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Walled S uc u es, Vol. 192, on No embe 2023, a ailable
a : h ps://doi.o g/10.1016/j. ws.2023.111148
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Highligh s
Nume ical p edic ions o in alamina and in e lamina damage in
hin composi e shells subjec ed o impac loads
L.M. Fe ei a, C.A.C.P. Coelho, P.N.B. Reis
•In es iga ion o he impac dynamics on composi e shells using he explici
ini e elemen me hod.
•Nume ical p edic ions o in alamina damage using a con inuum damage
mechanics model.
•Nume ical p edic ions o in e lamina damage using a su ace-based cohe-
si e model.
•P edic ion o ene gy dissipa ion o ms o di↵e en hicknesses.
Nume ical p edic ions o in alamina and in e lamina
damage in hin composi e shells subjec ed o impac
loads
L.M. Fe ei aa,b,⇤
, C.A.C.P. Coelhoc, P.N.B. Reisd
aG upo de Elas icidad y Resis encia de Ma e iales. Escuela T´ecnica Supe io de Ingenie ´ıa.
Uni e sidad de Se illa. Camino Descub imien os, S/N 41092 Se illa. Espa˜na
bEscuela Poli ´ecnica Supe io . Uni e sidad de Se illa. C/ Vi gen de ´
A ica, 7, Se illa,
41011. Espa˜na
cUnidade Depa amen al de Engenha ias. Escola Supe io de Tecnologia de Ab an es.
Ins i u o Poli ´ecnico de Toma . Rua 17 de Agos o de 1808 S/N 2200-370 Ab an es.
Po ugal
dUni e si y o Coimb a, CEMMPRE, ARISE, Depa men o Mechanical Enginee ing,
3030-194 Coimb a, Po ugal
Abs ac
This pape in es iga es he impac dynamics o hin semicylind ical wo en
composi e lamina e shells, wi h a pa icula ocus on unde s anding he in lu-
ence o hickness. U ilising he ini e elemen (FE) me hod, he s udy e al-
ua es bo h in alamina and in e lamina damage associa ed wi h he impac
esponse. The indings show ha he implemen a ion o he explici FE me hod,
along wi h a con inuum damage mechanics model, o he in alamina damage,
and a su ace-based cohesi e model, o he in e lamina damage, may be used
o co ec ly p edic he load his o ies, as well as he maximum impac o ce,
maximum displacemen , con ac ime and impac bending s i↵ness (IBS). The
nume ical p edic ions ep oduce well he linea esponse o he maximum im-
pac o ce and maximum displacemen o he hickness a ia ion, as well as he
2nd o de polynomial cu e o he IBS, wi h e o s anging om 2.7% o 15.9%.
Mo eo e , he damage a eas and he e↵ec o hickness on he damage se e i y
we e accu a ely eplica ed. These esul s’ alida ion enables he p edic ion o
he ene gy his o ies and he ensuing ene gy dissipa ion o ms. Acco ding o
he indings, he in alamina damage is a ound 5 imes mo e signi ican han
he o he ene gy dissipa ion o ms. The accu acy o he simula ion c ea es he
possibili y o mo e impac in es iga ions using a simila nume ical app oach,
educing he expendi u es o expe imen al es ing.
Keywo ds: Fini e elemen me hod (FEM), Con inuum damage mechanics
(CDM), Cohesi e beha iou , Low- eloci y impac , Wo en- ab ic composi es,
Composi e shells
P ep in submi ed o Thin-Walled S uc u es Feb ua y 1, 2024
1. In oduc ion
Composi e ma e ials ha e become inc easingly popula due o hei unique
combina ion o high s eng h, low weigh , and excellen a igue esis ance. How-
e e , hey a e suscep ible o damage om low- eloci y impac s ha can occu
du ing handling, anspo a ion, main enance, and se ice. These impac s can5
cause localised damage o he s uc u e, which can esul in educed s eng h,
s i↵ness, and du abili y o he composi e ma e ial [1–5]. The e o e, unde s and-
ing he damage mechanisms and beha iou o composi e ma e ials unde low-
eloci y impac s is o u mos impo ance o ensu e he eliabili y and sa e y o
composi e s uc u es. In his con ex , i is no su p ising ha li e a u e p esen s10
se e al s a egies o inc ease impac s eng h, such as he use o nanopa icles
[6], mul iaxial mesh ab ics [7], hyb id lamina es [8], sandwich composi es [9, 10]
o simply changing he s acking sequence o he lamina es [11].
