Characterization of Low-Velocity Impact Damage in Asymmetric Composite Shells

J. Appl. Compu . Mech., 11(1) (2025) 98-109
DOI: 10.22055/jacm.2024.45986.4446
ISSN: 2383-4536
jacm.scu.ac.i
Published online: June 14 2024
Shahid Cham an
Uni e si y o Ah az
Jou nal
o
Applied
and
Compu a ional
Mechanics
Resea ch Pape
Cha ac e iza ion o Low-Veloci y Impac Damage in Asymme ic
Composi e Shells
Luis Miguel Fe ei a
1,2
, Ca los A.C.P. Coelho
3
, Paulo N.B. Reis
4
1 G upo de Elas icidad y Resis encia de Ma e iales, Escuela Técnica Supe io de Ingenie ía, Uni e sidad de Se illa,
Camino Descub imien os, S/N 41092 Se illa, España, Email: lma [email protected]
2 Escuela Poli écnica Supe io , Uni e sidad de Se illa, C/ Vi gen de Á ica, 7, Se illa, 41011, España
3 Unidade Depa amen al de Engenha ias, Escola Supe io de Tecnologia de Ab an es, Ins i u o Poli écnico de Toma ,
Rua 17 de Agos o de 1808 S/N 2200-370 Ab an es, Po ugal, Email: cccampos@ip .p
4 Uni e si y o Coimb a, CEMMPRE, ARISE, Depa men o Mechanical Enginee ing, 3030-780 Coimb a, Po ugal, Email: paulo. [email protected]
Recei ed Janua y 29 2024; Re ised Ap il 21 2024; Accep ed o publica ion June 04 2024.
Co esponding au ho : L.M. Fe ei a (lma [email protected])
© 2024 Published by Shahid Cham an Uni e si y o Ah az
Abs ac . Based on nume ical modelling, his s udy in es iga es asymme ic semicylind ical composi e lamina e shells' damage
cha ac e is ics unde low- eloci y impac loads. Fo his pu pose, se e al asymme ic s acking sequences we e subjec ed o low-
eloci y impac and he esul s we e analysed in e ms o o ce, displacemen , con ac ime, and abso bed ene gy. I is concluded
ha he maximum impac o ce dec eases wi h an inc ease in he numbe o laye s o ien ed a 0, pa icula ly in he uppe hal o
he lamina e. The lamina es wi h a 45 o ien a ion in he uppe laye s p esen he lowes displacemen alues, whe eas he
lamina es wi h he uppe laye s o ien ed a 0 exhibi longe con ac imes. I is also obse ed ha in alamina damage is
esponsible o almos hal o he o al impac ene gy, ollowed by delamina ions and ic ion. S acking sequences wi h uppe laye s
a 45 exhibi sligh ly highe ene gy dissipa ion due o in alamina damage ( ib e ailu e) and in e lamina damage (delamina ion).
Keywo ds: Asymme ic composi es; Damage cha ac e iza ion; Nume ical modelling; Impac esponse.
1. In oduc ion
Nowadays, composi e ma e ials a e inc easingly eplacing adi ional me allic ma e ials due o he eno mous bene i s ha can
be ob ained om hei applica ion. This is he esul o hei excep ional pe o mance in e ms o as manu ac u ing, compe i i e
cos , supe io s a ic and dynamic cha ac e is ics, high speci ic s eng h and s i ness, and good co osion esis ance [1–4]. In
addi ion, hei low weigh allows o signi ican educ ions in uel consump ion, which makes hem pa icula ly a ac i e om an
ene gic poin o iew.
Despi e all he ad an ages epo ed, i s applica ion is s ill comp omised in many applica ions due o he low esis ance
h oughou he hickness. In ac , hey p o e o be pa icula ly sensi i e o low- eloci y impac s, e en s ha commonly occu in
se ice o main enance ac i i ies and p omo e damages ha a e di icul o de ec isually [5, 6]. Apa om ma ix c acking, ib e
ac u e and ib e–ma ix debonding, delamina ion is one o he mos impo an ailu e mechanisms because hey d as ically a ec
he esidual p ope ies o composi e ma e ials. Fo example, in e ms o ensile s eng h, he li e a u e epo s educ ions o
be ween 16% and 25% due o he deg ada ion o he ib e/ma ix in e ace and s ess concen a ion p omo ed by he delamina ions
[7–10]. Rega ding he bending p ope ies, educ ions o be ween 34% and 78% can be ound, depending on he posi ion o he
delamina ion along hickness and he layup sequence (symme ical o an i-symme ical layups) [11–13]. Finally, comp essi e
s eng h can be educed by a ound 60% due o he mul iple delamina ions ha in e ac du ing comp ession and g ow apidly unde
buckling loads [14–18]. Ama o e al. [19], o example, de eloped a de ailed s udy on he esidual impac s eng h o ca bon/epoxy
lamina es a e bending and concluded ha he magni ude o he ini ial damage has a de e minan in luence on he impac
esponse o he lamina es.
