISL ~ ~ iSl) Jc)) Ij) jl ~I jL9 )l (if) ~I) jl J ~ jL9
~ )l 1 ~~~ )IS isr is
01)4 ltIS lIIgtgt1S t) ISISa is))))4 ~~l
~ ~Lj (If jl is)~ ~Lj (If s1gt -5
middot~4A~
JJ)gt S~ ~~J ~ ~lJS ~)
~I~--JUIto ~~ is~ ~lSo ~4 ) gt~ ~Ir- )
II sJ4 ) Lltmin ~~ lo~llS ~ ~4 o~ JrS O~ sr Mcr ~Ir ~t) rlS 1~
jl ~t) rlS ytgt ) Llt -)J ~ Y- 4 1
) ~ 1 yi sr min (1tcrMmin)
) -jJ ~4 i s1~4 ~ sl) bull) y-I
L~11 JrS rgt s1 Jt ~tj rlSytgt
IS~)S IS~) ~v (iJ1- toJ
~4 ) I) ~)yJ1 hrJ 01~oJII (Grady) sJ
1 Ali W ~ 1 1 I_~ d ~sts) 1Sr ~ - ~ ) shy
5 4 sl-J ~jrolS II sl ) u~J ISI~
JjJ )~ sl~rb s)lf)4 I ~ ~I s1~J01o
0Li (All - A) ~ ) y-I s)lf)4 -gtlgtJb
)1 )r- r s) IS)) ) 1 ol 01
sr-) syJI 4 TIOOI034-C ~~1-4IJ ~
) ol 01 0Li ~lo sVi-t [OO]lOs JLJl
middotl41S (y- A)~ J~
5 ci)l r~1 -J )~ ) 1 y-I sjLJlo
u-J ~ ~ 010 OmiddotA em ojl)j ~ s1~1
- A ~) )IS 010 jI I) uL 0)Q u ) Y
laquoAll
sur-AI) jl sr-0 - 4 ~Iio sl) uL y-I ~ (wI ~I ~ s~JA ~x 0l1 ) ol ltlJ1)
~ 4JJ )~ jl ~ ytgt u W y-14 )l1S r~1
1IS s~JA 0l1 ol ciJ ~ ) lr--o 0 W1
t I ciL KA bull (All-) 1(-u ))) -- ~ shy
lt) jS ol ISW) )~ 1= + see
5 o)j))) -J ) I)) ~Io 46A 1S~4-- )
) ol ltlJI) ) 4 u llb1S 0Li tj Jk ) ~I ~ lgt sl) I) ~ bA9 u (w] ~I --
1 ~Iio ~li 01 ltlJ1) rblgt ~ 0t) r)p
) sl-J010 )gt5 r-S ssJ1 () jS
sur-A) sr-)~ 4 0 jl ~ jI u llb1S Li
~~ u ~IA bull1 olol ~ ~~ y-I
1S~ts ) s14JJ01o )gt5 ~I~ l1S
)1 ) suy ~ s~rb s) )4 )) ~
JIS
jll~ ~Ir-I ) ~ s1~J0l-o ~)gt5 ~
bulls)~ )IS JgtI j sr-0 - 4 ~ Ir-I -~ ~~ tIla sl) ~4 ~4 jI)~
(V)
1 I TTJCOn TTftXt bull TIflntbull TIflnertia -1 ) lt)) ~) j cu
(A)
rgt ~ Iy-I ) 1 jS ~I sr-)~ 4 s1~J0l-o ss) ssJ1 i)W -4its s~)sJ1
15t jS ~ (fV) ~I ~I) ol )r
Mii + fint = fext + fcon
sur-i )) M rr- ~t1)u JISk~
sur-i )) felU ~t sur-i )) fint ~)
~11S ~)j ~I) jI fcon sl-Jl-o ISW
(fr)
fint = 1BTSan (ff )
fext = 1NTb an + 1NTtar I (10)
) u01 )I- ~ ~bo ~~ ~ 4 4 laquosrgt ~W ~r raquo )gt5 ~
p) y-I ) ~ ~ IS ciJ )~ )I)li ~tj s4-0lS
~r-1 ~) sr-i su)) ~I ) 4 ~ ) sr )) ~ ~tj rlS ) sl-J10
) ~ytgt ~11S~~s fl3 ~~4-- ))
Ojt)j ~)) o~ k~ )~~srgt ~W
s)~~li ~bullbull lgt Ssect )IS )~ ~t) rl3
bullbullbullbull
TA
E 1468 GPa ~ =114GPa
G2 = 6184 GPa G23 = 4380 GPa
v =03 ~ =1730MPa A =1380MPa
1= 665 MPa 1 = 268 MPa
s= 1337 MPa p = 1550 kgm3
~ M
190N
T
~~X
(y) (All)
T3001034-C ~~I-~I ISI~ ~lAo IS~) (~)~u ISI-~ ISJIJJ~ 4IJiA (ill) It ~
a bull-amp----~~g----~a (y) (All)
KiP Reoldon H~lot1 Plo I D bull 1 P 5
bull -1 n t -15 n
-L Z
-25
- -5
-
5
-5 11 u u u 5 u 7 U 1
- I I I
25
lIIS-altlCllr -
~ E -_ I ~ 125 ~_tM
- C -- -
~ bull ~~~ ~E 0bull f4u -
bull ii ~h -125
0 j -
~ -25 25 50_
~ position (em)
~ r-I---
- _ algorINa 0 -4 ~ I---(SOIIXJISOloolJUJfgto6MX
~ r--- -U
TIaa
~ jl OJo1 ~ ~Is~ o~JI)~J) tIJ ui~ 4laii IT-~~ Jb ~io ~
[-]~)A jl4iS~ ~middot-r~middotlsec 1S~loj J) 4iSt ~ ytNu
bull Q
Qbull amp
amp a bull
(y) (All)
bull bull
bull bull bull bull
bull bull
bull bull bull
bull bull abull a ia bullbull a () lt)
45~oi IIgt ~ 4iw 454)~~ IIgtJs ~J 45l11 ~
1=- sec ()t=~ sec (11)= sec ()=++ bullbull sec (All)
( bull IJoZ 1gt11gt ~~ j)~sJ ~ lo ~u ~JsJ ~s j~j 45-Slsj ~ 1A4) r~)
- abull a
bull bull a
( ) (uJl)
1= + sec () t= middot middot0 sec (All) 45~oj)1gt I~ 4i 4514)~~ JI)s ~J 45l1IT ~
( bull loJoZ 1)111gt ~~ I)~ sJ ~ lo ~u ~J sJ 4s j~l 45-Sl s1 41A4) ul~)
f) Ibull JI Ibull bullbullc
bullt bullI
2 -Ut
Ja
ua
-
ua
1
-~Jlitt8lmiddotmiddot1 I I -
Ii lop
1 ~
~ Lfi ~ of
~
) IIgt )) ~j-S iSUb~ ~~) JLgti o~)by
)3) ~I jI o)~ ))gt5 jl ~ ~ ~r
jAl w~ iSl~~wl-o ))gt5 jI ~ Ub~~
)) Ub~~ u-W bull5~ o~ 0)4) ))gtY
t~ I~middot ~ IS )) If 1middot 1 1_~ramp- is~) isr) ) IS )r- r-
-wLS )lJ) ~Iu ()fl iS~ ~) 1$JJt
~l~I JLgti o)jl Ih) j) y (wlo
)LgtI )) 511gt o~ rlS ~I jl I) is)g3)
I$)Y iSly middotw4~ )) IIgt)IS i --b ~~
ul) ~ iSUb)rJb1) iSr)~ 4 ) S1)s ~))
f4W 4S l ul) is)lJ SUb~ )4 ~I )) ol
middotl41S is)~ isUb)rJb1) ~
~I~)li
oSjb ~~ iSl) ~~ jl ~~~
Syen ~Igt ) FfI(lf(V o ek jI d o ~ (~) wr-1J iSjL~yen ~W- Srshy
bull))- IS ~1))gt9 frY -Ii - - -i
) 4i (y
1 wlA JLgti bullJi) is wl~
)4 ~I ~ lA ~ 4 bull )y~1S r~1 ~it wlA 4 is~ i ~r)) iSl~ )4 ol is~)4 issJI
~ ~ )) l wlA 4 iSl~ yo )4 ~ I) )gt
Y )~ ~ ~ ~L W)1i bull ~~ IIgt)IS
~ (H) lt - ) is~ ))IS wl-o jl
140~ 0 5 If L~II cil 1( is u - J I)r-- 1 r- ~
~)IS wli -1- sec -1- - Osec is~Lj )) I)
~ )) wIj -gt y ~l-o ~~~ )b
))gt5 ~I )) 1 0 1 (i)
)4 yj 41 5 ~r )) 0it~ Ub~ jI iSl~~wl-o
)-IS jul isI~ yo
iSjW iSly ISL is)lJ ) )4 ~I )) Jlgt )) laquoiSl-~wl-o ))gt5J ~ o~~ I$)Y
~ts ~Io ~p ~I--o jI iSr0 4 is~4J )) ) ~I l ul) ~~lS d~b I)W
~fJ4 I - de Freitas M Silva A and Reis L (2000) Numerical evaluation of failure mechanisms on composite
specimens subjected to impact loading Composites Part B Engineering Vol 31 PP 199-207
2 - Mohammadi S (2003) Discontinuum Mechanics using Finite and Discrete Elements WITPress- UK
3 - Koh CG Owen D R J and Perie D (1995) Explicit dynamic analysis of elsto-plastic laminated
composite shells implementation of non-iterative stress update schemes for the Hoffinan yield criterion
Computational Mechanics Vol 16 PP 307-314
4 - Schellekens 1 C 1 (1992) Computational strategies for composite structures PhD thesis Technische
Universiteit Delft Holland
5 - Forouzan-sepehr S and Mohammadi S (2001) A contact based method for 3D delamination analysis of
composites subjected to impact loading in S ValliaPPan N Khalili (editors) Computational Mechanicsshy
New Frontiers for the New Millennium Proceedings of 1 Asian-Pactflc Congress on computational
Mechanics- PP 691-696
6 - Mohammadi S Forouzan-sepehr S and Asadollahi A (2002) Contact based delamination and fracture
analysis of composites Thin-Walled Structures Vol 40 No 7-8 PP 595-609
7 - Masters 1 E (1987) Basic failure modes of continuous fiber composites Engineering Materials
Handbook Vol 1 CompOSites ASM International USA
8 - Borovkov A Kiylo 0 Misnik Yu and Tripolnikov T (1999) Finite element stress and analysis of
multidirectional laminated composite structures 2 h-p- refinement and m- adaptive procedures
Zeitschrijiir Angewamte Mathematik undMechamle Vol 79 Suppl No2 PP S527-S528
9 - FEA (2000) LUSAS User Manual Ver 132 FEA Ltd
10 - Liu Sh (1994) Quasi-impact damage initiation and growth of thick-section and toughened composite
materials lnt J Solids andStructures Vol 31 No 22 PP 3079-3098
11 - Mi Y Crisfield M A (1996) Analytical derivation ofloaddisplacement relatiollShip for the DCB and
MMB andproofofthe FEA formulation IC-AERO Report 97-02 Dept Aeronautics Imperial College
London UK
12 - Mi Y Crisfield M A Davies G A O and Hellweg H B (1998) Progressive delamination using
interface elements J Composite Materials Vol 32 No 14 PP 1246-1272
13 - Grady J E Chamis C C and Aiello R A (1989) Dynamic delamination buckling in composite
laminates under impact loading computational simulation In Lagace PA (ed) Composite Materials
Fatigue and Fracture ASTM-STP 1012 PP 137-149
~ )) O)~ ~~ ~~ 0) 1 - Matrix Cracking 2 - Delamination 3 - Fibre Breakage 4 - Fragmentation 5 - Theory ofPlasticity 6 - Computational Contact Mechanics 7 - Solid Element 8 - Discrete Element Method (DEM) 9 - Generalised Hook Law 10 - Transversely Isotropic 11 - Anisotropic 12 - Associated Flow Rule 13 - Normal Gap 14 - Tangential Gap 15 - Penalty 16 - Remeshing 17 - Adapti vity
~ ~)IS ~~ g T 4 I) ub ~) (~I Jlgt 0-1 ))
~ ~ j19 9) )) ub 9) (SL tSl~101-0 )l9)
Jraquo 0-1 4 -~ 0-1 bull))JIS (S)Yo ~tsb1 j19
I bull S 11 At L 1 7 ) Gl 1gtlltWraquo (S (S - ~ 4gt IS
I )) 9 tSl~101-0 ~ ~) 01-0 ) ) u-
~11S )Po ))pS ) 0141 )Po tS~~t
- Lual lI laquo - () 1( )(Sj w- u - ) -r v bull shy
~tsb j19 )) (SL ~ iS~~ 4 tSl~l01-o ~4~ (-- - r) jS )) o~ 0)) 01 )b )~
(A)
i~) ~j~lS elL tSlj ~ )yo tS~~~
l c~ middot1 ) 1_ 1 l-gt I )1middotj Ur-- u u )-- Yo ) bull 0 tS ~
-
9) )) ~I) Yo)) I) lA~l ~ij iS~~ )
~) 0~ ~)ji ~ (~ j4) ub ~) 0~ o~ j19
)~ )~ 0-- ))J IS ()~) ub(S)Yo
~rU ~l ~) ~ij iS~~ 01-0 J)lgt1 01~ gN 1
~ ~j~lS ~~ ~)I ~l ~) iSI~ JgtI) o~
01 (f) jS )) ~ (i) jS )) 4-i1 ) j-i
(SL iS ~~ 0l--o J)lgt1 ~ -1 o~ 0)1)
(0)
(B)(C)
()bull
(D)
(E)
(c) J~ 1I)~ J) ~IT~~ ( IJ~~ IT~~ (y) 4Ow- dJ1 ~ (ill) ~ij ampSI~IJ~ JIa)f ~
middothJSt ~ ~ ) IJ~ tl)J (d IA~ ITI~ ()~))) ampSI~IJ~ J))gts jlif
E
o=o o=o
I I j I I ~ ~I I II
g~ltlgTIltg- () OltlgTIltg~ (~) IgTI=O (UJI)
o=o~
II ~~ J Ishy
(J) ()
jltl (0) J~J~ 01raquo00 () ~~J~ 01raquo00 (-l) =1 ~~ (ill) 1Slttll~1o JI08J C) ~
J~I jli JI u~~ () JIJsii
IgTIgtg- IgTI=g~1Ilt
-------4-8r
(~) (UJI)
J~ILi (-l) J~ jli (ill) IILoo ~I$l~~ ~ 1S1lttll~1o ~X~ ~Io ~IJ1 1S1uP ~
u1~ j~l )~ 14~u~ )ti) ~I ( J=bU s~ ~loj Ilf )gt gtjl- s-i )~ Jltgtb