Since he ea ly 1990s, impac analysis on composi e s uc u es has been a
subjec o s udy. The ea e , se e al nume ical esea ch s udies ha e been done15
using di↵e en abs ac ion scales and applied me hods. The ini e elemen (FE)
me hod has been used ex ensi ely o de elop models o unidi ec ional composi e
pla es and e alua e a ious pa ame e s such as ma e ial cha ac e is ics, impac
ene gy, and geome y. Ye , he e a e ela i ely ew s udies ha analyse he
impac dynamics on cylind ical shells, pa icula ly when i comes o composi es20
made o wo en ab ics. The mos ele an s udies ound in li e a u e ega ding
low- eloci y impac on cylind ical shells, a e dedica ed o analyse he e↵ec o
cu a u e o he shell on he impac o ce, displacemen (de lec ion) and con-
ac ime [12–15]. The indings o hese s udies a e consis en and e eal ha
he impac o ce inc eases wi h he inc ease in cu a u e, while de lec ion and25
con ac ime dec ease. In es iga ions ha e also been conduc ed o de e mine
how hickness a↵ec s he impac esponse o composi e lamina e pla es and
shells [16–21]. These s udies ha e shown ha inc easing he hickness o he
lamina es leads o no able e↵ec s on se e al impac - ela ed pa ame e s. I was
ound ha inc easing he hickness o he composi e lamina es esul s in in-30
c eased s i↵ness. This highe s i↵ness impa s he lamina es wi h he abili y
o wi hs and highe impac loads. As a esul , he lamina es exhibi smalle
de lec ions and educed con ac imes du ing impac e en s. Fu he mo e, he
damage onse and damage e olu ion we e s udied in [22], and i was ound ha
o unidi ec ional composi e pla es and shells, damage p og esses di↵e en ly.35
Al hough he nume ical app oach u ilizing FE models allows he simula ion o
complica ed s uc u es unde os ensibly complex ex e nal loads and bounda y
condi ions, om he nume ical pe spec i e, simula ing impac is s ill a complex
ask. Mo eo e , achie ing a sui able le el o accu acy in a ai amoun o ime
con inues o be a challenge [23, 24].40
Composi e ma e ials expe ience se e al di↵e en damage modes unde im-
⇤Co esponding au ho
Email add ess: [email p o ec ed] (L.M. Fe ei a)
2
pac loads such as ma ix c acking, delamina ion, ib e ailu e and pe o a ion,
which can conside ably lessen he ma e ial’s s eng h and s i↵ness [25]. I is
hen c ucial o de elop c edible FE models capable o o ecas ing hese dam-
age modes. Focus is he e on ab ic- ein o ced composi e lamina e shells wi h45
a semicylind ical c oss-sec ion. These composi es ha e p ac ical in e es o
impac - esis an cons uc ions like wind u bine blades o ai c a s uc u es.
The buil -in con inuum damage mechanics model (CDM) o ab ic ein o ced
composi es a ailable in ABAQUS [26] and de eloped by Johnson [27], is em-
ployed o model he in alamina damage, while he in e lamina damage, know50
as delamina ion, is modelled using he su ace-based cohesi e damage model
(S-BCM). The wo-s ep homogeniza ion me hod p oposed by Liu e al. [28] is
used o p edic he laminas’ p ope ies om he cons i uen s p ope ies. This
s udy ollows he expe imen al and nume ical wo k p e iously de eloped by he
au ho s [29–31]. Fi s ly, he e↵ec o hickness on he mul i-impac esponse55
o semicylind ical composi e lamina ed shells wi h 6-, 9-, and 12-laye s was ex-
pe imen ally analysed in [29]. Subsequen ly, based on he expe imen al esul s
ob ained, a FE model o a single hickness was gene a ed, and in which he
physical in alamina and in e lamina p og essi e damage models we e in o-
duced [30]. This wo k ocused on e↵ec o he FE mesh disc e iza ion and60
mass-scaling on he load his o y p edic ions and in e alua ing he e iciency and
eliabili y o he nume ical model. A e wa ds, he in luence o in e lamina
p ope ies on delamina ion p edic ions o a single hickness was s udied in [31].