Howe e , mos o he s udies a ailable in he li e a u e do no add ess asymme ical lamina es due o he dec ease in
pe o mance caused by in-plane and ou -o -plane in e ac ions. Due o hese in e ac ions, dis o ion can occu du ing he cu ing
p ocess, which inc eases he s ess le els and dec eases he load-ca ying capaci y. Howe e , hese nega i e aspec s o pe o mance
a e a ely assessed accu a ely o included in he design p ocess, which is why mos o he s udies a ailable in he li e a u e ocus
essen ially on symme ical lamina es.
Cha ac e iza ion o Low-Veloci y Impac Damage in Asymme ic Composi e Shells
99
Jou nal o Applied and Compu a ional Mechanics, Vol. 11, No. 1, (2025), 98-109
The s udies pe o med by Sasikuma e al. [20–22] a e an excep ion, in which he au ho s demons a e ha asymme ical
lamina es can be a good solu ion, compa ed o symme ical ones, o s uc u al applica ions in he ae onau ical ield. In hei i s
s udy [20], he au ho s p oposed an asymme ical lamina e wi h ply clus e ing on he impac ace o he lamina e, which was
compa ed wi h a lamina e wi h a simila con igu a ion, bu , in his case, he ply clus e ing is on he non-impac ed side. Wi h his
clus e ed ply block, he au ho s in end o induce high in e lamina shea s esses, which cause delamina ion a he in e ace a he
co esponding ply in e ace and, consequen ly, p omo e delamina ions a p e-de e mined egions. Based on expe imen al and
nume ical analyses, he au ho s concluded ha , when he ply clus e ing is loca ed on he impac ace o he lamina e, be e
esis ance o damage is ob ained. Compa ed o he lamina e wi h ply clus e ing on he non-impac ed side, bene i s o a ound 30%
we e ob ained in e ms o h eshold load o delamina ion and he p ojec ed delamina ion a ea was 20% lowe o low-impac
ene gies. The eason o his imp o emen was due o in alamina damage, which is he mos signi ican damage mechanism o
lamina es wi h clus e s a he non-impac ed side, causing a la ge ene gy dissipa ion han delamina ion. The e o e, s acking
sequences can be adap ed acco ding o he s ess s a es expec ed in gi en load cases. Subsequen ly, he au ho s combined he
concep s o asymme y and ply hyb idiza ion in o a lamina e design, in which hick plies can be mixed wi h hin plies o o m a
hyb id lamina e [21]. Mo eo e , he hicke plies can be posi ioned whe e desi ed wi hou aising conce ns abou posi ioning simila
hick plies o e he lamina e's midplane symme y line. Wi h his me hodology, au ho s ob ained abou 50% and 30% educ ion in
e ms o damage a ea and dissipa ed ene gy, espec i ely, o e he hin-ply lamina es. In addi ion o g ea e impac s eng h, he
comp essi e s eng h a e impac was also imp o ed by a ound 30% compa ed o ha obse ed o hin-ply lamina es. This s udy
allowed he au ho s o demons a e ha i is possible o mi iga e he weakness o hin plies agains impac and pos -impac loads
in an economical way. Finally, he au ho s s udied h ee asymme ical lamina es, in which he local ply clus e s we e placed on he
impac side, in he middle o he lamina e and on he non-impac ed side and compa ed he esul s wi h hose ob ained o a
symme ic lamina e (wi h no ply clus e s) [22]. Wi h his s udy, he au ho s p o ed ha damage can be imposed a he desi ed
loca ions h ough he design o he lamina e. Fu he mo e, he asymme ic lamina e wi h middle ply clus e s inc eased he
comp essi e s eng h a e impac by 10% compa ed o he o he con igu a ions wi h ply clus e s and buckled less, al hough ha ing
less impac esis ance han he symme ic lamina e. The e o e, his s a egy can be an op imal solu ion o applica ion o ai c a
skins.