t4~ ~19 olol ~ ~4 jgt ~ )gt gtgtIs ~
1S~4- [ 1 )$oo (Mi) Is sll ~~) Is sll jlsro 4~ tY~ bullgt alP J~
4)1 s1~)0l-o ~ )~ ~) gt ~ ~Irgt sl) J~ J) ~ jl3 sl) 01~
-s ~I gt ~ )gt bull)5 Jb )gt 41 sLAuJo ~jlgtjl jl IS--t LA~) ~ bulls)lb1 sxlt)A
gt=Is ogt) 4W ~41s ISL pS19 ~ 1S~4- sLA)gt)
0 Jl)
$-~ ~ lAl jl s Ib )l I) ~ 1S4d~~ 0illil
g r =1 gr I a r =1 G r 1j5 ~I )l llIll15 ~
-sI1gt -s ~1)4 lAl ~j 1 1S1r middot~4 15
)~ 1sAgt 15 ISJI )l K
_x-a x~a(x-a)shy
o xlta
() ~sLo ~I jllSr0M )l ~ l15 ~j4
$-~~ ~ ~ 1 p~ ~19 $-~~ l 1S1r
middotlpound1 Igt - ~ l (~~L) bullbull ( ) -sir Vr-) IS ) bull s-- ~
Jl ~I ~j 1 - ISI~~I tll)ySj
~I)l ci))tse ISI~~I 1S9) 1Jllao ~ ~4 ) lol jI )~ ~ oM~115 )~
Dc = diag(D(g) LJ(g) LJ(g)]
Sr(K) SN(K) tl~fj ISlA~I)4 ~tU 4
tll)gtSj jlpoundl ~ ISL s- $-~~ ojllil H -r
)~ g ISI~~I
-N S (I()=~ gmax
N 1 -N-N +1( gmax - go
(11)
(11)
D(g) ISL ~19 ~ ~Ir il s Ib
l115 1J rj ~I) jl LJ(g)
(n)
$-~~ ISI~~I IS~ 1 ~I) otIb
l )l sbgt l )~ $-~ ~ l Ib )l jt s-
)~ o~ ci )2i )l tl~fj lS Ollgtlto
j5 ~ lA~~ $-I~
tl~fj Ollgtlto)l lAl1 ~)lil bullll~tU
)~ Ie ~1)4 4 1(=
(rf)
ISlA4Iil- 4 ISI~~I IS~ 1 ~I) o~ ~
~115 1J ri ~I) il s- $-~~
00)
s- $-~~ OlW toi ISlA~I)4 01) ~I) )l
Dc (r0) ~I) )l )2i l) l Ao 4 jt
l tl~fj ~jLo ~ S(K) y1 ~~jLo
middot~415 5r
lA~~ 1 S~I 1Sr~l1~ ISiWoM 1S1r 10
IS~) ~~il ~4 ~ laquo~~~ 1S1bgtgtgt )
bull 1 lL l ci ~ ts -LL LslSo- _ 15 Y) 15 bull V shy
Lo L)JS bull lAo ~ 6- t L bull bull - 1- t$Ir- - y r oJ)
~Ib middot~415 (y - r f) ISlA)l )l ~4-sI
bullli15 o~l ~4 ~Ir ~ rlAo ~I 1Sr)tse
~ jl ~s ~19 s- $-~~ ISIbgt ~ 6J 1S1r
~~)l )~ ~~ l1~ ~)~ ~(gNltO)
bull10 a r aN ~4 ~Ir yG1 4 oM~115
IS~ )br otIb ISIbgt olj ~l 1~ ~ ~I
)~ s- $-~~ )lr ISI~~I
(rv) (rr)
gN~O
gNgtO K~O
gNgtO KgtOSN(K)ltl (iO)
gNgtO
Er K~O
(l-Sr(KraquoEr K gt 0 Sr(K) lt 1 Oy(g) =
K gt 0 Sr(K) ~ 1 (Jr lt a r(l-)ar a-gr KgtO Sr(K)~l (Jr=a (if)
IA-)I ~ ll kl bull ~ IS- bull r ~gt
is)iI)~ ~Ir - ~~ - )~~)I gt Jgt gNltO
~ltgt~gtIS- is-)l0~ S jy 0~ J ~j4 0lt -N-gN ltgmax
~ jI o~ 1~ iSlA-)I J ~j4 gt -NgN -gmax
Jgt)gtS 0~ J ~ jL9 )gt y 0lt -T-gT ltgmax IS-~- (gt gt
J gt)gtS jI ~ ~I jL9 )gt j-iJ gt-TgJ -gma
I J
I 8T
J
1i)J ~Ioo slt40-J sl) () ~ij slt40-J sl) (AlI)~ s~lt40-~) sl~lI~~ dMi ~I)V ~
(0 =jJ(-CFN)) J~ jli)J ~Ioo slt40-J sl) (-) J~
iSlA) ltIS JAJ 0-11 )0 jI)gt JIlIIgtI iS~4
ciy )gt I) ~j~1S iSlA~~ J))gt5 ~ IV II shy
jl bull is)lfjL bull - ~1)j4 0~ ~IAIj) 4j~
yly )) ~ ~41S o~ I~ iS~WI ~) 0~
iSl) is~ is)l) I~ iS~WI 4 ~ ) I~ ~I ) ~ yIb bull) 0-11 )) lIIgtgt1S ~ )4 0-11 -5 )) I~ 0W1 ~ ljoJb SIA-)I jl iSl~gt 4 IA-)I jI
~ iS~WI iSr)S 4 gtgt o~ ci fo It ~OJLIIIAltgt)ImiddotL middotmiddot(Ijl gtgt t~J r-- JY bull u U--) Y IS Igt 1)
(lb)i1S (~I ~ ~)) o~~ iSyJl
)l iSl-)l0~ ISL ~ ~ iSl) Jc)) Ij) jl ~I jL9 )l (if) ~I) jl J ~ jL9
~ )l 1 ~~~ )IS isr is
01)4 ltIS lIIgtgt1S t) ISISa is))))4 ~~l
~ ~Lj (If jl is)~ ~Lj (If s1gt -5
middot~4A~
JJ)gt S~ ~~J ~ ~lJS ~)
~I~--JUIto ~~ is~ ~lSo ~4 ) gt~ ~Ir- )
II sJ4 ) Lltmin ~~ lo~llS ~ ~4 o~ JrS O~ sr Mcr ~Ir ~t) rlS 1~
jl ~t) rlS ytgt ) Llt -)J ~ Y- 4 1
) ~ 1 yi sr min (1tcrMmin)
) -jJ ~4 i s1~4 ~ sl) bull) y-I
L~11 JrS rgt s1 Jt ~tj rlSytgt
IS~)S IS~) ~v (iJ1- toJ
~4 ) I) ~)yJ1 hrJ 01~oJII (Grady) sJ
1 Ali W ~ 1 1 I_~ d ~sts) 1Sr ~ - ~ ) shy
5 4 sl-J ~jrolS II sl ) u~J ISI~
JjJ )~ sl~rb s)lf)4 I ~ ~I s1~J01o
0Li (All - A) ~ ) y-I s)lf)4 -gtlgtJb
)1 )r- r s) IS)) ) 1 ol 01
sr-) syJI 4 TIOOI034-C ~~1-4IJ ~
) ol 01 0Li ~lo sVi-t [OO]lOs JLJl
middotl41S (y- A)~ J~
5 ci)l r~1 -J )~ ) 1 y-I sjLJlo
u-J ~ ~ 010 OmiddotA em ojl)j ~ s1~1
- A ~) )IS 010 jI I) uL 0)Q u ) Y
laquoAll
sur-AI) jl sr-0 - 4 ~Iio sl) uL y-I ~ (wI ~I ~ s~JA ~x 0l1 ) ol ltlJ1)
~ 4JJ )~ jl ~ ytgt u W y-14 )l1S r~1
1IS s~JA 0l1 ol ciJ ~ ) lr--o 0 W1
t I ciL KA bull (All-) 1(-u ))) -- ~ shy
lt) jS ol ISW) )~ 1= + see
5 o)j))) -J ) I)) ~Io 46A 1S~4-- )
) ol ltlJI) ) 4 u llb1S 0Li tj Jk ) ~I ~ lgt sl) I) ~ bA9 u (w] ~I --
1 ~Iio ~li 01 ltlJ1) rblgt ~ 0t) r)p
) sl-J010 )gt5 r-S ssJ1 () jS
sur-A) sr-)~ 4 0 jl ~ jI u llb1S Li
~~ u ~IA bull1 olol ~ ~~ y-I
1S~ts ) s14JJ01o )gt5 ~I~ l1S
)1 ) suy ~ s~rb s) )4 )) ~
JIS
jll~ ~Ir-I ) ~ s1~J0l-o ~)gt5 ~
bulls)~ )IS JgtI j sr-0 - 4 ~ Ir-I -~ ~~ tIla sl) ~4 ~4 jI)~
(V)
1 I TTJCOn TTftXt bull TIflntbull TIflnertia -1 ) lt)) ~) j cu
(A)
rgt ~ Iy-I ) 1 jS ~I sr-)~ 4 s1~J0l-o ss) ssJ1 i)W -4its s~)sJ1
15t jS ~ (fV) ~I ~I) ol )r
Mii + fint = fext + fcon
sur-i )) M rr- ~t1)u JISk~
sur-i )) felU ~t sur-i )) fint ~)
~11S ~)j ~I) jI fcon sl-Jl-o ISW
(fr)
fint = 1BTSan (ff )
fext = 1NTb an + 1NTtar I (10)
) u01 )I- ~ ~bo ~~ ~ 4 4 laquosrgt ~W ~r raquo )gt5 ~
p) y-I ) ~ ~ IS ciJ )~ )I)li ~tj s4-0lS
~r-1 ~) sr-i su)) ~I ) 4 ~ ) sr )) ~ ~tj rlS ) sl-J10
) ~ytgt ~11S~~s fl3 ~~4-- ))
Ojt)j ~)) o~ k~ )~~srgt ~W
s)~~li ~bullbull lgt Ssect )IS )~ ~t) rl3
bullbullbullbull
TA
E 1468 GPa ~ =114GPa
G2 = 6184 GPa G23 = 4380 GPa
v =03 ~ =1730MPa A =1380MPa
1= 665 MPa 1 = 268 MPa
s= 1337 MPa p = 1550 kgm3
~ M
190N
T
~~X
(y) (All)
T3001034-C ~~I-~I ISI~ ~lAo IS~) (~)~u ISI-~ ISJIJJ~ 4IJiA (ill) It ~
a bull-amp----~~g----~a (y) (All)
KiP Reoldon H~lot1 Plo I D bull 1 P 5
bull -1 n t -15 n
-L Z
-25
- -5
-
5
-5 11 u u u 5 u 7 U 1
- I I I
25
lIIS-altlCllr -
~ E -_ I ~ 125 ~_tM
- C -- -
~ bull ~~~ ~E 0bull f4u -
bull ii ~h -125
0 j -
~ -25 25 50_
~ position (em)
~ r-I---
- _ algorINa 0 -4 ~ I---(SOIIXJISOloolJUJfgto6MX
~ r--- -U
TIaa
~ jl OJo1 ~ ~Is~ o~JI)~J) tIJ ui~ 4laii IT-~~ Jb ~io ~
[-]~)A jl4iS~ ~middot-r~middotlsec 1S~loj J) 4iSt ~ ytNu
bull Q
Qbull amp
amp a bull
(y) (All)
bull bull
bull bull bull bull
bull bull
bull bull bull
bull bull abull a ia bullbull a () lt)
45~oi IIgt ~ 4iw 454)~~ IIgtJs ~J 45l11 ~
1=- sec ()t=~ sec (11)= sec ()=++ bullbull sec (All)
( bull IJoZ 1gt11gt ~~ j)~sJ ~ lo ~u ~JsJ ~s j~j 45-Slsj ~ 1A4) r~)
- abull a
bull bull a
( ) (uJl)
1= + sec () t= middot middot0 sec (All) 45~oj)1gt I~ 4i 4514)~~ JI)s ~J 45l1IT ~
( bull loJoZ 1)111gt ~~ I)~ sJ ~ lo ~u ~J sJ 4s j~l 45-Sl s1 41A4) ul~)
f) Ibull JI Ibull bullbullc
bullt bullI
2 -Ut
Ja
ua
-
ua
1
-~Jlitt8lmiddotmiddot1 I I -
Ii lop
1 ~
~ Lfi ~ of
~
) IIgt )) ~j-S iSUb~ ~~) JLgti o~)by
)3) ~I jI o)~ ))gt5 jl ~ ~ ~r
jAl w~ iSl~~wl-o ))gt5 jI ~ Ub~~
)) Ub~~ u-W bull5~ o~ 0)4) ))gtY
t~ I~middot ~ IS )) If 1middot 1 1_~ramp- is~) isr) ) IS )r- r-
-wLS )lJ) ~Iu ()fl iS~ ~) 1$JJt
~l~I JLgti o)jl Ih) j) y (wlo
)LgtI )) 511gt o~ rlS ~I jl I) is)g3)
I$)Y iSly middotw4~ )) IIgt)IS i --b ~~
ul) ~ iSUb)rJb1) iSr)~ 4 ) S1)s ~))
f4W 4S l ul) is)lJ SUb~ )4 ~I )) ol
middotl41S is)~ isUb)rJb1) ~
~I~)li
oSjb ~~ iSl) ~~ jl ~~~
Syen ~Igt ) FfI(lf(V o ek jI d o ~ (~) wr-1J iSjL~yen ~W- Srshy
bull))- IS ~1))gt9 frY -Ii - - -i
) 4i (y
1 wlA JLgti bullJi) is wl~
)4 ~I ~ lA ~ 4 bull )y~1S r~1 ~it wlA 4 is~ i ~r)) iSl~ )4 ol is~)4 issJI
~ ~ )) l wlA 4 iSl~ yo )4 ~ I) )gt
Y )~ ~ ~ ~L W)1i bull ~~ IIgt)IS
~ (H) lt - ) is~ ))IS wl-o jl
140~ 0 5 If L~II cil 1( is u - J I)r-- 1 r- ~
~)IS wli -1- sec -1- - Osec is~Lj )) I)
~ )) wIj -gt y ~l-o ~~~ )b
))gt5 ~I )) 1 0 1 (i)
)4 yj 41 5 ~r )) 0it~ Ub~ jI iSl~~wl-o
)-IS jul isI~ yo
iSjW iSly ISL is)lJ ) )4 ~I )) Jlgt )) laquoiSl-~wl-o ))gt5J ~ o~~ I$)Y
~ts ~Io ~p ~I--o jI iSr0 4 is~4J )) ) ~I l ul) ~~lS d~b I)W
~fJ4 I - de Freitas M Silva A and Reis L (2000) Numerical evaluation of failure mechanisms on composite
specimens subjected to impact loading Composites Part B Engineering Vol 31 PP 199-207
2 - Mohammadi S (2003) Discontinuum Mechanics using Finite and Discrete Elements WITPress- UK
3 - Koh CG Owen D R J and Perie D (1995) Explicit dynamic analysis of elsto-plastic laminated
composite shells implementation of non-iterative stress update schemes for the Hoffinan yield criterion
Computational Mechanics Vol 16 PP 307-314
4 - Schellekens 1 C 1 (1992) Computational strategies for composite structures PhD thesis Technische
Universiteit Delft Holland
5 - Forouzan-sepehr S and Mohammadi S (2001) A contact based method for 3D delamination analysis of
composites subjected to impact loading in S ValliaPPan N Khalili (editors) Computational Mechanicsshy
New Frontiers for the New Millennium Proceedings of 1 Asian-Pactflc Congress on computational
Mechanics- PP 691-696
6 - Mohammadi S Forouzan-sepehr S and Asadollahi A (2002) Contact based delamination and fracture
analysis of composites Thin-Walled Structures Vol 40 No 7-8 PP 595-609
7 - Masters 1 E (1987) Basic failure modes of continuous fiber composites Engineering Materials
Handbook Vol 1 CompOSites ASM International USA
8 - Borovkov A Kiylo 0 Misnik Yu and Tripolnikov T (1999) Finite element stress and analysis of