Finally, he p esen pape ep esen s an expansion o he analysis and alida-
ion p ocess o encompass di↵e en hicknesses, while s i ing o comp ehend65
he unde lying damage mechanisms a bo h he in alamina and in e lamina
le els.
The e o e, o summa ize, he cu en wo k se es as a con inua ion o he
p e ious nume ical in es iga ion and complemen s he expe imen al indings. I
in oduces no el con ibu ions, including he de elopmen and alida ion o FE70
models capable o in es iga ing he impac dynamics o semicylind ical wo en
composi e lamina e shells wi h di↵e en hicknesses. Mo eo e , he s udy o-
cuses on p edic ing and e alua ing he in alamina and in e lamina damage
modes, as well as iden i ying he ene gy dissipa ion mechanisms ha occu du -
ing low- eloci y impac e en s. As a as he au ho s a e awa e, hese opics75
in he domain o hin semicylind ical composi e shells, a e s ill lacking comp e-
hensi e unde s anding and esea ch.
2. Damage models
Low- eloci y impac s on composi e lamina es can cause ib e ailu e and ma-
ix c acking (in alamina damage), as well sepa a ion o he in e ace egions,80
known as delamina ion (in e lamina damage) [32, 33]. To model hese damage
mechanisms in semicylind ical wo en composi e lamina e shells, a CDM a he
lamina le el o add ess he in alamina damage, and a S-BCM a he lamina’s
in e ace o accoun o he in e lamina damage, we e implemen ed. These
3

damage models a e ully desc ibed in [26, 34, 35], hus only he main aspec s o 85
he CDM and S-BCM will be b ie ly desc ibed in he ollowing subsec ions.
2.1. In alamina damage model
To e alua e he complex damage e olu ion a he in alamina le el, he
buil -in cons i u i e model o ab ic ein o ced composi es a ailable in ABAQUS/Explici
[36], de eloped by Johnson [27] and based on Lade eze and Ledan ec wo k90
[37], was employed. This damage model is applied as a buil -in VUMAT use
sub ou ine and accessed by naming he use -de ined ma e ial wi h he s ing
“ABQ PLY FABRIC” [26]. This VUMAT sub ou ine is compa ible only wi h
plane-s ess elemen s and conside s each ab ic ein o ced lamina as a homo-
geneous o ho opic elas ic ma e ial ha wi hs ands s i↵ness educ ion due o95
ib e ailu e and/o ma ix c acking and plas ic de o ma ion unde shea load-
ing. I uses he maximum s ess ailu e c i e ion o de e mine he damage onse
o he ib es, and a damage e olu ion model based on he ac u e ene gies o
con ol he s i↵ness educ ion.
The Hooke’s law o a deg aded o ho opic ma e ial is exp essed as,100
"=2
6
4
S1
(1d1)S12 0
S21 S2
(1d2)0
00S6
(1d12)
3
7
5(1)
whe e Sij a e he componen s o he compliance ma ix o he undamaged o -
ho opic ma e ial, is he nominal Cauchy s ess enso , "is he elas ic s ain
enso , and d1,d2and d12 a e he damage coe icien s. No ice ha he damage
coe icien s d1and d2a e associa ed wi h ib e ac u e along di ec ions 1 and 2,
espec i ely, and d12 is associa ed wi h he ma ix mic o-c acking due o shea 105
de o ma ion.