Based on he abo e bene i s and because esea ch in o cylind ical shells is ex emely impo an due o he inc easing use o
complex s uc u es, his s udy aims o cha ac e ise he damage in asymme ical semicylind ical composi e lamina e shells
subjec ed o low- eloci y impac loads. In ac , mos o he wo ks a ailable in he li e a u e epo s udies o la pla es subjec ed o
low- eloci y impac s and, in he case o semicylind ical composi e lamina es, al hough hey a e sca ce, hey ocus on he in luence
o geome ic pa ame e s, bounda y condi ions and di e en ma e ials/layup con igu a ions [23–26]. Mo e speci ically, de e mining
he ene gy dissipa ion mechanisms ha occu du ing low- eloci y impac e en s, as well as p edic ing and analysing he ypes o
in alamina and in e lamina damage, a e he main objec i es o his wo k. The in en ion is o con inue he s udies o Sasikuma
e al. [20–22] bu o semicylind ical composi e lamina ed shells using, o his pu pose, a nume ical app oach al eady alida ed in
p e ious wo k de eloped by he au ho s [13, 27–29]. Fo his pu pose, and main aining he o e all numbe o laye s, au ho s used
he ollowing s acking sequences [0
4
,45
4
], [0
6
,45
2
], [0
7
,45
1
], [45
4
,0
4
], [45
6
,0
2
] and [45
7
,0
1
] o g oup laye s wi h di e en numbe s o
cons i uen s loca ed on he impac and non-impac aces, wi h he aim o imposing delamina ions a di e en speci ic loca ions
h oughou he hickness. The esul s will be discussed wi h each o he and compa ed wi h he same symme ic con igu a ion.
2. Nume ical Model
This sec ion p o ides an o e iew o he cons i u i e models used in he Fini e Elemen (FE) simula ions o e alua e he damage
ob ained in asymme ic cu ed composi e lamina es subjec ed o low- eloci y impac s. These models we e in eg a ed in o he
s udy using ABAQUS/Explici FE so wa e [30]. They we e de ined based on p e ious nume ical models de eloped o composi e
lamina e shells ein o ced wi h E-glass plain-wea ed ab ics [23, 27–29]. I should be no ed ha he expe imen al e idence
p esen ed in [25] se ed as he basis o his s udy. In his way, he composi e semicylind ical shells we e manu ac u ed h ough
esin ans e moulding, wi h an in e nal adius o 50 mm, a leng h o 100 mm, and an a e age hickness o 2.53 mm. These shells
comp ise o eigh laye s o wo en ca bon ib e ab ic (160 g/cm
2
, plain-wea e), sou ced om Composi e Ma e ials I aly (CIT), wi h
SR1500 epoxy esin and SD2503 ha dene , bo h p o ided by Sicomin (Châ eauneu -les-Ma igues, F ance). Figu e 1 p esen s he
expe imen al se up employed, including he es ing equipmen and specimen suppo de ice, ne e heless, mo e de ails abou he
expe imen al p ocedu e can be ob ained in [25].
Fig. 1. Expe imen al se up and gene a ed FE model o a semicylind ical composi e shell.
100
L.M. Fe ei a e al., Vol. 11, No. 1, 2025
Jou nal o Applied and Compu a ional Mechanics, Vol. 11, No. 1, (2025), 98-109
Table 1. In alamina s i ness and s eng h p ope ies o he composi e laye s.
Desc ip ion Symbol Uni s Value
Densi y
𝜌
kg/m3 1600
Young’s modulus
𝐸
1
=
𝐸
2
GPa 69
Poisson’s a io
𝜈
12
- 0.04
In-plane shea modulus
𝐺
12
GPa 7.1
Tensile s eng h
𝑋
1
+
=
𝑋
2
+
MPa 640
Comp essi e s eng h
𝑋
1
−
=
𝑋
2
−
MPa 540
Shea s eng h
𝑆
MPa 180
Table 2. Damage e olu ion pa ame e s and shea plas ici y coe icien s.