multidirectional laminated composite structures 2 h-p- refinement and m- adaptive procedures
Zeitschrijiir Angewamte Mathematik undMechamle Vol 79 Suppl No2 PP S527-S528
9 - FEA (2000) LUSAS User Manual Ver 132 FEA Ltd
10 - Liu Sh (1994) Quasi-impact damage initiation and growth of thick-section and toughened composite
materials lnt J Solids andStructures Vol 31 No 22 PP 3079-3098
11 - Mi Y Crisfield M A (1996) Analytical derivation ofloaddisplacement relatiollShip for the DCB and
MMB andproofofthe FEA formulation IC-AERO Report 97-02 Dept Aeronautics Imperial College
London UK
12 - Mi Y Crisfield M A Davies G A O and Hellweg H B (1998) Progressive delamination using
interface elements J Composite Materials Vol 32 No 14 PP 1246-1272
13 - Grady J E Chamis C C and Aiello R A (1989) Dynamic delamination buckling in composite
laminates under impact loading computational simulation In Lagace PA (ed) Composite Materials
Fatigue and Fracture ASTM-STP 1012 PP 137-149
~ )) O)~ ~~ ~~ 0) 1 - Matrix Cracking 2 - Delamination 3 - Fibre Breakage 4 - Fragmentation 5 - Theory ofPlasticity 6 - Computational Contact Mechanics 7 - Solid Element 8 - Discrete Element Method (DEM) 9 - Generalised Hook Law 10 - Transversely Isotropic 11 - Anisotropic 12 - Associated Flow Rule 13 - Normal Gap 14 - Tangential Gap 15 - Penalty 16 - Remeshing 17 - Adapti vity
E
o=o o=o
I I j I I ~ ~I I II
g~ltlgTIltg- () OltlgTIltg~ (~) IgTI=O (UJI)
o=o~
II ~~ J Ishy
(J) ()
jltl (0) J~J~ 01raquo00 () ~~J~ 01raquo00 (-l) =1 ~~ (ill) 1Slttll~1o JI08J C) ~
J~I jli JI u~~ () JIJsii
IgTIgtg- IgTI=g~1Ilt
-------4-8r
(~) (UJI)
J~ILi (-l) J~ jli (ill) IILoo ~I$l~~ ~ 1S1lttll~1o ~X~ ~Io ~IJ1 1S1uP ~
u1~ j~l )~ 14~u~ )ti) ~I ( J=bU s~ ~loj Ilf )gt gtjl- s-i )~ Jltgtb
t4~ ~19 olol ~ ~4 jgt ~ )gt gtgtIs ~
1S~4- [ 1 )$oo (Mi) Is sll ~~) Is sll jlsro 4~ tY~ bullgt alP J~
4)1 s1~)0l-o ~ )~ ~) gt ~ ~Irgt sl) J~ J) ~ jl3 sl) 01~
-s ~I gt ~ )gt bull)5 Jb )gt 41 sLAuJo ~jlgtjl jl IS--t LA~) ~ bulls)lb1 sxlt)A
gt=Is ogt) 4W ~41s ISL pS19 ~ 1S~4- sLA)gt)
0 Jl)
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g r =1 gr I a r =1 G r 1j5 ~I )l llIll15 ~
-sI1gt -s ~1)4 lAl ~j 1 1S1r middot~4 15
)~ 1sAgt 15 ISJI )l K
_x-a x~a(x-a)shy
o xlta
() ~sLo ~I jllSr0M )l ~ l15 ~j4
$-~~ ~ ~ 1 p~ ~19 $-~~ l 1S1r
middotlpound1 Igt - ~ l (~~L) bullbull ( ) -sir Vr-) IS ) bull s-- ~
Jl ~I ~j 1 - ISI~~I tll)ySj
~I)l ci))tse ISI~~I 1S9) 1Jllao ~ ~4 ) lol jI )~ ~ oM~115 )~
Dc = diag(D(g) LJ(g) LJ(g)]
Sr(K) SN(K) tl~fj ISlA~I)4 ~tU 4
tll)gtSj jlpoundl ~ ISL s- $-~~ ojllil H -r
)~ g ISI~~I
-N S (I()=~ gmax
N 1 -N-N +1( gmax - go
(11)
(11)
D(g) ISL ~19 ~ ~Ir il s Ib
l115 1J rj ~I) jl LJ(g)
(n)
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l )l sbgt l )~ $-~ ~ l Ib )l jt s-
)~ o~ ci )2i )l tl~fj lS Ollgtlto
j5 ~ lA~~ $-I~
tl~fj Ollgtlto)l lAl1 ~)lil bullll~tU
)~ Ie ~1)4 4 1(=
(rf)
ISlA4Iil- 4 ISI~~I IS~ 1 ~I) o~ ~
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00)
s- $-~~ OlW toi ISlA~I)4 01) ~I) )l
Dc (r0) ~I) )l )2i l) l Ao 4 jt
l tl~fj ~jLo ~ S(K) y1 ~~jLo
middot~415 5r
lA~~ 1 S~I 1Sr~l1~ ISiWoM 1S1r 10
IS~) ~~il ~4 ~ laquo~~~ 1S1bgtgtgt )
bull 1 lL l ci ~ ts -LL LslSo- _ 15 Y) 15 bull V shy
Lo L)JS bull lAo ~ 6- t L bull bull - 1- t$Ir- - y r oJ)
~Ib middot~415 (y - r f) ISlA)l )l ~4-sI
bullli15 o~l ~4 ~Ir ~ rlAo ~I 1Sr)tse
~ jl ~s ~19 s- $-~~ ISIbgt ~ 6J 1S1r
~~)l )~ ~~ l1~ ~)~ ~(gNltO)
bull10 a r aN ~4 ~Ir yG1 4 oM~115
IS~ )br otIb ISIbgt olj ~l 1~ ~ ~I
)~ s- $-~~ )lr ISI~~I
(rv) (rr)
gN~O
gNgtO K~O
gNgtO KgtOSN(K)ltl (iO)
gNgtO
Er K~O
(l-Sr(KraquoEr K gt 0 Sr(K) lt 1 Oy(g) =
K gt 0 Sr(K) ~ 1 (Jr lt a r(l-)ar a-gr KgtO Sr(K)~l (Jr=a (if)
IA-)I ~ ll kl bull ~ IS- bull r ~gt
is)iI)~ ~Ir - ~~ - )~~)I gt Jgt gNltO
~ltgt~gtIS- is-)l0~ S jy 0~ J ~j4 0lt -N-gN ltgmax
~ jI o~ 1~ iSlA-)I J ~j4 gt -NgN -gmax
Jgt)gtS 0~ J ~ jL9 )gt y 0lt -T-gT ltgmax IS-~- (gt gt
J gt)gtS jI ~ ~I jL9 )gt j-iJ gt-TgJ -gma
I J
I 8T
J
1i)J ~Ioo slt40-J sl) () ~ij slt40-J sl) (AlI)~ s~lt40-~) sl~lI~~ dMi ~I)V ~
(0 =jJ(-CFN)) J~ jli)J ~Ioo slt40-J sl) (-) J~
iSlA) ltIS JAJ 0-11 )0 jI)gt JIlIIgtI iS~4
ciy )gt I) ~j~1S iSlA~~ J))gt5 ~ IV II shy
jl bull is)lfjL bull - ~1)j4 0~ ~IAIj) 4j~
yly )) ~ ~41S o~ I~ iS~WI ~) 0~
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~ iS~WI iSr)S 4 gtgt o~ ci fo It ~OJLIIIAltgt)ImiddotL middotmiddot(Ijl gtgt t~J r-- JY bull u U--) Y IS Igt 1)
(lb)i1S (~I ~ ~)) o~~ iSyJl
)l iSl-)l0~ ISL ~ ~ iSl) Jc)) Ij) jl ~I jL9 )l (if) ~I) jl J ~ jL9
~ )l 1 ~~~ )IS isr is
01)4 ltIS lIIgtgt1S t) ISISa is))))4 ~~l
~ ~Lj (If jl is)~ ~Lj (If s1gt -5
middot~4A~
JJ)gt S~ ~~J ~ ~lJS ~)
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II sJ4 ) Lltmin ~~ lo~llS ~ ~4 o~ JrS O~ sr Mcr ~Ir ~t) rlS 1~
jl ~t) rlS ytgt ) Llt -)J ~ Y- 4 1
) ~ 1 yi sr min (1tcrMmin)
) -jJ ~4 i s1~4 ~ sl) bull) y-I
L~11 JrS rgt s1 Jt ~tj rlSytgt
IS~)S IS~) ~v (iJ1- toJ
~4 ) I) ~)yJ1 hrJ 01~oJII (Grady) sJ
1 Ali W ~ 1 1 I_~ d ~sts) 1Sr ~ - ~ ) shy
5 4 sl-J ~jrolS II sl ) u~J ISI~
JjJ )~ sl~rb s)lf)4 I ~ ~I s1~J01o
0Li (All - A) ~ ) y-I s)lf)4 -gtlgtJb
)1 )r- r s) IS)) ) 1 ol 01
sr-) syJI 4 TIOOI034-C ~~1-4IJ ~
) ol 01 0Li ~lo sVi-t [OO]lOs JLJl
middotl41S (y- A)~ J~
5 ci)l r~1 -J )~ ) 1 y-I sjLJlo
u-J ~ ~ 010 OmiddotA em ojl)j ~ s1~1
- A ~) )IS 010 jI I) uL 0)Q u ) Y
laquoAll
sur-AI) jl sr-0 - 4 ~Iio sl) uL y-I ~ (wI ~I ~ s~JA ~x 0l1 ) ol ltlJ1)
~ 4JJ )~ jl ~ ytgt u W y-14 )l1S r~1
1IS s~JA 0l1 ol ciJ ~ ) lr--o 0 W1
t I ciL KA bull (All-) 1(-u ))) -- ~ shy
lt) jS ol ISW) )~ 1= + see
5 o)j))) -J ) I)) ~Io 46A 1S~4-- )
) ol ltlJI) ) 4 u llb1S 0Li tj Jk ) ~I ~ lgt sl) I) ~ bA9 u (w] ~I --
1 ~Iio ~li 01 ltlJ1) rblgt ~ 0t) r)p
) sl-J010 )gt5 r-S ssJ1 () jS
sur-A) sr-)~ 4 0 jl ~ jI u llb1S Li
~~ u ~IA bull1 olol ~ ~~ y-I
1S~ts ) s14JJ01o )gt5 ~I~ l1S
)1 ) suy ~ s~rb s) )4 )) ~
JIS
jll~ ~Ir-I ) ~ s1~J0l-o ~)gt5 ~
bulls)~ )IS JgtI j sr-0 - 4 ~ Ir-I -~ ~~ tIla sl) ~4 ~4 jI)~
(V)
1 I TTJCOn TTftXt bull TIflntbull TIflnertia -1 ) lt)) ~) j cu
(A)
rgt ~ Iy-I ) 1 jS ~I sr-)~ 4 s1~J0l-o ss) ssJ1 i)W -4its s~)sJ1
15t jS ~ (fV) ~I ~I) ol )r
Mii + fint = fext + fcon
sur-i )) M rr- ~t1)u JISk~
sur-i )) felU ~t sur-i )) fint ~)
~11S ~)j ~I) jI fcon sl-Jl-o ISW
(fr)
fint = 1BTSan (ff )
fext = 1NTb an + 1NTtar I (10)
) u01 )I- ~ ~bo ~~ ~ 4 4 laquosrgt ~W ~r raquo )gt5 ~
p) y-I ) ~ ~ IS ciJ )~ )I)li ~tj s4-0lS
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) ~ytgt ~11S~~s fl3 ~~4-- ))
Ojt)j ~)) o~ k~ )~~srgt ~W
s)~~li ~bullbull lgt Ssect )IS )~ ~t) rl3
bullbullbullbull
TA
E 1468 GPa ~ =114GPa
G2 = 6184 GPa G23 = 4380 GPa
v =03 ~ =1730MPa A =1380MPa
1= 665 MPa 1 = 268 MPa
s= 1337 MPa p = 1550 kgm3
~ M
190N
T
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(y) (All)
T3001034-C ~~I-~I ISI~ ~lAo IS~) (~)~u ISI-~ ISJIJJ~ 4IJiA (ill) It ~
a bull-amp----~~g----~a (y) (All)
KiP Reoldon H~lot1 Plo I D bull 1 P 5
bull -1 n t -15 n
-L Z
-25
- -5
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5
-5 11 u u u 5 u 7 U 1
- I I I
25
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[-]~)A jl4iS~ ~middot-r~middotlsec 1S~loj J) 4iSt ~ ytNu
bull Q
Qbull amp
amp a bull
(y) (All)
bull bull
bull bull bull bull
bull bull
bull bull bull
bull bull abull a ia bullbull a () lt)
45~oi IIgt ~ 4iw 454)~~ IIgtJs ~J 45l11 ~
1=- sec ()t=~ sec (11)= sec ()=++ bullbull sec (All)
( bull IJoZ 1gt11gt ~~ j)~sJ ~ lo ~u ~JsJ ~s j~j 45-Slsj ~ 1A4) r~)
- abull a
bull bull a
( ) (uJl)
1= + sec () t= middot middot0 sec (All) 45~oj)1gt I~ 4i 4514)~~ JI)s ~J 45l1IT ~
( bull loJoZ 1)111gt ~~ I)~ sJ ~ lo ~u ~J sJ 4s j~l 45-Sl s1 41A4) ul~)
f) Ibull JI Ibull bullbullc
bullt bullI
2 -Ut
Ja
ua
-
ua
1
-~Jlitt8lmiddotmiddot1 I I -
Ii lop
1 ~
~ Lfi ~ of
~
) IIgt )) ~j-S iSUb~ ~~) JLgti o~)by
)3) ~I jI o)~ ))gt5 jl ~ ~ ~r
jAl w~ iSl~~wl-o ))gt5 jI ~ Ub~~
)) Ub~~ u-W bull5~ o~ 0)4) ))gtY
t~ I~middot ~ IS )) If 1middot 1 1_~ramp- is~) isr) ) IS )r- r-
-wLS )lJ) ~Iu ()fl iS~ ~) 1$JJt
~l~I JLgti o)jl Ih) j) y (wlo
)LgtI )) 511gt o~ rlS ~I jl I) is)g3)
I$)Y iSly middotw4~ )) IIgt)IS i --b ~~
ul) ~ iSUb)rJb1) iSr)~ 4 ) S1)s ~))
f4W 4S l ul) is)lJ SUb~ )4 ~I )) ol
middotl41S is)~ isUb)rJb1) ~
~I~)li
oSjb ~~ iSl) ~~ jl ~~~
Syen ~Igt ) FfI(lf(V o ek jI d o ~ (~) wr-1J iSjL~yen ~W- Srshy
bull))- IS ~1))gt9 frY -Ii - - -i
) 4i (y
1 wlA JLgti bullJi) is wl~
)4 ~I ~ lA ~ 4 bull )y~1S r~1 ~it wlA 4 is~ i ~r)) iSl~ )4 ol is~)4 issJI
~ ~ )) l wlA 4 iSl~ yo )4 ~ I) )gt
Y )~ ~ ~ ~L W)1i bull ~~ IIgt)IS