As men ioned be o e, he CDM uses he maximum s ess c i e ion o de-
e mine he damage onse o he ib es, and o simula e he wo ailu e modes
( ib e ension and ib e comp ession). The e o e, he elas ic domain, a any
gi en ime, is calcula ed in e ms o he damage ac i a ion unc ions, F↵, as110
F↵=˜↵
X↵
 ↵0wi h↵=1±,2±,12 (2)
whe e ˜↵and X↵a e he ensile/comp essi e/shea e↵ec i e s esses and s eng hs,
espec i ely, and ↵a e he damage h esholds, which a e ini ially de ined wi h
a alue o 1. A e eaching he damage onse , ha is, when ˜↵
X↵= 1, he
e olu ion he damage coe icien s, d1and d2, associa ed wi h he ensile and
comp essi e loading, a e ob ained using equa ions 3 and 4, while he damage115
coe icien d12 associa ed wi h shea loading, is ob ained by equa ion 5,
d1,2=11
1,2
eA1,2( 1,21) (3)
A1,2=2g1,2
0Lch
G1,2
g1,2
0Lch
wi h g1,2
0=X2
1,2
2E1,2
(4)
4
d12 =min [↵12 ln ( 12),d
max
12 ] (5)
whe e 1,2and 12 co espond o he damage h esholds o he ensile/comp essi e
and shea loading, espec i ely, G1,2
o he ac u e ene gies pe uni a ea, g1,2
0
o he elas ic ene gy densi y a he damage onse , and Lch o he cha ac e is ic
leng h o he elemen . The shea damage pa ame e ↵12 is ob ained h ough a120
calib a ion p ocedu e de ailed in [26].
A he in alamina le el, he shea damage esponse is d i en by he ma ix’s
nonlinea beha io caused by he ma ix mic oc acking, and i in ol es bo h
s i↵ness loss and plas ici y. The yield and ha dening unc ions ep esen ed in
equa ions 6 and 7, espec i ely, a e used by he VUMAT sub ou ine o de ine125
he plas ici y esponse o he ma ix,
Fpl =|˜12|˜0(¯"pl)0 (6)
˜0(¯"pl)=˜y0+C(¯"pl)p(7)
whe e ˜12 is he e↵ec i e shea s ess, ˜y0is he ini ial e↵ec i e shea s ess, and
¯"pl is plas ic s ain due shea de o ma ion. The ha dening unc ion’s coe icien
and powe e m a e deno ed by Cand he supe sc ip p, espec i ely.
To be able o alida e he nume ical models based on he expe imen al e -130
idence p esen ed in [29], he s i↵ness p ope ies o he wo en ab ic composi e
laminas we e es ima ed om he cons i uen s’ p ope ies o he es ed speci-
mens, using he wo-s ep homogeniza ion me hodology p esen ed by Liu e al.
[28]. The ob ained elas ic p ope ies a e consis en wi h hose epo ed in li e -
a u e o plain wea e E-glass wo en ab ic composi es [38–40]. This mul iscale135
app oach in ol es i s es ima ing he e↵ec i e p ope ies o he ows om he
ib e and ma ix p ope ies and hen p edic ing he lamina p ope ies om he
p ope ies o he ows and he ma ix. This me hodology was implemen ed us-
ing he so wa e TexGen4SC [41, 42]. Each lamina is composed o a polyes e
esin ma ix (AROPOL FS 1963 wi h MEKP-50 ha dene ) ein o ced wi h a140
bi-axial E-glass plain wea e ab ic (EC9 68×2). The lamina’s s i↵ness p op-
e ies we e es ima ed om he elas ic cons an s ex ac ed om [43–46]. The
emaining p ope ies and coe icien s equi ed o implemen he VUMAT sub-
ou ine, such as he s eng h p ope ies, ac u e oughness and shea plas ici y,
we e aken om li e a u e [38, 47–51]. The lamina’s in alamina p ope ies145
a e shown in Table 1. No ice ha a good ag eemen be ween he expe imen al
esul s and he nume ical p edic ions was a ained in p e ious wo k de eloped
by he au ho s, and in which he same p ope ies and coe icien s we e employed
[30, 31].
The ans e se shea s i↵ness o he laminas mus be de ined o he VUMAT150
sub ou ine [26] because i canno be calcula ed by ABAQUS/Explici [36] o
composi e shell elemen s. Conside ing ha each lamina can be hough o as a
homogeneous shell wi h o ho opic elas ic p ope ies, equa ions 8 we e used o
calcula e he ans e se shea s i↵ness,
5
Table 1: In alamina p ope ies de ined o each lamina [30].