Desc ip ion Symbol Uni s Value
Maximum shea damage
𝑑
12
𝑚𝑎𝑥
- 1
Shea damage pa ame e
𝛼
12
- 0.3221
Ini ial e ec i e shea yield s ess
𝜎

𝑦
0
MPa 80
Coe icien in ha dening equa ion
𝐶
- 788
Powe e m in ha dening equa ion
𝑝
- 0.552
2.1. Fini e Elemen Disc e iza ion
The wo en ab ic laye s we e modelled using con inuum shell elemen s (SC8R) ha inco po a e educed in eg a ion and a
s i ness hou glass o mula ion. Fo he impac o , disc e e igid elemen s (R3D4) we e employed, while he suppo s we e modelled
as analy ical igid bodies. To s ike a balance be ween compu a ional e iciency and nume ical p edic ion accu acy, i was c ucial o
op imize he FE mesh disc e iza ion, especially in he icini y o he impac egion. Fo his pu pose, a seeding s a egy was applied
along bo h he cu ed and s aigh edges o he semicylind ical shell, inc easing he FE mesh densi y p ecisely in he impac egion.
Simul aneously, he mesh densi y was educed p og essi ely beyond his c i ical a ea. The FE mesh disc e iza ion used in his s udy
is shown in Fig. 1.
The 8-laye FE model gene a ed o his s udy consis s o 48,000 linea hexahed al elemen s o ype SC8R and 949 linea
quad ila e al elemen s o ype R3D4. A seeding s a egy was implemen ed, leading o a a ia ion in elemen size ac oss he laminas.
Wi hin he impac egion, elemen s wi h an app oxima e global size o 0.3 mm we e applied, p og essi ely expanding o 2 mm in
egions a he om he impac zone. I espec i e o he s acking sequence unde examina ion, a consis en FE mesh disc e iza ion
was adop ed, ea u ing iden ical cha ac e is ic leng h and aspec a io in all simula ions. This me hod gua an ees he compa abili y
o p edic ions ac oss di e se s acking sequences. To expedi e solu ion compu a ions a semi-au oma ed uni o m mass scaling
s a egy was implemen ed. To p e en any in luence o mass scaling on he esul s, i is essen ial o keep he kine ic ene gies
esul ing om he mass scaling e ec below 5 o 10% o he o al in e nal ene gy [30]. The e o e, in his s udy, he kine ic ene gies
accoun o less han 3% o he o al in e nal ene gy.
2.2. Bounda y Condi ions
The FE model conside s he geome ical cha ac e is ics o he specimens examined in [25]. These specimens p esen a semi-
ci cula c oss-sec ional shape wi h an in e nal adius o 50 mm and a leng h o 100 mm, as shown in Fig. 1. They consis o 8
composi e ab ic laye s, esul ing in a composi e hickness o 2.53 mm. To accu a ely simula e he expe imen al se up, wo ixed
igid body suppo s we e added: a la e al suppo and a bo om suppo . Mo eo e , o op imize compu a ional e iciency, he FE
model exploi ed geome ic symme ies, ocusing on one-qua e o he composi e shell. Symme y bounda y condi ions we e
imposed on he plane pa allel o he yz-plane and one o he su aces pa allel o he xy-plane, as depic ed in Fig. 1. The impac o
used in he simula ions had a lumped mass o 2.826 kg wi h a hemisphe ical head o 10 mm diame e . An impac eloci y o 1.88
m/s was chosen o ma ch he 5 J impac ene gy used in he expe imen al campaign [25]. Addi ionally, all o a ional deg ees o
eedom o he impac o we e cons ained, allowing only displacemen s along he y-axis.
2.3. In alamina P ope ies
A Con inuum Damage Model (CDM) was used o model he in alamina damage wi hin he ABAQUS/Explici [30]. This model
was implemen ed using he in eg a ed VUMAT sub ou ine ABQ_PLY_FABRIC, de eloped by Johnson e al. [31], which is based on he
Lade eze and LeDan ec damage model [32]. This sub ou ine is designed o compa ibili y wi h plane-s ess elemen s and ea s
each wo en ab ic- ein o ced lamina as an o ho opic elas ic ma e ial. The ma e ial's s uc u al in eg i y deg ades due o ac o s
such as ib e ailu e, ma ix c acking, and plas ic de o ma ion unde shea -loading condi ions. I u ilizes he maximum s ess ailu e
c i e ion o iden i y he onse o damage wi hin he ib es and inco po a es a damage e olu ion model based on ac u e ene gies
o go e n he subsequen educ ion in s i ness. De ailed in o ma ion abou his cons i u i e model is a ailable in [27–29]. The
cons i u i e ma e ial model implemen ed equi es he de ini ion o he laminae s i ness and s eng h p ope ies, in bo h he
longi udinal and ans e se di ec ions o he ib es. The in alamina ma e ial p ope ies alues we e app oxima ed om he esul s
p esen ed by Hou and Ruiz in [33], and a e shown in Table 1.