~ (H) lt - ) is~ ))IS wl-o jl
140~ 0 5 If L~II cil 1( is u - J I)r-- 1 r- ~
~)IS wli -1- sec -1- - Osec is~Lj )) I)
~ )) wIj -gt y ~l-o ~~~ )b
))gt5 ~I )) 1 0 1 (i)
)4 yj 41 5 ~r )) 0it~ Ub~ jI iSl~~wl-o
)-IS jul isI~ yo
iSjW iSly ISL is)lJ ) )4 ~I )) Jlgt )) laquoiSl-~wl-o ))gt5J ~ o~~ I$)Y
~ts ~Io ~p ~I--o jI iSr0 4 is~4J )) ) ~I l ul) ~~lS d~b I)W
~fJ4 I - de Freitas M Silva A and Reis L (2000) Numerical evaluation of failure mechanisms on composite
specimens subjected to impact loading Composites Part B Engineering Vol 31 PP 199-207
2 - Mohammadi S (2003) Discontinuum Mechanics using Finite and Discrete Elements WITPress- UK
3 - Koh CG Owen D R J and Perie D (1995) Explicit dynamic analysis of elsto-plastic laminated
composite shells implementation of non-iterative stress update schemes for the Hoffinan yield criterion
Computational Mechanics Vol 16 PP 307-314
4 - Schellekens 1 C 1 (1992) Computational strategies for composite structures PhD thesis Technische
Universiteit Delft Holland
5 - Forouzan-sepehr S and Mohammadi S (2001) A contact based method for 3D delamination analysis of
composites subjected to impact loading in S ValliaPPan N Khalili (editors) Computational Mechanicsshy
New Frontiers for the New Millennium Proceedings of 1 Asian-Pactflc Congress on computational
Mechanics- PP 691-696
6 - Mohammadi S Forouzan-sepehr S and Asadollahi A (2002) Contact based delamination and fracture
analysis of composites Thin-Walled Structures Vol 40 No 7-8 PP 595-609
7 - Masters 1 E (1987) Basic failure modes of continuous fiber composites Engineering Materials
Handbook Vol 1 CompOSites ASM International USA
8 - Borovkov A Kiylo 0 Misnik Yu and Tripolnikov T (1999) Finite element stress and analysis of
multidirectional laminated composite structures 2 h-p- refinement and m- adaptive procedures
Zeitschrijiir Angewamte Mathematik undMechamle Vol 79 Suppl No2 PP S527-S528
9 - FEA (2000) LUSAS User Manual Ver 132 FEA Ltd
10 - Liu Sh (1994) Quasi-impact damage initiation and growth of thick-section and toughened composite
materials lnt J Solids andStructures Vol 31 No 22 PP 3079-3098
11 - Mi Y Crisfield M A (1996) Analytical derivation ofloaddisplacement relatiollShip for the DCB and
MMB andproofofthe FEA formulation IC-AERO Report 97-02 Dept Aeronautics Imperial College
London UK
12 - Mi Y Crisfield M A Davies G A O and Hellweg H B (1998) Progressive delamination using
interface elements J Composite Materials Vol 32 No 14 PP 1246-1272
13 - Grady J E Chamis C C and Aiello R A (1989) Dynamic delamination buckling in composite
laminates under impact loading computational simulation In Lagace PA (ed) Composite Materials
Fatigue and Fracture ASTM-STP 1012 PP 137-149
~ )) O)~ ~~ ~~ 0) 1 - Matrix Cracking 2 - Delamination 3 - Fibre Breakage 4 - Fragmentation 5 - Theory ofPlasticity 6 - Computational Contact Mechanics 7 - Solid Element 8 - Discrete Element Method (DEM) 9 - Generalised Hook Law 10 - Transversely Isotropic 11 - Anisotropic 12 - Associated Flow Rule 13 - Normal Gap 14 - Tangential Gap 15 - Penalty 16 - Remeshing 17 - Adapti vity
$-~ ~ lAl jl s Ib )l I) ~ 1S4d~~ 0illil
g r =1 gr I a r =1 G r 1j5 ~I )l llIll15 ~
-sI1gt -s ~1)4 lAl ~j 1 1S1r middot~4 15
)~ 1sAgt 15 ISJI )l K
_x-a x~a(x-a)shy
o xlta
() ~sLo ~I jllSr0M )l ~ l15 ~j4
$-~~ ~ ~ 1 p~ ~19 $-~~ l 1S1r
middotlpound1 Igt - ~ l (~~L) bullbull ( ) -sir Vr-) IS ) bull s-- ~
Jl ~I ~j 1 - ISI~~I tll)ySj
~I)l ci))tse ISI~~I 1S9) 1Jllao ~ ~4 ) lol jI )~ ~ oM~115 )~
Dc = diag(D(g) LJ(g) LJ(g)]
Sr(K) SN(K) tl~fj ISlA~I)4 ~tU 4
tll)gtSj jlpoundl ~ ISL s- $-~~ ojllil H -r
)~ g ISI~~I
-N S (I()=~ gmax
N 1 -N-N +1( gmax - go
(11)
(11)
D(g) ISL ~19 ~ ~Ir il s Ib
l115 1J rj ~I) jl LJ(g)
(n)
$-~~ ISI~~I IS~ 1 ~I) otIb
l )l sbgt l )~ $-~ ~ l Ib )l jt s-
)~ o~ ci )2i )l tl~fj lS Ollgtlto
j5 ~ lA~~ $-I~
tl~fj Ollgtlto)l lAl1 ~)lil bullll~tU
)~ Ie ~1)4 4 1(=
(rf)
ISlA4Iil- 4 ISI~~I IS~ 1 ~I) o~ ~
~115 1J ri ~I) il s- $-~~
00)
s- $-~~ OlW toi ISlA~I)4 01) ~I) )l
Dc (r0) ~I) )l )2i l) l Ao 4 jt
l tl~fj ~jLo ~ S(K) y1 ~~jLo
middot~415 5r
lA~~ 1 S~I 1Sr~l1~ ISiWoM 1S1r 10
IS~) ~~il ~4 ~ laquo~~~ 1S1bgtgtgt )
bull 1 lL l ci ~ ts -LL LslSo- _ 15 Y) 15 bull V shy
Lo L)JS bull lAo ~ 6- t L bull bull - 1- t$Ir- - y r oJ)
~Ib middot~415 (y - r f) ISlA)l )l ~4-sI
bullli15 o~l ~4 ~Ir ~ rlAo ~I 1Sr)tse
~ jl ~s ~19 s- $-~~ ISIbgt ~ 6J 1S1r
~~)l )~ ~~ l1~ ~)~ ~(gNltO)
bull10 a r aN ~4 ~Ir yG1 4 oM~115
IS~ )br otIb ISIbgt olj ~l 1~ ~ ~I
)~ s- $-~~ )lr ISI~~I
(rv) (rr)
gN~O
gNgtO K~O
gNgtO KgtOSN(K)ltl (iO)
gNgtO
Er K~O
(l-Sr(KraquoEr K gt 0 Sr(K) lt 1 Oy(g) =
K gt 0 Sr(K) ~ 1 (Jr lt a r(l-)ar a-gr KgtO Sr(K)~l (Jr=a (if)
IA-)I ~ ll kl bull ~ IS- bull r ~gt
is)iI)~ ~Ir - ~~ - )~~)I gt Jgt gNltO
~ltgt~gtIS- is-)l0~ S jy 0~ J ~j4 0lt -N-gN ltgmax
~ jI o~ 1~ iSlA-)I J ~j4 gt -NgN -gmax
Jgt)gtS 0~ J ~ jL9 )gt y 0lt -T-gT ltgmax IS-~- (gt gt
J gt)gtS jI ~ ~I jL9 )gt j-iJ gt-TgJ -gma
I J
I 8T
J
1i)J ~Ioo slt40-J sl) () ~ij slt40-J sl) (AlI)~ s~lt40-~) sl~lI~~ dMi ~I)V ~
(0 =jJ(-CFN)) J~ jli)J ~Ioo slt40-J sl) (-) J~
iSlA) ltIS JAJ 0-11 )0 jI)gt JIlIIgtI iS~4
ciy )gt I) ~j~1S iSlA~~ J))gt5 ~ IV II shy
jl bull is)lfjL bull - ~1)j4 0~ ~IAIj) 4j~
yly )) ~ ~41S o~ I~ iS~WI ~) 0~
iSl) is~ is)l) I~ iS~WI 4 ~ ) I~ ~I ) ~ yIb bull) 0-11 )) lIIgtgt1S ~ )4 0-11 -5 )) I~ 0W1 ~ ljoJb SIA-)I jl iSl~gt 4 IA-)I jI
~ iS~WI iSr)S 4 gtgt o~ ci fo It ~OJLIIIAltgt)ImiddotL middotmiddot(Ijl gtgt t~J r-- JY bull u U--) Y IS Igt 1)
(lb)i1S (~I ~ ~)) o~~ iSyJl
)l iSl-)l0~ ISL ~ ~ iSl) Jc)) Ij) jl ~I jL9 )l (if) ~I) jl J ~ jL9
~ )l 1 ~~~ )IS isr is
01)4 ltIS lIIgtgt1S t) ISISa is))))4 ~~l
~ ~Lj (If jl is)~ ~Lj (If s1gt -5
middot~4A~
JJ)gt S~ ~~J ~ ~lJS ~)
~I~--JUIto ~~ is~ ~lSo ~4 ) gt~ ~Ir- )
II sJ4 ) Lltmin ~~ lo~llS ~ ~4 o~ JrS O~ sr Mcr ~Ir ~t) rlS 1~
jl ~t) rlS ytgt ) Llt -)J ~ Y- 4 1
) ~ 1 yi sr min (1tcrMmin)
) -jJ ~4 i s1~4 ~ sl) bull) y-I
L~11 JrS rgt s1 Jt ~tj rlSytgt
IS~)S IS~) ~v (iJ1- toJ
~4 ) I) ~)yJ1 hrJ 01~oJII (Grady) sJ
1 Ali W ~ 1 1 I_~ d ~sts) 1Sr ~ - ~ ) shy
5 4 sl-J ~jrolS II sl ) u~J ISI~
JjJ )~ sl~rb s)lf)4 I ~ ~I s1~J01o
0Li (All - A) ~ ) y-I s)lf)4 -gtlgtJb
)1 )r- r s) IS)) ) 1 ol 01
sr-) syJI 4 TIOOI034-C ~~1-4IJ ~
) ol 01 0Li ~lo sVi-t [OO]lOs JLJl
middotl41S (y- A)~ J~
5 ci)l r~1 -J )~ ) 1 y-I sjLJlo
u-J ~ ~ 010 OmiddotA em ojl)j ~ s1~1
- A ~) )IS 010 jI I) uL 0)Q u ) Y
laquoAll
sur-AI) jl sr-0 - 4 ~Iio sl) uL y-I ~ (wI ~I ~ s~JA ~x 0l1 ) ol ltlJ1)
~ 4JJ )~ jl ~ ytgt u W y-14 )l1S r~1
1IS s~JA 0l1 ol ciJ ~ ) lr--o 0 W1
t I ciL KA bull (All-) 1(-u ))) -- ~ shy
lt) jS ol ISW) )~ 1= + see
5 o)j))) -J ) I)) ~Io 46A 1S~4-- )
) ol ltlJI) ) 4 u llb1S 0Li tj Jk ) ~I ~ lgt sl) I) ~ bA9 u (w] ~I --
1 ~Iio ~li 01 ltlJ1) rblgt ~ 0t) r)p
) sl-J010 )gt5 r-S ssJ1 () jS
sur-A) sr-)~ 4 0 jl ~ jI u llb1S Li
~~ u ~IA bull1 olol ~ ~~ y-I
1S~ts ) s14JJ01o )gt5 ~I~ l1S
)1 ) suy ~ s~rb s) )4 )) ~
JIS
jll~ ~Ir-I ) ~ s1~J0l-o ~)gt5 ~
bulls)~ )IS JgtI j sr-0 - 4 ~ Ir-I -~ ~~ tIla sl) ~4 ~4 jI)~
(V)
1 I TTJCOn TTftXt bull TIflntbull TIflnertia -1 ) lt)) ~) j cu
(A)
rgt ~ Iy-I ) 1 jS ~I sr-)~ 4 s1~J0l-o ss) ssJ1 i)W -4its s~)sJ1
15t jS ~ (fV) ~I ~I) ol )r
Mii + fint = fext + fcon
sur-i )) M rr- ~t1)u JISk~
sur-i )) felU ~t sur-i )) fint ~)
~11S ~)j ~I) jI fcon sl-Jl-o ISW
(fr)
fint = 1BTSan (ff )
fext = 1NTb an + 1NTtar I (10)
) u01 )I- ~ ~bo ~~ ~ 4 4 laquosrgt ~W ~r raquo )gt5 ~
p) y-I ) ~ ~ IS ciJ )~ )I)li ~tj s4-0lS
~r-1 ~) sr-i su)) ~I ) 4 ~ ) sr )) ~ ~tj rlS ) sl-J10
) ~ytgt ~11S~~s fl3 ~~4-- ))
Ojt)j ~)) o~ k~ )~~srgt ~W
s)~~li ~bullbull lgt Ssect )IS )~ ~t) rl3
bullbullbullbull
TA
E 1468 GPa ~ =114GPa
G2 = 6184 GPa G23 = 4380 GPa
v =03 ~ =1730MPa A =1380MPa
1= 665 MPa 1 = 268 MPa
s= 1337 MPa p = 1550 kgm3
~ M
190N
T
~~X
(y) (All)
T3001034-C ~~I-~I ISI~ ~lAo IS~) (~)~u ISI-~ ISJIJJ~ 4IJiA (ill) It ~
a bull-amp----~~g----~a (y) (All)
KiP Reoldon H~lot1 Plo I D bull 1 P 5
bull -1 n t -15 n
-L Z
-25
- -5
-
5
-5 11 u u u 5 u 7 U 1
- I I I
25
lIIS-altlCllr -
~ E -_ I ~ 125 ~_tM
- C -- -
~ bull ~~~ ~E 0bull f4u -
bull ii ~h -125
0 j -
~ -25 25 50_
~ position (em)
~ r-I---
- _ algorINa 0 -4 ~ I---(SOIIXJISOloolJUJfgto6MX
~ r--- -U
TIaa
~ jl OJo1 ~ ~Is~ o~JI)~J) tIJ ui~ 4laii IT-~~ Jb ~io ~
[-]~)A jl4iS~ ~middot-r~middotlsec 1S~loj J) 4iSt ~ ytNu
bull Q
Qbull amp
amp a bull
(y) (All)
bull bull
bull bull bull bull
bull bull
bull bull bull
bull bull abull a ia bullbull a () lt)
45~oi IIgt ~ 4iw 454)~~ IIgtJs ~J 45l11 ~
1=- sec ()t=~ sec (11)= sec ()=++ bullbull sec (All)