P ope y Symbol Uni s Value
Densi y ⇢kg/m31900
S i↵ness p ope ies
E+,
1=E+,
2GPa 21.9
E3GPa 8.6
G12 GPa 3.4
G13 GPa 2.4
⌫12 - 0.14
S eng h p ope ies
X+
1=X+
2MPa 250
X
1=X
2MPa 200
X12 MPa 40
F ac u e oughness G1,2
J/m24500
Shea plas ici y
dmax
12 -1
˜y0MPa 25
C- 800
p- 0.552
k s
1=5
6G13 , k s
2=5
6G23 , k s
12 = 0 (8)
whe e G13 and G23 a e he ou -o -plane shea moduli o he lamina, is he155
hickness o he lamina, and 5/6 is a shea co ec ion coe icien ha is ob-
ained by compa ing he ans e se shea ene gy o ha o an 3D s uc u e
in pu e bending, as sugges ed in [36]. Conside ing he ou -o -plane shea mod-
uli calcula ed by he homogeniza ion p ocess, he ollowing alues we e used in
he de ini ion o he in alamina p ope ies: k s
1=k s
2=3.5⇥105N/m and160
k s
12 = 0.
2.2. In e lamina damage model
To accoun o he in e lamina damage, i.e. delamina ion, he bond be ween
he laminas o he composi e lamina e was modelled using a S-BCM. This model
is p ima ily in ended o negligible small in e ace hicknesses and o↵e s e y165
simila capabili ies o cohesi e elemen s. The cohesi e beha iou is de ined as
a su ace in e ac ion p ope y, and iden ically o he cohesi e elemen s i is
go e ned by a ac ion-sepa a ion cons i u i e model. Hence, he in e lamina
ac u e beha iou (delamina ion) is de ined as a cons i u i e ela ion be ween
he ac ion ⌧and he sepa a ion , see Fig. 1.170
The ini ial linea esponse un il he damage onse i eached is con olled
by he alue de ined o he no mal knand angen ial ks,k
cohesi e s i↵nesses.
These pa ame e s in luence he pe o mance o he FE model and o which he e
a e di↵e en app oaches a ailable in li e a u e o ob ain i s alue [52–55]. Fo
ins ance, Daude ille e al. [52] de e mined he cohesi e s i↵ness as a unc ion175
6
Figu e 1: Bilinea ac ion-sepa a ion esponse o he cohesi e su ace.
o he in e ace’s hickness and he elas ic modulus o he esin- ich laye , while
Zou e al. [53] sugges ed he use o in e ace s i↵ness alues be ween 105and
107 imes he in e ace s eng h di ided by leng h uni . Ano he app oach was
p esen ed by Tu on e al. [55], in which he in e ace s i↵ness is calcula ed as
unc ion o he elas ic p ope ies o he lamina e. The cohesi e s i↵ness in his180
s udy is se a 106N/mm3, as sugges ed by Camanho e al. [54]. Also, i is
conside ed ha i s alue is he same o all di ec ions, ha is, kn=ks=k , as
used in [30, 31, 55–57] wi h sa is ac o y esul s. I is no ewo hy ha conside ing
high alues o he cohesi e s i↵ness po en ially leads o con e gence p oblems,
on he o he hand, he use o low alues may a↵ec he global s i↵ness and hus185
comp omise he alida ion o he FE model [56].
The ollowing s ess-based quad a ic ailu e c i e ion was employed o p edic
he damage ini ia ion,
✓h⌧ni
⌧0
n◆2
+✓⌧s
⌧0
s◆2
+✓⌧
⌧0
◆2
= 1 (9)
whe e ⌧n,⌧
sand ⌧ ep esen he in e ace no mal and shea con ac s esses,
and ⌧0
n,⌧0
sand ⌧0
ep esen he co esponding in e ace s eng hs. The Macaulay190
b acke s hiindica e ha he comp essi e s ess doesn’ con ibu e o damage.
The ollowing in e lamina s eng hs we e used in he S-BCM: ⌧0
n= 15 MPa
and ⌧0
s=⌧0
= 30 MPa [30]. Once he onse o damage is eached, ha is,
when he quad a ic in e ac ion unc ion o he s ess a ios eaches 1, he cohe-
7
Figu e 7: E↵ec o hickness on he nume ical and expe imen al [29] maximum displacemen
esul s.
4.2. De o ma ion his o ies
The de o ma ion his o ies o he 6-, 9- and 12-laye composi e lamina es a
di↵e en s ep imes a e shown in Fig. 8. The selec ed ime s eps o analysis
a e ep esen ed in Fig. 4, deno ed as Ai,B
iand Ci, which co espond o he
ollowing con ac imes: Ai o hal o he peak o ce ime; Bi o he peak o ce340
ime; Ci o hal o he ime be ween he peak o ce and he o al con ac ime.