The coe icien s go e ning he e olu ion o damage a e de e mined based on he ac u e ene gies associa ed wi h ensile and
comp essi e loading in bo h he longi udinal and ans e se di ec ions o he ib es (deno ed as 𝐺
𝑓
1+
,𝐺
𝑓
1−
,𝐺
𝑓
2+
and 𝐺
𝑓
2−
). Addi ionally,
hese coe icien s depend on pa ame e s 𝑑
12
𝑚𝑎𝑥
and 𝛼
12
. As o he coe icien s go e ning shea plas ici y, hey encompass he ini ial
e ec i e shea yield s ess 𝜎
𝑦0
and he alues o C and p. These pa ame e s and coe icien s a e de e mined h ough he
expe imen al p ocedu e de ailed in [34]. Howe e , conside ing he in icacy o he expe imen al p ocedu e, hese coe icien s we e
es ima ed om [27–29] and a p elimina y pa ame ic s udy was pe o med o adjus hem o he expe imen al e idence. I should
be no ed ha gi en he s uc u al cha ac e is ics o he wo en ab ic ein o cemen (plain wea e), he ac u e ene gies associa ed
wi h bo h he longi udinal and ans e se di ec ions we e assumed o be equi alen . In his way, a alue o 2000 J/m
2
was de ined
o he ac u e ene gies. A simila p ocedu e was implemen ed o he damage e olu ion pa ame e s 𝑑
12
𝑚𝑎𝑥
and 𝛼
12
, and he shea
plas ici y coe icien s, 𝜎
𝑦0
, C and p. The alues employed a e p esen ed in Table 2.
Cha ac e iza ion o Low-Veloci y Impac Damage in Asymme ic Composi e Shells
101
Jou nal o Applied and Compu a ional Mechanics, Vol. 11, No. 1, (2025), 98-109
Table 3. In e lamina p ope ies.
Desc ip ion Symbol Uni s Value
Cohesi e s i ness
𝐾
𝑛𝑛
=
𝐾
𝑠𝑠
=
𝐾
𝑡𝑡
N/mm3 106
Maximum nominal s ess
𝜏
𝑛
0
=
𝜏
𝑠
0
=
𝜏
𝑡
0
MPa 73
F ac u e ene gy
𝐺
𝑛
𝑐
=
𝐺
𝑠
𝑐
=
𝐺
𝑡
𝑐
J/m2 300
In e ac ion pa ame e
𝜂
- 1.45
2.4. In e lamina P ope ies
In he con ex o he cu en s udy, a s ess-based c i e ion was employed o he ac ion-sepa a ion esponse. In his way, he
elas ic beha iou o he cohesi e su aces can be exp essed as:
𝜏
=
𝐾𝜀
⟺
{
𝜏
𝑛
𝜏
𝑠
𝜏
𝑡
}
=
⎣
⎢
⎡
𝐾
𝑛𝑛
0
0
0
𝐾
𝑠𝑠
0
0
0
𝐾
𝑡𝑡
⎦
⎥
⎤
{
𝜀
𝑛
𝜀
𝑠
𝜀
𝑡
}
(1)
whe e 𝜏 deno es he nominal s ess enso , 𝜀 ep esen s he nominal elas ic s ain enso , and 𝐾 co esponds o he elas ici y ma ix.