( bull IJoZ 1gt11gt ~~ j)~sJ ~ lo ~u ~JsJ ~s j~j 45-Slsj ~ 1A4) r~)
- abull a
bull bull a
( ) (uJl)
1= + sec () t= middot middot0 sec (All) 45~oj)1gt I~ 4i 4514)~~ JI)s ~J 45l1IT ~
( bull loJoZ 1)111gt ~~ I)~ sJ ~ lo ~u ~J sJ 4s j~l 45-Sl s1 41A4) ul~)
f) Ibull JI Ibull bullbullc
bullt bullI
2 -Ut
Ja
ua
-
ua
1
-~Jlitt8lmiddotmiddot1 I I -
Ii lop
1 ~
~ Lfi ~ of
~
) IIgt )) ~j-S iSUb~ ~~) JLgti o~)by
)3) ~I jI o)~ ))gt5 jl ~ ~ ~r
jAl w~ iSl~~wl-o ))gt5 jI ~ Ub~~
)) Ub~~ u-W bull5~ o~ 0)4) ))gtY
t~ I~middot ~ IS )) If 1middot 1 1_~ramp- is~) isr) ) IS )r- r-
-wLS )lJ) ~Iu ()fl iS~ ~) 1$JJt
~l~I JLgti o)jl Ih) j) y (wlo
)LgtI )) 511gt o~ rlS ~I jl I) is)g3)
I$)Y iSly middotw4~ )) IIgt)IS i --b ~~
ul) ~ iSUb)rJb1) iSr)~ 4 ) S1)s ~))
f4W 4S l ul) is)lJ SUb~ )4 ~I )) ol
middotl41S is)~ isUb)rJb1) ~
~I~)li
oSjb ~~ iSl) ~~ jl ~~~
Syen ~Igt ) FfI(lf(V o ek jI d o ~ (~) wr-1J iSjL~yen ~W- Srshy
bull))- IS ~1))gt9 frY -Ii - - -i
) 4i (y
1 wlA JLgti bullJi) is wl~
)4 ~I ~ lA ~ 4 bull )y~1S r~1 ~it wlA 4 is~ i ~r)) iSl~ )4 ol is~)4 issJI
~ ~ )) l wlA 4 iSl~ yo )4 ~ I) )gt
Y )~ ~ ~ ~L W)1i bull ~~ IIgt)IS
~ (H) lt - ) is~ ))IS wl-o jl
140~ 0 5 If L~II cil 1( is u - J I)r-- 1 r- ~
~)IS wli -1- sec -1- - Osec is~Lj )) I)
~ )) wIj -gt y ~l-o ~~~ )b
))gt5 ~I )) 1 0 1 (i)
)4 yj 41 5 ~r )) 0it~ Ub~ jI iSl~~wl-o
)-IS jul isI~ yo
iSjW iSly ISL is)lJ ) )4 ~I )) Jlgt )) laquoiSl-~wl-o ))gt5J ~ o~~ I$)Y
~ts ~Io ~p ~I--o jI iSr0 4 is~4J )) ) ~I l ul) ~~lS d~b I)W
~fJ4 I - de Freitas M Silva A and Reis L (2000) Numerical evaluation of failure mechanisms on composite
specimens subjected to impact loading Composites Part B Engineering Vol 31 PP 199-207
2 - Mohammadi S (2003) Discontinuum Mechanics using Finite and Discrete Elements WITPress- UK
3 - Koh CG Owen D R J and Perie D (1995) Explicit dynamic analysis of elsto-plastic laminated
composite shells implementation of non-iterative stress update schemes for the Hoffinan yield criterion
Computational Mechanics Vol 16 PP 307-314
4 - Schellekens 1 C 1 (1992) Computational strategies for composite structures PhD thesis Technische
Universiteit Delft Holland
5 - Forouzan-sepehr S and Mohammadi S (2001) A contact based method for 3D delamination analysis of
composites subjected to impact loading in S ValliaPPan N Khalili (editors) Computational Mechanicsshy
New Frontiers for the New Millennium Proceedings of 1 Asian-Pactflc Congress on computational
Mechanics- PP 691-696
6 - Mohammadi S Forouzan-sepehr S and Asadollahi A (2002) Contact based delamination and fracture
analysis of composites Thin-Walled Structures Vol 40 No 7-8 PP 595-609
7 - Masters 1 E (1987) Basic failure modes of continuous fiber composites Engineering Materials
Handbook Vol 1 CompOSites ASM International USA
8 - Borovkov A Kiylo 0 Misnik Yu and Tripolnikov T (1999) Finite element stress and analysis of
multidirectional laminated composite structures 2 h-p- refinement and m- adaptive procedures
Zeitschrijiir Angewamte Mathematik undMechamle Vol 79 Suppl No2 PP S527-S528
9 - FEA (2000) LUSAS User Manual Ver 132 FEA Ltd
10 - Liu Sh (1994) Quasi-impact damage initiation and growth of thick-section and toughened composite
materials lnt J Solids andStructures Vol 31 No 22 PP 3079-3098
11 - Mi Y Crisfield M A (1996) Analytical derivation ofloaddisplacement relatiollShip for the DCB and
MMB andproofofthe FEA formulation IC-AERO Report 97-02 Dept Aeronautics Imperial College
London UK
12 - Mi Y Crisfield M A Davies G A O and Hellweg H B (1998) Progressive delamination using
interface elements J Composite Materials Vol 32 No 14 PP 1246-1272
13 - Grady J E Chamis C C and Aiello R A (1989) Dynamic delamination buckling in composite
laminates under impact loading computational simulation In Lagace PA (ed) Composite Materials
Fatigue and Fracture ASTM-STP 1012 PP 137-149
~ )) O)~ ~~ ~~ 0) 1 - Matrix Cracking 2 - Delamination 3 - Fibre Breakage 4 - Fragmentation 5 - Theory ofPlasticity 6 - Computational Contact Mechanics 7 - Solid Element 8 - Discrete Element Method (DEM) 9 - Generalised Hook Law 10 - Transversely Isotropic 11 - Anisotropic 12 - Associated Flow Rule 13 - Normal Gap 14 - Tangential Gap 15 - Penalty 16 - Remeshing 17 - Adapti vity
gN~O
gNgtO K~O
gNgtO KgtOSN(K)ltl (iO)
gNgtO
Er K~O
(l-Sr(KraquoEr K gt 0 Sr(K) lt 1 Oy(g) =
K gt 0 Sr(K) ~ 1 (Jr lt a r(l-)ar a-gr KgtO Sr(K)~l (Jr=a (if)
IA-)I ~ ll kl bull ~ IS- bull r ~gt
is)iI)~ ~Ir - ~~ - )~~)I gt Jgt gNltO
~ltgt~gtIS- is-)l0~ S jy 0~ J ~j4 0lt -N-gN ltgmax
~ jI o~ 1~ iSlA-)I J ~j4 gt -NgN -gmax
Jgt)gtS 0~ J ~ jL9 )gt y 0lt -T-gT ltgmax IS-~- (gt gt
J gt)gtS jI ~ ~I jL9 )gt j-iJ gt-TgJ -gma
I J
I 8T
J
1i)J ~Ioo slt40-J sl) () ~ij slt40-J sl) (AlI)~ s~lt40-~) sl~lI~~ dMi ~I)V ~
(0 =jJ(-CFN)) J~ jli)J ~Ioo slt40-J sl) (-) J~
iSlA) ltIS JAJ 0-11 )0 jI)gt JIlIIgtI iS~4
ciy )gt I) ~j~1S iSlA~~ J))gt5 ~ IV II shy
jl bull is)lfjL bull - ~1)j4 0~ ~IAIj) 4j~
yly )) ~ ~41S o~ I~ iS~WI ~) 0~
iSl) is~ is)l) I~ iS~WI 4 ~ ) I~ ~I ) ~ yIb bull) 0-11 )) lIIgtgt1S ~ )4 0-11 -5 )) I~ 0W1 ~ ljoJb SIA-)I jl iSl~gt 4 IA-)I jI
~ iS~WI iSr)S 4 gtgt o~ ci fo It ~OJLIIIAltgt)ImiddotL middotmiddot(Ijl gtgt t~J r-- JY bull u U--) Y IS Igt 1)
(lb)i1S (~I ~ ~)) o~~ iSyJl
)l iSl-)l0~ ISL ~ ~ iSl) Jc)) Ij) jl ~I jL9 )l (if) ~I) jl J ~ jL9
~ )l 1 ~~~ )IS isr is
01)4 ltIS lIIgtgt1S t) ISISa is))))4 ~~l
~ ~Lj (If jl is)~ ~Lj (If s1gt -5
middot~4A~
JJ)gt S~ ~~J ~ ~lJS ~)
~I~--JUIto ~~ is~ ~lSo ~4 ) gt~ ~Ir- )
II sJ4 ) Lltmin ~~ lo~llS ~ ~4 o~ JrS O~ sr Mcr ~Ir ~t) rlS 1~
jl ~t) rlS ytgt ) Llt -)J ~ Y- 4 1
) ~ 1 yi sr min (1tcrMmin)
) -jJ ~4 i s1~4 ~ sl) bull) y-I
L~11 JrS rgt s1 Jt ~tj rlSytgt
IS~)S IS~) ~v (iJ1- toJ
~4 ) I) ~)yJ1 hrJ 01~oJII (Grady) sJ
1 Ali W ~ 1 1 I_~ d ~sts) 1Sr ~ - ~ ) shy
5 4 sl-J ~jrolS II sl ) u~J ISI~
JjJ )~ sl~rb s)lf)4 I ~ ~I s1~J01o
0Li (All - A) ~ ) y-I s)lf)4 -gtlgtJb
)1 )r- r s) IS)) ) 1 ol 01
sr-) syJI 4 TIOOI034-C ~~1-4IJ ~
) ol 01 0Li ~lo sVi-t [OO]lOs JLJl
middotl41S (y- A)~ J~
5 ci)l r~1 -J )~ ) 1 y-I sjLJlo
u-J ~ ~ 010 OmiddotA em ojl)j ~ s1~1
- A ~) )IS 010 jI I) uL 0)Q u ) Y
laquoAll
sur-AI) jl sr-0 - 4 ~Iio sl) uL y-I ~ (wI ~I ~ s~JA ~x 0l1 ) ol ltlJ1)
~ 4JJ )~ jl ~ ytgt u W y-14 )l1S r~1
1IS s~JA 0l1 ol ciJ ~ ) lr--o 0 W1
t I ciL KA bull (All-) 1(-u ))) -- ~ shy
lt) jS ol ISW) )~ 1= + see
5 o)j))) -J ) I)) ~Io 46A 1S~4-- )
) ol ltlJI) ) 4 u llb1S 0Li tj Jk ) ~I ~ lgt sl) I) ~ bA9 u (w] ~I --
1 ~Iio ~li 01 ltlJ1) rblgt ~ 0t) r)p
) sl-J010 )gt5 r-S ssJ1 () jS
sur-A) sr-)~ 4 0 jl ~ jI u llb1S Li
~~ u ~IA bull1 olol ~ ~~ y-I
1S~ts ) s14JJ01o )gt5 ~I~ l1S
)1 ) suy ~ s~rb s) )4 )) ~
JIS
jll~ ~Ir-I ) ~ s1~J0l-o ~)gt5 ~
bulls)~ )IS JgtI j sr-0 - 4 ~ Ir-I -~ ~~ tIla sl) ~4 ~4 jI)~
(V)
1 I TTJCOn TTftXt bull TIflntbull TIflnertia -1 ) lt)) ~) j cu
(A)
rgt ~ Iy-I ) 1 jS ~I sr-)~ 4 s1~J0l-o ss) ssJ1 i)W -4its s~)sJ1
15t jS ~ (fV) ~I ~I) ol )r
Mii + fint = fext + fcon
sur-i )) M rr- ~t1)u JISk~
sur-i )) felU ~t sur-i )) fint ~)
~11S ~)j ~I) jI fcon sl-Jl-o ISW
(fr)
fint = 1BTSan (ff )
fext = 1NTb an + 1NTtar I (10)
) u01 )I- ~ ~bo ~~ ~ 4 4 laquosrgt ~W ~r raquo )gt5 ~
p) y-I ) ~ ~ IS ciJ )~ )I)li ~tj s4-0lS
~r-1 ~) sr-i su)) ~I ) 4 ~ ) sr )) ~ ~tj rlS ) sl-J10
) ~ytgt ~11S~~s fl3 ~~4-- ))
Ojt)j ~)) o~ k~ )~~srgt ~W
s)~~li ~bullbull lgt Ssect )IS )~ ~t) rl3
bullbullbullbull
TA
E 1468 GPa ~ =114GPa
G2 = 6184 GPa G23 = 4380 GPa
v =03 ~ =1730MPa A =1380MPa
1= 665 MPa 1 = 268 MPa
s= 1337 MPa p = 1550 kgm3
~ M
190N
T
~~X
(y) (All)
T3001034-C ~~I-~I ISI~ ~lAo IS~) (~)~u ISI-~ ISJIJJ~ 4IJiA (ill) It ~
a bull-amp----~~g----~a (y) (All)
KiP Reoldon H~lot1 Plo I D bull 1 P 5
bull -1 n t -15 n
-L Z
-25
- -5
-
5
-5 11 u u u 5 u 7 U 1
- I I I
25
lIIS-altlCllr -
~ E -_ I ~ 125 ~_tM
- C -- -
~ bull ~~~ ~E 0bull f4u -
bull ii ~h -125
0 j -
~ -25 25 50_
~ position (em)
~ r-I---
- _ algorINa 0 -4 ~ I---(SOIIXJISOloolJUJfgto6MX
~ r--- -U
TIaa
~ jl OJo1 ~ ~Is~ o~JI)~J) tIJ ui~ 4laii IT-~~ Jb ~io ~
[-]~)A jl4iS~ ~middot-r~middotlsec 1S~loj J) 4iSt ~ ytNu
bull Q
Qbull amp
amp a bull
(y) (All)
bull bull
bull bull bull bull
bull bull
bull bull bull
bull bull abull a ia bullbull a () lt)
45~oi IIgt ~ 4iw 454)~~ IIgtJs ~J 45l11 ~
1=- sec ()t=~ sec (11)= sec ()=++ bullbull sec (All)
( bull IJoZ 1gt11gt ~~ j)~sJ ~ lo ~u ~JsJ ~s j~j 45-Slsj ~ 1A4) r~)
- abull a
bull bull a
( ) (uJl)
1= + sec () t= middot middot0 sec (All) 45~oj)1gt I~ 4i 4514)~~ JI)s ~J 45l1IT ~
( bull loJoZ 1)111gt ~~ I)~ sJ ~ lo ~u ~J sJ 4s j~l 45-Sl s1 41A4) ul~)
f) Ibull JI Ibull bullbullc
bullt bullI
2 -Ut