He e, he subsc ip i=6,9,12, iden i ies he con igu a ion o he lamina e.
A no able end can be obse ed whe ein an inc ease in hickness esul s
in a co esponding inc ease in he s i↵ness o he composi e lamina e. Among
he lamina es s udied, he 6-laye lamina e exhibi s he highes deg ee o de-345
o ma ion, ollowed by he 9-laye and 12-laye lamina es. As an icipa ed, he
de o ma ion s eadily in ensi ies un il i eaches he peak o ce, a which poin
he impac o ebounds and he specimen commences i s elas ic eco e y.
4.3. Impac bending s i↵ness
The s udies de eloped by Liu [64] and Da id-Wes e al. [65] sugges ha 350
he impac bending s i↵ness is an impo an pa ame e o e alua e he damage
esis ance o a composi e, in pa icula delamina ions. Acco ding o hese au-
ho s, he slope o he ascending b anch o he load-displacemen cu e de ines
he IBS, because he pla e is unde bending a he beginning o he impac
14

Figu e 8: De o ma ion his o ies o he 6-, 9- and 12-laye composi e lamina es.
15
Figu e 9: E↵ec o hickness on he nume ical and expe imen al [29] IBS esul s.
egime [65]. In his s udy, he IBS is calcula ed om he expe imen al and nu-355
me ical cu es depic ed in Fig. 5, and Table 2 p esen s and compa es he alues
ob ained. I should be no ed ha he IBS p edic ions o he 6-laye FE model
had he la ges pe cen age o e o . This is mos likely because damage begins
o appea a sligh ly di↵e en loads han simula ed. Ac ually, un il eaching
he peak o ce, he expe imen s shown a smoo he damage g ow h han he360
simula ions. This di↵e ence in he ini ial beha iou can be a ibu ed o he
use o he semi-au oma ic mass scaling echnique in he nume ical models [30].
Ne e heless, all he p edic ed IBS alues a e wi hin he limi s o he expe i-
men al e idence. The e olu ion o he IBS wi h hickness is shown in Fig. 9.
The igu e ou lines he FE models capabili y o accu a ely ep oduce he 2nd
365
o de polynomial cu e ollowed by he expe imen s, and which a e ep esen ed
by he plo ed end lines.
4.4. Damage
The nume ical p edic ions o he in alamina damage (ou pu a iables
SDV1 o SDV5) and he in e lamina damage (ou pu a iable CSDMG>0.6)370
we e o e lapped o allow a comple e ep esen a ion o he damage se e i y o
he di↵e en lamina e hicknesses, see Figs. 10, 11 and 12. No ice ha he
ou pu iden i ie CSDMG, ep esen s he scala s i↵ness deg ada ion o cohesi e
su aces, and measu es delamina ion a e damage ini ia ion. When i eaches
16
Figu e 10: Nume ically p edic ed ensile and comp essi e damage along he ib e di ec ions
and delamina ed a ea o he 6-laye lamina e.
he alue o 1, he in e ace is conside ed o be ully delamina ed. Mo eo e , he375
CDM o ab ic ein o ced composi es used in his s udy does no di↵e en ia e
be ween ib e and ma ix damage a he in alamina le el, i includes only
he ou pu s a iables o ensile/comp essi e damage along he ib e di ec ions
and he shea damage. The e o e, i limi s a mo e de ailed iden i ica ion o he
damage modes a he in alamina le el.380
The simula ions show ha lamina e’s hickness a↵ec s how se e e he dam-
age is. The 6-laye FE model sus ained damage commencing a he poin o
impac and ex ending he ull leng h o he shell. The 9-laye FE model p e-
dic ed a less se e e damage bu qui e simila o he one ob ained wi h he hinne
lamina e. On he o he hand, damage is es ic ed o he impac loca ion o 385
he 12-laye FE model. This esponse can be explained by he ac ha mo e
in e aces a e a ailable o dissipa e he impac ene gy as hickness inc eases and
consequen ly, he e is less ene gy a ailable o inc ease damage. These esul s
a e consis en wi h he expe imen al indings, which showed ha he damaged
se e i y inc eases wi h dec easing hickness [29]. Mo eo e , i co ela es wi h390
he la ge displacemen s obse ed in hinne lamina es, see Fig. 5.