The subsc ip s 𝑛, 𝑠, and 𝑡 a e used o speci ically designa e he no mal and shea di ec ions, espec i ely. I should be no ed ha
he o -diagonal elemen s in he elas ici y ma ix a e ze o, as he e is no coupling beha iou be ween he no mal and shea
componen s. The ini ial linea esponse, e ec i e un il damage ini ia ion occu s, is con olled by he p esc ibed alues o cohesi e
s i ness: 𝐾
𝑛𝑛
o he no mal di ec ion, and 𝐾
𝑠𝑠
and 𝐾
𝑡𝑡
o he shea di ec ions. In he p esen s udy, he cohesi e s i ness is se o
10
6
N/mm
3
, ollowing he ecommenda ion o Camanho e al. [35]. Addi ionally, i is assumed ha his alue emains consis en
ac oss all di ec ions, i.e., 𝐾
𝑛𝑛
=𝐾
𝑠𝑠
=𝐾
𝑡𝑡
, a simpli ica ion ha has been alida ed in se e al p e ious s udies yielding sa is ac o y
esul s [27–29, 36–38]. The quad a ic ailu e c i e ion based on s ess, as ep esen ed in Eq. (2), is u ilized o an icipa e he ini ia ion
o damage. In his equa ion, 𝜏
𝑛
, 𝜏
𝑠
, and 𝜏
𝑡
s and o he no mal and shea con ac s esses a he in e ace, while 𝜏
𝑛
0
, 𝜏
𝑠0
, and 𝜏
𝑡0
ep esen he peak alues o he nominal s ess. I 's wo h no ing ha he Macaulay b acke s 〈 〉 signi y ha comp essi e s ess
does no ini ia e damage:
(
〈
𝜏
𝑛
〉
𝜏
𝑛
0
)
2
+
(
𝜏
𝑠
𝜏
𝑠
0
)
2
+
(
𝜏
𝑡
𝜏
𝑡
0
)
2
=
1
(2)
Once he damage ini ia ion is eached, cha ac e ized by he quad a ic in e ac ion unc ion eaching a alue o 1, he cohesi e
s i ness expe iences deg ada ion. Equa ion (3) delinea es he p og essi e weakening o he cohesi e su ace. The a iable 𝐷 deno es
he scala damage coe icien ha ep esen s he o e all damage in he ma e ial. Fu he mo e, 𝜏
𝑛
,𝜏
𝑠
and 𝜏
𝑡
ep esen he s ess
componen s p edic ed by he elas ic ac ion-sepa a ion beha iou wi hou damage:
𝜏
𝑛
=
(
1
−
𝐷
)
𝜏

𝑛
,
wi h
𝜏

𝑛
≥
0
𝜏
𝑠
=
(
1
−
𝐷
)
𝜏

𝑠
𝜏
𝑡
=
(
1
−
𝐷
)
𝜏

𝑡
(3)
The ac u e ene gies de ine he e olu ion o he damage coe icien s om he ini ia ion o damage o ul ima e ailu e. The
calcula ion o ac u e ene gy 𝐺
𝑐
adhe es o he Benzeggagh and Kenane (B-K) c i e ion unde mixed-mode loading [39], as
exp essed in Eq. (4), and assuming ha he c i ical ac u e ene gies du ing de o ma ion along shea di ec ions 𝑡 and 𝑛, a e iden ical:
𝐺
𝑐
=
𝐺
𝑛
𝑐
+
(
𝐺
𝑠
𝑐
−
𝐺
𝑛
𝑐
)
(
𝐺
𝑠
𝐺
𝑇
)
𝜂
,
wi h
𝐺
𝑆
=
𝐺
𝑠
+
𝐺
𝑛
and
𝐺
𝑇
=
𝐺
𝑛
+
𝐺
𝑆
(4)
In his equa ion, 𝐺
𝑛
and 𝐺
𝑠
signi y he wo k done by he ac ion in he no mal and shea di ec ions, while 𝐺
𝑛
𝑐
and 𝐺
𝑠
𝑐
ep esen
he c i ical s ain ene gy elease a es equi ed o cause ailu e in he no mal and shea di ec ions. The pa ame e 𝜂 is an in e ac ion
pa ame e wi hin his con ex . The in e lamina p ope ies u ilized in his s udy a e de ailed in Table 3. The alues o he maximum
nominal s ess 𝜏
𝑛
0
=𝜏
𝑠0
=𝜏
𝑡0
and ac u e ene gy 𝐺
𝑛
𝑐
=𝐺
𝑠
𝑐
=𝐺
𝑡𝑐
we e ob ained om [40, 41]. Fu he mo e, he in e ac ion pa ame e 𝜂
was he one adop ed in [27, 28].