Ja
ua
-
ua
1
-~Jlitt8lmiddotmiddot1 I I -
Ii lop
1 ~
~ Lfi ~ of
~
) IIgt )) ~j-S iSUb~ ~~) JLgti o~)by
)3) ~I jI o)~ ))gt5 jl ~ ~ ~r
jAl w~ iSl~~wl-o ))gt5 jI ~ Ub~~
)) Ub~~ u-W bull5~ o~ 0)4) ))gtY
t~ I~middot ~ IS )) If 1middot 1 1_~ramp- is~) isr) ) IS )r- r-
-wLS )lJ) ~Iu ()fl iS~ ~) 1$JJt
~l~I JLgti o)jl Ih) j) y (wlo
)LgtI )) 511gt o~ rlS ~I jl I) is)g3)
I$)Y iSly middotw4~ )) IIgt)IS i --b ~~
ul) ~ iSUb)rJb1) iSr)~ 4 ) S1)s ~))
f4W 4S l ul) is)lJ SUb~ )4 ~I )) ol
middotl41S is)~ isUb)rJb1) ~
~I~)li
oSjb ~~ iSl) ~~ jl ~~~
Syen ~Igt ) FfI(lf(V o ek jI d o ~ (~) wr-1J iSjL~yen ~W- Srshy
bull))- IS ~1))gt9 frY -Ii - - -i
) 4i (y
1 wlA JLgti bullJi) is wl~
)4 ~I ~ lA ~ 4 bull )y~1S r~1 ~it wlA 4 is~ i ~r)) iSl~ )4 ol is~)4 issJI
~ ~ )) l wlA 4 iSl~ yo )4 ~ I) )gt
Y )~ ~ ~ ~L W)1i bull ~~ IIgt)IS
~ (H) lt - ) is~ ))IS wl-o jl
140~ 0 5 If L~II cil 1( is u - J I)r-- 1 r- ~
~)IS wli -1- sec -1- - Osec is~Lj )) I)
~ )) wIj -gt y ~l-o ~~~ )b
))gt5 ~I )) 1 0 1 (i)
)4 yj 41 5 ~r )) 0it~ Ub~ jI iSl~~wl-o
)-IS jul isI~ yo
iSjW iSly ISL is)lJ ) )4 ~I )) Jlgt )) laquoiSl-~wl-o ))gt5J ~ o~~ I$)Y
~ts ~Io ~p ~I--o jI iSr0 4 is~4J )) ) ~I l ul) ~~lS d~b I)W
~fJ4 I - de Freitas M Silva A and Reis L (2000) Numerical evaluation of failure mechanisms on composite
specimens subjected to impact loading Composites Part B Engineering Vol 31 PP 199-207
2 - Mohammadi S (2003) Discontinuum Mechanics using Finite and Discrete Elements WITPress- UK
3 - Koh CG Owen D R J and Perie D (1995) Explicit dynamic analysis of elsto-plastic laminated
composite shells implementation of non-iterative stress update schemes for the Hoffinan yield criterion
Computational Mechanics Vol 16 PP 307-314
4 - Schellekens 1 C 1 (1992) Computational strategies for composite structures PhD thesis Technische
Universiteit Delft Holland
5 - Forouzan-sepehr S and Mohammadi S (2001) A contact based method for 3D delamination analysis of
composites subjected to impact loading in S ValliaPPan N Khalili (editors) Computational Mechanicsshy
New Frontiers for the New Millennium Proceedings of 1 Asian-Pactflc Congress on computational
Mechanics- PP 691-696
6 - Mohammadi S Forouzan-sepehr S and Asadollahi A (2002) Contact based delamination and fracture
analysis of composites Thin-Walled Structures Vol 40 No 7-8 PP 595-609
7 - Masters 1 E (1987) Basic failure modes of continuous fiber composites Engineering Materials
Handbook Vol 1 CompOSites ASM International USA
8 - Borovkov A Kiylo 0 Misnik Yu and Tripolnikov T (1999) Finite element stress and analysis of
multidirectional laminated composite structures 2 h-p- refinement and m- adaptive procedures
Zeitschrijiir Angewamte Mathematik undMechamle Vol 79 Suppl No2 PP S527-S528
9 - FEA (2000) LUSAS User Manual Ver 132 FEA Ltd
10 - Liu Sh (1994) Quasi-impact damage initiation and growth of thick-section and toughened composite
materials lnt J Solids andStructures Vol 31 No 22 PP 3079-3098
11 - Mi Y Crisfield M A (1996) Analytical derivation ofloaddisplacement relatiollShip for the DCB and
MMB andproofofthe FEA formulation IC-AERO Report 97-02 Dept Aeronautics Imperial College
London UK
12 - Mi Y Crisfield M A Davies G A O and Hellweg H B (1998) Progressive delamination using
interface elements J Composite Materials Vol 32 No 14 PP 1246-1272
13 - Grady J E Chamis C C and Aiello R A (1989) Dynamic delamination buckling in composite
laminates under impact loading computational simulation In Lagace PA (ed) Composite Materials
Fatigue and Fracture ASTM-STP 1012 PP 137-149
~ )) O)~ ~~ ~~ 0) 1 - Matrix Cracking 2 - Delamination 3 - Fibre Breakage 4 - Fragmentation 5 - Theory ofPlasticity 6 - Computational Contact Mechanics 7 - Solid Element 8 - Discrete Element Method (DEM) 9 - Generalised Hook Law 10 - Transversely Isotropic 11 - Anisotropic 12 - Associated Flow Rule 13 - Normal Gap 14 - Tangential Gap 15 - Penalty 16 - Remeshing 17 - Adapti vity
II sJ4 ) Lltmin ~~ lo~llS ~ ~4 o~ JrS O~ sr Mcr ~Ir ~t) rlS 1~
jl ~t) rlS ytgt ) Llt -)J ~ Y- 4 1
) ~ 1 yi sr min (1tcrMmin)
) -jJ ~4 i s1~4 ~ sl) bull) y-I
L~11 JrS rgt s1 Jt ~tj rlSytgt
IS~)S IS~) ~v (iJ1- toJ
~4 ) I) ~)yJ1 hrJ 01~oJII (Grady) sJ
1 Ali W ~ 1 1 I_~ d ~sts) 1Sr ~ - ~ ) shy
5 4 sl-J ~jrolS II sl ) u~J ISI~
JjJ )~ sl~rb s)lf)4 I ~ ~I s1~J01o
0Li (All - A) ~ ) y-I s)lf)4 -gtlgtJb
)1 )r- r s) IS)) ) 1 ol 01
sr-) syJI 4 TIOOI034-C ~~1-4IJ ~
) ol 01 0Li ~lo sVi-t [OO]lOs JLJl
middotl41S (y- A)~ J~
5 ci)l r~1 -J )~ ) 1 y-I sjLJlo
u-J ~ ~ 010 OmiddotA em ojl)j ~ s1~1
- A ~) )IS 010 jI I) uL 0)Q u ) Y
laquoAll
sur-AI) jl sr-0 - 4 ~Iio sl) uL y-I ~ (wI ~I ~ s~JA ~x 0l1 ) ol ltlJ1)
~ 4JJ )~ jl ~ ytgt u W y-14 )l1S r~1
1IS s~JA 0l1 ol ciJ ~ ) lr--o 0 W1
t I ciL KA bull (All-) 1(-u ))) -- ~ shy
lt) jS ol ISW) )~ 1= + see
5 o)j))) -J ) I)) ~Io 46A 1S~4-- )
) ol ltlJI) ) 4 u llb1S 0Li tj Jk ) ~I ~ lgt sl) I) ~ bA9 u (w] ~I --
1 ~Iio ~li 01 ltlJ1) rblgt ~ 0t) r)p
) sl-J010 )gt5 r-S ssJ1 () jS
sur-A) sr-)~ 4 0 jl ~ jI u llb1S Li
~~ u ~IA bull1 olol ~ ~~ y-I
1S~ts ) s14JJ01o )gt5 ~I~ l1S
)1 ) suy ~ s~rb s) )4 )) ~
JIS
jll~ ~Ir-I ) ~ s1~J0l-o ~)gt5 ~
bulls)~ )IS JgtI j sr-0 - 4 ~ Ir-I -~ ~~ tIla sl) ~4 ~4 jI)~
(V)
1 I TTJCOn TTftXt bull TIflntbull TIflnertia -1 ) lt)) ~) j cu
(A)
rgt ~ Iy-I ) 1 jS ~I sr-)~ 4 s1~J0l-o ss) ssJ1 i)W -4its s~)sJ1
15t jS ~ (fV) ~I ~I) ol )r
Mii + fint = fext + fcon
sur-i )) M rr- ~t1)u JISk~
sur-i )) felU ~t sur-i )) fint ~)
~11S ~)j ~I) jI fcon sl-Jl-o ISW
(fr)
fint = 1BTSan (ff )
fext = 1NTb an + 1NTtar I (10)
) u01 )I- ~ ~bo ~~ ~ 4 4 laquosrgt ~W ~r raquo )gt5 ~
p) y-I ) ~ ~ IS ciJ )~ )I)li ~tj s4-0lS
~r-1 ~) sr-i su)) ~I ) 4 ~ ) sr )) ~ ~tj rlS ) sl-J10
) ~ytgt ~11S~~s fl3 ~~4-- ))
Ojt)j ~)) o~ k~ )~~srgt ~W
s)~~li ~bullbull lgt Ssect )IS )~ ~t) rl3
bullbullbullbull
TA
E 1468 GPa ~ =114GPa
G2 = 6184 GPa G23 = 4380 GPa
v =03 ~ =1730MPa A =1380MPa
1= 665 MPa 1 = 268 MPa
s= 1337 MPa p = 1550 kgm3
~ M
190N
T
~~X
(y) (All)
T3001034-C ~~I-~I ISI~ ~lAo IS~) (~)~u ISI-~ ISJIJJ~ 4IJiA (ill) It ~
a bull-amp----~~g----~a (y) (All)
KiP Reoldon H~lot1 Plo I D bull 1 P 5
bull -1 n t -15 n
-L Z
-25
- -5
-
5
-5 11 u u u 5 u 7 U 1
- I I I
25
lIIS-altlCllr -
~ E -_ I ~ 125 ~_tM
- C -- -
~ bull ~~~ ~E 0bull f4u -
bull ii ~h -125
0 j -
~ -25 25 50_
~ position (em)
~ r-I---
- _ algorINa 0 -4 ~ I---(SOIIXJISOloolJUJfgto6MX
~ r--- -U
TIaa
~ jl OJo1 ~ ~Is~ o~JI)~J) tIJ ui~ 4laii IT-~~ Jb ~io ~
[-]~)A jl4iS~ ~middot-r~middotlsec 1S~loj J) 4iSt ~ ytNu
bull Q
Qbull amp
amp a bull
(y) (All)
bull bull
bull bull bull bull
bull bull
bull bull bull
bull bull abull a ia bullbull a () lt)
45~oi IIgt ~ 4iw 454)~~ IIgtJs ~J 45l11 ~
1=- sec ()t=~ sec (11)= sec ()=++ bullbull sec (All)
( bull IJoZ 1gt11gt ~~ j)~sJ ~ lo ~u ~JsJ ~s j~j 45-Slsj ~ 1A4) r~)
- abull a
bull bull a
( ) (uJl)
1= + sec () t= middot middot0 sec (All) 45~oj)1gt I~ 4i 4514)~~ JI)s ~J 45l1IT ~
( bull loJoZ 1)111gt ~~ I)~ sJ ~ lo ~u ~J sJ 4s j~l 45-Sl s1 41A4) ul~)
f) Ibull JI Ibull bullbullc
bullt bullI
2 -Ut
Ja
ua
-
ua
1
-~Jlitt8lmiddotmiddot1 I I -
Ii lop
1 ~
~ Lfi ~ of
~
) IIgt )) ~j-S iSUb~ ~~) JLgti o~)by
)3) ~I jI o)~ ))gt5 jl ~ ~ ~r
jAl w~ iSl~~wl-o ))gt5 jI ~ Ub~~
)) Ub~~ u-W bull5~ o~ 0)4) ))gtY
t~ I~middot ~ IS )) If 1middot 1 1_~ramp- is~) isr) ) IS )r- r-
-wLS )lJ) ~Iu ()fl iS~ ~) 1$JJt
~l~I JLgti o)jl Ih) j) y (wlo
)LgtI )) 511gt o~ rlS ~I jl I) is)g3)
I$)Y iSly middotw4~ )) IIgt)IS i --b ~~
ul) ~ iSUb)rJb1) iSr)~ 4 ) S1)s ~))
f4W 4S l ul) is)lJ SUb~ )4 ~I )) ol
middotl41S is)~ isUb)rJb1) ~
~I~)li
oSjb ~~ iSl) ~~ jl ~~~
Syen ~Igt ) FfI(lf(V o ek jI d o ~ (~) wr-1J iSjL~yen ~W- Srshy
bull))- IS ~1))gt9 frY -Ii - - -i
) 4i (y
1 wlA JLgti bullJi) is wl~
)4 ~I ~ lA ~ 4 bull )y~1S r~1 ~it wlA 4 is~ i ~r)) iSl~ )4 ol is~)4 issJI
~ ~ )) l wlA 4 iSl~ yo )4 ~ I) )gt
Y )~ ~ ~ ~L W)1i bull ~~ IIgt)IS
~ (H) lt - ) is~ ))IS wl-o jl
140~ 0 5 If L~II cil 1( is u - J I)r-- 1 r- ~
~)IS wli -1- sec -1- - Osec is~Lj )) I)
~ )) wIj -gt y ~l-o ~~~ )b
))gt5 ~I )) 1 0 1 (i)
)4 yj 41 5 ~r )) 0it~ Ub~ jI iSl~~wl-o
)-IS jul isI~ yo
iSjW iSly ISL is)lJ ) )4 ~I )) Jlgt )) laquoiSl-~wl-o ))gt5J ~ o~~ I$)Y
~ts ~Io ~p ~I--o jI iSr0 4 is~4J )) ) ~I l ul) ~~lS d~b I)W
~fJ4 I - de Freitas M Silva A and Reis L (2000) Numerical evaluation of failure mechanisms on composite
specimens subjected to impact loading Composites Part B Engineering Vol 31 PP 199-207
2 - Mohammadi S (2003) Discontinuum Mechanics using Finite and Discrete Elements WITPress- UK
3 - Koh CG Owen D R J and Perie D (1995) Explicit dynamic analysis of elsto-plastic laminated