Mo eo e , i is also possible o app ecia e in Figs. 10 o 12, ha ega dless
o he hickness, he damaged incu ed in he bo om laye s o he shell is
mo e se e e in compa ison o he op laye s. I is known ha du ing a low-
eloci y impac e en , he bo om laye s o he shell, loca ed opposi e o he395
impac side, expe ience ensile s esses esul ing in ma e ial ( ib e and ma ix)
elonga ion. Con e sely, he op laye o he shell, which comes in o di ec con ac
17
Figu e 11: Nume ically p edic ed ensile and comp essi e damage along he ib e di ec ions
and delamina ed a ea o he 9-laye lamina e.
Figu e 12: Nume ically p edic ed ensile and comp essi e damage along he ib e di ec ions
and delamina ed a ea o he 12-laye lamina e.
18
Figu e 13: Delamina ion p edic ions along he di↵e en in e aces o he 6-, 9-, and 12-laye
composi e lamina es.
wi h he impac o , expe iences comp ession o ces. These comp ession o ces
induce localized de o ma ion in he impac ed egion which unde goes plas ic
de o ma ion and comp ession. Al hough he CDM does no p o ide speci ic400
iden i ica ion o he a ious damage modes, he nume ical p edic ions sugges
ha a he in alamina le el, he mos p ominen damage mechanisms a e ib e
b eakage and/o ma ix c acking. These damage modes a e closely associa ed
wi h he ensile s esses de eloped in he bo om laye s du ing he impac e en .
The delamina ion a eas p edic ed o each in e ace o he lamina es a e il-405
lus a ed in Fig. 13. Once again, i is e iden ha delamina ion p ima ily occu s
wi hin he impac egion. Howe e , as p e iously obse ed, he delamina ion in
he 6- and 9-laye lamina es p opaga es along he leng h o he shell. Rega ding
he in e aces, i is no ewo hy ha o he same lamina e hickness, hey gen-
e ally exhibi simila delamina ion a eas in e ms o size and se e i y. Howe e ,410
he e is an excep ion obse ed o in e ace 7 o he 12-laye lamina e. This
pa icula in e ace is loca ed app oxima ely in he middle o he lamina e’s
hickness, be ween laye 7 and laye 8. The p edic ed delamina ion egion o
his in e ace is sligh ly la ge and mo e se e e compa ed o he o he in e aces.
Ne e heless, he o e all esul s ha e a good co ela ion wi h he expe imen al415
e idence p esen ed in Fig. 14.
The p edic ed impac oo p in s, esul ing om he o e lapping o he in-
alamina and in e lamina damage modes a e compa ed wi h he ac ual impac
oo p in s ob ained expe imen ally, in Fig. 14. No ice ha he damage on he
es ed specimens was cap u ed h ough pho og aphy using in ense backligh ,420
19

Figu e 14: Nume ical and expe imen al [29] impac oo p in s o he 6-, 9- and 12-laye
composi e lamina es.
aking ad an age o he anslucen cha ac e is ic o he lamina es. Despi e he
limi a ions on he accu acy o he non-des uc i e es ing echnique employed
o assess he damage ex ension, he p ojec ed damage a eas a e gene ally well
p edic ed by he FE models. The uni o m FE mesh size used, con ibu ed o
he co ec p edic ions o he damaged a eas ha can be seen along he leng h425
o he lamina es. Howe e , i should be no ed ha hey end o be sligh ly
o e es ima ed a ound he impac loca ion. The sca e ed poin s ha can be
app ecia ed in he simula ions o he 6- and 9-laye lamina es ou side he con-
cen a ed damaged a eas, co espond o isola ed nodes which ha e expe ienced
delamina ion.430
4.5. Ene gy his o ies
In he loading s age o a low- eloci y impac es , a sizeable po ion o he
kine ic ene gy ha is ans e ed om he impac o o he lamina e is con e ed
in o elas ic ene gy. The emaining ene gy is dissipa ed owing o ic ion and o
he di↵e en ailu e modes ha occu a he in alamina and in e lamina le -435
els. The elas ic ene gy ha he specimen s o es is eleased du ing he unloading
s age, causing he impac o o ebound. As he impac o loses con ac wi h he
specimen, he ene gy s abilizes [66, 67]. Since in he expe imen al se up he im-
pac o ’s mass and he d op heigh emained consis en ac oss di↵e en hickness
a ia ions, he peak alues obse ed on he ene gy- ime cu es emained iden i-440
cal. This beha iou can be app ecia ed in he ene gy his o ies o he 6-, 9- and
12-laye lamina es shown in Fig. 15. O e all, a good nume ical-expe imen al
co ela ion can be app ecia ed. No ice ha he nume ical p edic ed impac en-
e gy cu es o he 6- and 9-laye lamina es p esen a ugged beha iou du ing
20
Figu e 15: E↵ec o hickness on he nume ical and expe imen al [29] ene gy- ime esul s.
he unloading s age, which is due o he ib a ions o he FE model. On he445
o he hand, gi en i s highe s i↵ness, he 12-laye lamina e p esen s a smoo he
beha iou .
The alida ion o simula ions o he ene gy and load his o ies, along wi h he
well p edic ed damage a eas, opens he possibili y o iden i ying he amoun o
ene gy ha is dissipa ed h ough in alamina damage, delamina ion and ic-450
ion. The expe imen ally measu ed impac ene gy con e ed om he impac o ,
and he nume ical p edic ions o he impac ene gy and he subsequen dissi-
pa ed ene gy o ms ob ained wi h 6-, 9- and 12-laye s FE models, a e shown in
Figs. 16, 17 and 18, espec i ely.
Rega dless o he hickness unde conside a ion, he in alamina damage455
ou weighs he o he ene gy dissipa ion o ms by abou 5 imes, con i ming ha
i is he p ima y damage mode. The ene gy dissipa ion due o delamina ion
and ic ion is negligible, howe e , a sligh inc ease as hickness inc eases can be
obse ed. The la ge numbe o in e aces may explain his beha iou . Mo e-
o e , he high in e lamina ac u e oughness and low in-plane s eng h o he460
wo en ab ic composi es may jus i y he p opensi y o in alamina damage
p opaga ion a he han delamina ion.
The o al ans e ed ene gy cu e’s peak, which co esponds o he ins ance
o maximum displacemen , is co ec ly p edic ed, and he ene gy balance is
accu a ely ep oduced. I is no ewo hy o men ion ha he o al ene gy (ou pu 465
ETOTAL), emains s able, which indica es a co ec de ini ion o he s ep ime
21
Figu e 16: Nume ical and expe imen al [29] ene gy his o y o he 6-laye lamina e.
Figu e 17: Nume ical and expe imen al [29] ene gy his o y o he 9-laye lamina e.
22
Figu e 18: Nume ical and expe imen al [29] ene gy his o y o he 12-laye lamina e.
inc emen s. Also, he ex e nal ene gy (ALLAE ou pu ), is a small ac ion o
he in e nal ene gy (ALLIE ou pu ), meaning he hou glass con ol me hod is
adequa e.
5. Conclusions470
The in alamina and in e lamina damage and he impac esponse o hin
semicylind ical wo en composi e lamina e shells unde low- eloci y impac loads
was simula ed using he ini e elemen me hod, wi h pa icula ocus on e al-
ua ing he e↵ec o hickness. The nume ical p edic ions we e compa ed wi h
he indings o he p e ious expe imen al wo k conduc ed by he au ho s.475
The esul s ob ained in his s udy, demons a e ha he low- eloci y impac
esponse o hin semicylind ical wo en composi e lamina e shells can be eli-
ably simula ed using he explici FE me hod oge he wi h a CDM, o accoun
o in alamina damage, and a S-BCM, o accoun o in e lamina damage.
The nume ical models we e able o sa is ac o y p edic he load his o ies, as480
well as he maximum impac o ce, maximum displacemen , con ac ime, and
IBS. Fo example, he simula ions we e able o ep oduce he expe imen al lin-
ea esponse o he maximum impac o ce and maximum displacemen o he
hickness a ia ion, as well as he 2nd o de polynomial cu e o he IBS ollowed
by he expe imen s.485
23
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