composite shells implementation of non-iterative stress update schemes for the Hoffinan yield criterion
Computational Mechanics Vol 16 PP 307-314
4 - Schellekens 1 C 1 (1992) Computational strategies for composite structures PhD thesis Technische
Universiteit Delft Holland
5 - Forouzan-sepehr S and Mohammadi S (2001) A contact based method for 3D delamination analysis of
composites subjected to impact loading in S ValliaPPan N Khalili (editors) Computational Mechanicsshy
New Frontiers for the New Millennium Proceedings of 1 Asian-Pactflc Congress on computational
Mechanics- PP 691-696
6 - Mohammadi S Forouzan-sepehr S and Asadollahi A (2002) Contact based delamination and fracture
analysis of composites Thin-Walled Structures Vol 40 No 7-8 PP 595-609
7 - Masters 1 E (1987) Basic failure modes of continuous fiber composites Engineering Materials
Handbook Vol 1 CompOSites ASM International USA
8 - Borovkov A Kiylo 0 Misnik Yu and Tripolnikov T (1999) Finite element stress and analysis of
multidirectional laminated composite structures 2 h-p- refinement and m- adaptive procedures
Zeitschrijiir Angewamte Mathematik undMechamle Vol 79 Suppl No2 PP S527-S528
9 - FEA (2000) LUSAS User Manual Ver 132 FEA Ltd
10 - Liu Sh (1994) Quasi-impact damage initiation and growth of thick-section and toughened composite
materials lnt J Solids andStructures Vol 31 No 22 PP 3079-3098
11 - Mi Y Crisfield M A (1996) Analytical derivation ofloaddisplacement relatiollShip for the DCB and
MMB andproofofthe FEA formulation IC-AERO Report 97-02 Dept Aeronautics Imperial College
London UK
12 - Mi Y Crisfield M A Davies G A O and Hellweg H B (1998) Progressive delamination using
interface elements J Composite Materials Vol 32 No 14 PP 1246-1272
13 - Grady J E Chamis C C and Aiello R A (1989) Dynamic delamination buckling in composite
laminates under impact loading computational simulation In Lagace PA (ed) Composite Materials
Fatigue and Fracture ASTM-STP 1012 PP 137-149
~ )) O)~ ~~ ~~ 0) 1 - Matrix Cracking 2 - Delamination 3 - Fibre Breakage 4 - Fragmentation 5 - Theory ofPlasticity 6 - Computational Contact Mechanics 7 - Solid Element 8 - Discrete Element Method (DEM) 9 - Generalised Hook Law 10 - Transversely Isotropic 11 - Anisotropic 12 - Associated Flow Rule 13 - Normal Gap 14 - Tangential Gap 15 - Penalty 16 - Remeshing 17 - Adapti vity
bullbullbullbull
TA
E 1468 GPa ~ =114GPa
G2 = 6184 GPa G23 = 4380 GPa
v =03 ~ =1730MPa A =1380MPa
1= 665 MPa 1 = 268 MPa
s= 1337 MPa p = 1550 kgm3
~ M
190N
T
~~X
(y) (All)
T3001034-C ~~I-~I ISI~ ~lAo IS~) (~)~u ISI-~ ISJIJJ~ 4IJiA (ill) It ~
a bull-amp----~~g----~a (y) (All)
KiP Reoldon H~lot1 Plo I D bull 1 P 5
bull -1 n t -15 n
-L Z
-25
- -5
-
5
-5 11 u u u 5 u 7 U 1
- I I I
25
lIIS-altlCllr -
~ E -_ I ~ 125 ~_tM
- C -- -
~ bull ~~~ ~E 0bull f4u -
bull ii ~h -125
0 j -
~ -25 25 50_
~ position (em)
~ r-I---
- _ algorINa 0 -4 ~ I---(SOIIXJISOloolJUJfgto6MX
~ r--- -U
TIaa
~ jl OJo1 ~ ~Is~ o~JI)~J) tIJ ui~ 4laii IT-~~ Jb ~io ~
[-]~)A jl4iS~ ~middot-r~middotlsec 1S~loj J) 4iSt ~ ytNu
bull Q
Qbull amp
amp a bull
(y) (All)
bull bull
bull bull bull bull
bull bull
bull bull bull
bull bull abull a ia bullbull a () lt)
45~oi IIgt ~ 4iw 454)~~ IIgtJs ~J 45l11 ~
1=- sec ()t=~ sec (11)= sec ()=++ bullbull sec (All)
( bull IJoZ 1gt11gt ~~ j)~sJ ~ lo ~u ~JsJ ~s j~j 45-Slsj ~ 1A4) r~)
- abull a
bull bull a
( ) (uJl)
1= + sec () t= middot middot0 sec (All) 45~oj)1gt I~ 4i 4514)~~ JI)s ~J 45l1IT ~
( bull loJoZ 1)111gt ~~ I)~ sJ ~ lo ~u ~J sJ 4s j~l 45-Sl s1 41A4) ul~)
f) Ibull JI Ibull bullbullc
bullt bullI
2 -Ut
Ja
ua
-
ua
1
-~Jlitt8lmiddotmiddot1 I I -
Ii lop
1 ~
~ Lfi ~ of
~
) IIgt )) ~j-S iSUb~ ~~) JLgti o~)by
)3) ~I jI o)~ ))gt5 jl ~ ~ ~r
jAl w~ iSl~~wl-o ))gt5 jI ~ Ub~~
)) Ub~~ u-W bull5~ o~ 0)4) ))gtY
t~ I~middot ~ IS )) If 1middot 1 1_~ramp- is~) isr) ) IS )r- r-
-wLS )lJ) ~Iu ()fl iS~ ~) 1$JJt
~l~I JLgti o)jl Ih) j) y (wlo
)LgtI )) 511gt o~ rlS ~I jl I) is)g3)
I$)Y iSly middotw4~ )) IIgt)IS i --b ~~
ul) ~ iSUb)rJb1) iSr)~ 4 ) S1)s ~))
f4W 4S l ul) is)lJ SUb~ )4 ~I )) ol
middotl41S is)~ isUb)rJb1) ~
~I~)li
oSjb ~~ iSl) ~~ jl ~~~
Syen ~Igt ) FfI(lf(V o ek jI d o ~ (~) wr-1J iSjL~yen ~W- Srshy
bull))- IS ~1))gt9 frY -Ii - - -i
) 4i (y
1 wlA JLgti bullJi) is wl~
)4 ~I ~ lA ~ 4 bull )y~1S r~1 ~it wlA 4 is~ i ~r)) iSl~ )4 ol is~)4 issJI
~ ~ )) l wlA 4 iSl~ yo )4 ~ I) )gt
Y )~ ~ ~ ~L W)1i bull ~~ IIgt)IS
~ (H) lt - ) is~ ))IS wl-o jl
140~ 0 5 If L~II cil 1( is u - J I)r-- 1 r- ~
~)IS wli -1- sec -1- - Osec is~Lj )) I)
~ )) wIj -gt y ~l-o ~~~ )b
))gt5 ~I )) 1 0 1 (i)
)4 yj 41 5 ~r )) 0it~ Ub~ jI iSl~~wl-o
)-IS jul isI~ yo
iSjW iSly ISL is)lJ ) )4 ~I )) Jlgt )) laquoiSl-~wl-o ))gt5J ~ o~~ I$)Y
~ts ~Io ~p ~I--o jI iSr0 4 is~4J )) ) ~I l ul) ~~lS d~b I)W
~fJ4 I - de Freitas M Silva A and Reis L (2000) Numerical evaluation of failure mechanisms on composite
specimens subjected to impact loading Composites Part B Engineering Vol 31 PP 199-207
2 - Mohammadi S (2003) Discontinuum Mechanics using Finite and Discrete Elements WITPress- UK
3 - Koh CG Owen D R J and Perie D (1995) Explicit dynamic analysis of elsto-plastic laminated
composite shells implementation of non-iterative stress update schemes for the Hoffinan yield criterion
Computational Mechanics Vol 16 PP 307-314
4 - Schellekens 1 C 1 (1992) Computational strategies for composite structures PhD thesis Technische
Universiteit Delft Holland
5 - Forouzan-sepehr S and Mohammadi S (2001) A contact based method for 3D delamination analysis of
composites subjected to impact loading in S ValliaPPan N Khalili (editors) Computational Mechanicsshy
New Frontiers for the New Millennium Proceedings of 1 Asian-Pactflc Congress on computational
Mechanics- PP 691-696
6 - Mohammadi S Forouzan-sepehr S and Asadollahi A (2002) Contact based delamination and fracture
analysis of composites Thin-Walled Structures Vol 40 No 7-8 PP 595-609
7 - Masters 1 E (1987) Basic failure modes of continuous fiber composites Engineering Materials
Handbook Vol 1 CompOSites ASM International USA
8 - Borovkov A Kiylo 0 Misnik Yu and Tripolnikov T (1999) Finite element stress and analysis of
multidirectional laminated composite structures 2 h-p- refinement and m- adaptive procedures
Zeitschrijiir Angewamte Mathematik undMechamle Vol 79 Suppl No2 PP S527-S528
9 - FEA (2000) LUSAS User Manual Ver 132 FEA Ltd
10 - Liu Sh (1994) Quasi-impact damage initiation and growth of thick-section and toughened composite
materials lnt J Solids andStructures Vol 31 No 22 PP 3079-3098
11 - Mi Y Crisfield M A (1996) Analytical derivation ofloaddisplacement relatiollShip for the DCB and
MMB andproofofthe FEA formulation IC-AERO Report 97-02 Dept Aeronautics Imperial College
London UK
12 - Mi Y Crisfield M A Davies G A O and Hellweg H B (1998) Progressive delamination using
interface elements J Composite Materials Vol 32 No 14 PP 1246-1272
13 - Grady J E Chamis C C and Aiello R A (1989) Dynamic delamination buckling in composite
laminates under impact loading computational simulation In Lagace PA (ed) Composite Materials
Fatigue and Fracture ASTM-STP 1012 PP 137-149
~ )) O)~ ~~ ~~ 0) 1 - Matrix Cracking 2 - Delamination 3 - Fibre Breakage 4 - Fragmentation 5 - Theory ofPlasticity 6 - Computational Contact Mechanics 7 - Solid Element 8 - Discrete Element Method (DEM) 9 - Generalised Hook Law 10 - Transversely Isotropic 11 - Anisotropic 12 - Associated Flow Rule 13 - Normal Gap 14 - Tangential Gap 15 - Penalty 16 - Remeshing 17 - Adapti vity
bull bull
bull bull bull bull
bull bull
bull bull bull
bull bull abull a ia bullbull a () lt)
45~oi IIgt ~ 4iw 454)~~ IIgtJs ~J 45l11 ~
1=- sec ()t=~ sec (11)= sec ()=++ bullbull sec (All)
( bull IJoZ 1gt11gt ~~ j)~sJ ~ lo ~u ~JsJ ~s j~j 45-Slsj ~ 1A4) r~)
- abull a
bull bull a
( ) (uJl)
1= + sec () t= middot middot0 sec (All) 45~oj)1gt I~ 4i 4514)~~ JI)s ~J 45l1IT ~
( bull loJoZ 1)111gt ~~ I)~ sJ ~ lo ~u ~J sJ 4s j~l 45-Sl s1 41A4) ul~)
f) Ibull JI Ibull bullbullc
bullt bullI
2 -Ut
Ja
ua
-
ua
1
-~Jlitt8lmiddotmiddot1 I I -
Ii lop
1 ~
~ Lfi ~ of
~
) IIgt )) ~j-S iSUb~ ~~) JLgti o~)by
)3) ~I jI o)~ ))gt5 jl ~ ~ ~r
jAl w~ iSl~~wl-o ))gt5 jI ~ Ub~~
)) Ub~~ u-W bull5~ o~ 0)4) ))gtY
t~ I~middot ~ IS )) If 1middot 1 1_~ramp- is~) isr) ) IS )r- r-
-wLS )lJ) ~Iu ()fl iS~ ~) 1$JJt
~l~I JLgti o)jl Ih) j) y (wlo
)LgtI )) 511gt o~ rlS ~I jl I) is)g3)
I$)Y iSly middotw4~ )) IIgt)IS i --b ~~
ul) ~ iSUb)rJb1) iSr)~ 4 ) S1)s ~))
f4W 4S l ul) is)lJ SUb~ )4 ~I )) ol
middotl41S is)~ isUb)rJb1) ~
~I~)li
oSjb ~~ iSl) ~~ jl ~~~
Syen ~Igt ) FfI(lf(V o ek jI d o ~ (~) wr-1J iSjL~yen ~W- Srshy
bull))- IS ~1))gt9 frY -Ii - - -i
) 4i (y
1 wlA JLgti bullJi) is wl~
)4 ~I ~ lA ~ 4 bull )y~1S r~1 ~it wlA 4 is~ i ~r)) iSl~ )4 ol is~)4 issJI
~ ~ )) l wlA 4 iSl~ yo )4 ~ I) )gt
Y )~ ~ ~ ~L W)1i bull ~~ IIgt)IS
~ (H) lt - ) is~ ))IS wl-o jl
140~ 0 5 If L~II cil 1( is u - J I)r-- 1 r- ~
~)IS wli -1- sec -1- - Osec is~Lj )) I)
~ )) wIj -gt y ~l-o ~~~ )b
))gt5 ~I )) 1 0 1 (i)
)4 yj 41 5 ~r )) 0it~ Ub~ jI iSl~~wl-o
)-IS jul isI~ yo
iSjW iSly ISL is)lJ ) )4 ~I )) Jlgt )) laquoiSl-~wl-o ))gt5J ~ o~~ I$)Y
~ts ~Io ~p ~I--o jI iSr0 4 is~4J )) ) ~I l ul) ~~lS d~b I)W
~fJ4 I - de Freitas M Silva A and Reis L (2000) Numerical evaluation of failure mechanisms on composite
specimens subjected to impact loading Composites Part B Engineering Vol 31 PP 199-207
2 - Mohammadi S (2003) Discontinuum Mechanics using Finite and Discrete Elements WITPress- UK
3 - Koh CG Owen D R J and Perie D (1995) Explicit dynamic analysis of elsto-plastic laminated
composite shells implementation of non-iterative stress update schemes for the Hoffinan yield criterion
Computational Mechanics Vol 16 PP 307-314
4 - Schellekens 1 C 1 (1992) Computational strategies for composite structures PhD thesis Technische
Universiteit Delft Holland
5 - Forouzan-sepehr S and Mohammadi S (2001) A contact based method for 3D delamination analysis of
composites subjected to impact loading in S ValliaPPan N Khalili (editors) Computational Mechanicsshy
New Frontiers for the New Millennium Proceedings of 1 Asian-Pactflc Congress on computational
Mechanics- PP 691-696
6 - Mohammadi S Forouzan-sepehr S and Asadollahi A (2002) Contact based delamination and fracture
analysis of composites Thin-Walled Structures Vol 40 No 7-8 PP 595-609
7 - Masters 1 E (1987) Basic failure modes of continuous fiber composites Engineering Materials
Handbook Vol 1 CompOSites ASM International USA
8 - Borovkov A Kiylo 0 Misnik Yu and Tripolnikov T (1999) Finite element stress and analysis of
multidirectional laminated composite structures 2 h-p- refinement and m- adaptive procedures
Zeitschrijiir Angewamte Mathematik undMechamle Vol 79 Suppl No2 PP S527-S528
9 - FEA (2000) LUSAS User Manual Ver 132 FEA Ltd
10 - Liu Sh (1994) Quasi-impact damage initiation and growth of thick-section and toughened composite
materials lnt J Solids andStructures Vol 31 No 22 PP 3079-3098
11 - Mi Y Crisfield M A (1996) Analytical derivation ofloaddisplacement relatiollShip for the DCB and
MMB andproofofthe FEA formulation IC-AERO Report 97-02 Dept Aeronautics Imperial College
London UK
12 - Mi Y Crisfield M A Davies G A O and Hellweg H B (1998) Progressive delamination using
interface elements J Composite Materials Vol 32 No 14 PP 1246-1272
13 - Grady J E Chamis C C and Aiello R A (1989) Dynamic delamination buckling in composite
laminates under impact loading computational simulation In Lagace PA (ed) Composite Materials
Fatigue and Fracture ASTM-STP 1012 PP 137-149
~ )) O)~ ~~ ~~ 0) 1 - Matrix Cracking 2 - Delamination 3 - Fibre Breakage 4 - Fragmentation 5 - Theory ofPlasticity 6 - Computational Contact Mechanics 7 - Solid Element 8 - Discrete Element Method (DEM) 9 - Generalised Hook Law 10 - Transversely Isotropic 11 - Anisotropic 12 - Associated Flow Rule 13 - Normal Gap 14 - Tangential Gap 15 - Penalty 16 - Remeshing 17 - Adapti vity
) IIgt )) ~j-S iSUb~ ~~) JLgti o~)by
)3) ~I jI o)~ ))gt5 jl ~ ~ ~r
jAl w~ iSl~~wl-o ))gt5 jI ~ Ub~~
)) Ub~~ u-W bull5~ o~ 0)4) ))gtY
t~ I~middot ~ IS )) If 1middot 1 1_~ramp- is~) isr) ) IS )r- r-
-wLS )lJ) ~Iu ()fl iS~ ~) 1$JJt
~l~I JLgti o)jl Ih) j) y (wlo
)LgtI )) 511gt o~ rlS ~I jl I) is)g3)
I$)Y iSly middotw4~ )) IIgt)IS i --b ~~
ul) ~ iSUb)rJb1) iSr)~ 4 ) S1)s ~))
f4W 4S l ul) is)lJ SUb~ )4 ~I )) ol
middotl41S is)~ isUb)rJb1) ~
~I~)li
oSjb ~~ iSl) ~~ jl ~~~
Syen ~Igt ) FfI(lf(V o ek jI d o ~ (~) wr-1J iSjL~yen ~W- Srshy
bull))- IS ~1))gt9 frY -Ii - - -i
) 4i (y
1 wlA JLgti bullJi) is wl~
)4 ~I ~ lA ~ 4 bull )y~1S r~1 ~it wlA 4 is~ i ~r)) iSl~ )4 ol is~)4 issJI
~ ~ )) l wlA 4 iSl~ yo )4 ~ I) )gt
Y )~ ~ ~ ~L W)1i bull ~~ IIgt)IS
~ (H) lt - ) is~ ))IS wl-o jl
140~ 0 5 If L~II cil 1( is u - J I)r-- 1 r- ~
~)IS wli -1- sec -1- - Osec is~Lj )) I)
~ )) wIj -gt y ~l-o ~~~ )b
))gt5 ~I )) 1 0 1 (i)
)4 yj 41 5 ~r )) 0it~ Ub~ jI iSl~~wl-o
)-IS jul isI~ yo
iSjW iSly ISL is)lJ ) )4 ~I )) Jlgt )) laquoiSl-~wl-o ))gt5J ~ o~~ I$)Y
~ts ~Io ~p ~I--o jI iSr0 4 is~4J )) ) ~I l ul) ~~lS d~b I)W
~fJ4 I - de Freitas M Silva A and Reis L (2000) Numerical evaluation of failure mechanisms on composite
specimens subjected to impact loading Composites Part B Engineering Vol 31 PP 199-207
2 - Mohammadi S (2003) Discontinuum Mechanics using Finite and Discrete Elements WITPress- UK
3 - Koh CG Owen D R J and Perie D (1995) Explicit dynamic analysis of elsto-plastic laminated
composite shells implementation of non-iterative stress update schemes for the Hoffinan yield criterion
Computational Mechanics Vol 16 PP 307-314
4 - Schellekens 1 C 1 (1992) Computational strategies for composite structures PhD thesis Technische
Universiteit Delft Holland
5 - Forouzan-sepehr S and Mohammadi S (2001) A contact based method for 3D delamination analysis of
composites subjected to impact loading in S ValliaPPan N Khalili (editors) Computational Mechanicsshy
New Frontiers for the New Millennium Proceedings of 1 Asian-Pactflc Congress on computational
Mechanics- PP 691-696
6 - Mohammadi S Forouzan-sepehr S and Asadollahi A (2002) Contact based delamination and fracture
analysis of composites Thin-Walled Structures Vol 40 No 7-8 PP 595-609
7 - Masters 1 E (1987) Basic failure modes of continuous fiber composites Engineering Materials
Handbook Vol 1 CompOSites ASM International USA
8 - Borovkov A Kiylo 0 Misnik Yu and Tripolnikov T (1999) Finite element stress and analysis of
multidirectional laminated composite structures 2 h-p- refinement and m- adaptive procedures
Zeitschrijiir Angewamte Mathematik undMechamle Vol 79 Suppl No2 PP S527-S528
9 - FEA (2000) LUSAS User Manual Ver 132 FEA Ltd
10 - Liu Sh (1994) Quasi-impact damage initiation and growth of thick-section and toughened composite
materials lnt J Solids andStructures Vol 31 No 22 PP 3079-3098
11 - Mi Y Crisfield M A (1996) Analytical derivation ofloaddisplacement relatiollShip for the DCB and
MMB andproofofthe FEA formulation IC-AERO Report 97-02 Dept Aeronautics Imperial College
London UK
12 - Mi Y Crisfield M A Davies G A O and Hellweg H B (1998) Progressive delamination using
interface elements J Composite Materials Vol 32 No 14 PP 1246-1272
13 - Grady J E Chamis C C and Aiello R A (1989) Dynamic delamination buckling in composite
laminates under impact loading computational simulation In Lagace PA (ed) Composite Materials
Fatigue and Fracture ASTM-STP 1012 PP 137-149
~ )) O)~ ~~ ~~ 0) 1 - Matrix Cracking 2 - Delamination 3 - Fibre Breakage 4 - Fragmentation 5 - Theory ofPlasticity 6 - Computational Contact Mechanics 7 - Solid Element 8 - Discrete Element Method (DEM) 9 - Generalised Hook Law 10 - Transversely Isotropic 11 - Anisotropic 12 - Associated Flow Rule 13 - Normal Gap 14 - Tangential Gap 15 - Penalty 16 - Remeshing 17 - Adapti vity
8 - Borovkov A Kiylo 0 Misnik Yu and Tripolnikov T (1999) Finite element stress and analysis of
multidirectional laminated composite structures 2 h-p- refinement and m- adaptive procedures
Zeitschrijiir Angewamte Mathematik undMechamle Vol 79 Suppl No2 PP S527-S528
9 - FEA (2000) LUSAS User Manual Ver 132 FEA Ltd
10 - Liu Sh (1994) Quasi-impact damage initiation and growth of thick-section and toughened composite
materials lnt J Solids andStructures Vol 31 No 22 PP 3079-3098
11 - Mi Y Crisfield M A (1996) Analytical derivation ofloaddisplacement relatiollShip for the DCB and
MMB andproofofthe FEA formulation IC-AERO Report 97-02 Dept Aeronautics Imperial College
London UK
12 - Mi Y Crisfield M A Davies G A O and Hellweg H B (1998) Progressive delamination using
interface elements J Composite Materials Vol 32 No 14 PP 1246-1272
13 - Grady J E Chamis C C and Aiello R A (1989) Dynamic delamination buckling in composite
laminates under impact loading computational simulation In Lagace PA (ed) Composite Materials
Fatigue and Fracture ASTM-STP 1012 PP 137-149
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