2.5. Con ac In e ac ions
A penal y en o cemen con ac me hodology was used o simula e su ace- o-su ace in e ac ions be ween he composi e shell,
impac o , suppo s, and in e aces be ween laminas. F ic ion coe icien s we e speci ied o di e en con ac pai s, conside ing he
na u e o he ma e ials and in e aces. The ic ion coe icien alues, deno ed as 𝜇, pe inen o me al-composi e con ac s and ully
delamina ed in e aces, we e ob ained om li e a u e. Subsequen ly, a alue o 𝜇=0.3 was speci ied o he con ac be ween he
hemisphe ical head o he impac o and he uppe su ace o he composi e lamina e. Fu he mo e, a alue o 𝜇=0.7 was employed
o desc ibe he in e ac ion be ween he suppo su aces and he composi e lamina e su aces. The ic ion coe icien a he
in e ace be ween he laye s was se o 𝜇=0.5.
3. Valida ion o he Nume ical Model
The alida ion p ocess p esen ed in his sec ion in ol es a di ec compa ison be ween he nume ical p edic ions and he
expe imen al esul s desc ibed in [25]. The specimens used in he expe imen al es s had eigh wo en ab ic laye s s acked in a
single di ec ion, wi h he wa p o we di ec ion aligned pa allel o he semicylind ical axis. This s acking sequence will be deno ed
as [0]
8
. No ice ha he alida ion o he nume ical model is c ucial o ensu e i s accu acy and eliabili y. To achie e his, he model's
p edic ions we e compa ed wi h expe imen al da a ob ained om symme ic specimens, which se ed as a benchma k o
assessing i s pe o mance. Despi e he asymme y in oduced in subsequen analyses, he key pa ame e s main ained hei
uni o mi y ac oss he asymme ical FE models. This included p ese ing iden ical geome ic con igu a ions, bounda y condi ions,
and ma e ial p ope ies, ensu ing a consis en basis o compa ison and e alua ion.
102
L.M. Fe ei a e al., Vol. 11, No. 1, 2025
Jou nal o Applied and Compu a ional Mechanics, Vol. 11, No. 1, (2025), 98-109
Table 4. Asymme ic s acking sequences analysed.
S acking Sequence Simpli ied no a ion
(0/0/0/0/45/45/45/45) [04,454]
(0/0/0/0/0/0/45/45) [06,452]
(0/0/0/0/0/0/0/45) [07,451]
(45/45/45/45/0/0/0/0) [454,04]
(45/45/45/45/45/45/0/0) [456,02]
(45/45/45/45/45/45/45/0) [457,01]
To assess he model's accu acy, he nume ical and expe imen al o ce- ime and ene gy- ime cu es a e analysed, as shown in
Fig. 2(a). I is e iden ha he nume ical p edic ions exhibi a sa is ac o y ag eemen wi h he expe imen al e idence ac oss he
o ce and ene gy his o y cu es. The maximum o ce, a pa ame e ha is o en associa ed wi h he impac 's peak load-bea ing
capaci y, shows a sa is ac o y nume ical-expe imen al co ela ion. Al hough he nume ical p edic ion indica es a sligh ly lowe
alue, his de ia ion is wi hin an accep able e o ma gin o a ound 8.5%. The elas ic ene gy, which ep esen s he ene gy abso bed
by he ma e ial up o he poin o maximum impac o ce, exhibi s good ag eemen wi h negligible e o . I can be seen in Fig. 2(b)
ha he o al ene gy, as indica ed by he ABAQUS/Explici ou pu ETOTAL, emains s able h oughou he simula ion, e lec ing he
p ope de ini ion o ime inc emen s. Fu he mo e, he a io be ween he a i icial s ain ene gy (ALLAE ou pu ) and in e nal ene gy
(ALLIE ou pu ) ea i ms he app op ia eness o he hou glass con ol me hod ha was implemen ed.
In summa y, al hough small de ia ions a e no iceable in he con ex o maximum o ce, he o e all alignmen be ween FE
model's p edic ions and he impac esponse o he semicylind ical composi e shells es ed is indica i e o he e ec i eness and
eliabili y o he FE model.
4. Resul s
In his sec ion, nume ical p edic ions ela ed o he impac esponse o cu ed lamina ed composi es in ol ing asymme ical
s acking sequences a e p esen ed and discussed. Fo his pu pose, eigh wo en ab ic laye s a e placed in wo di e en di ec ions,
speci ically 0 and 45 in ela ion o he semicylind ical axis, and he con igu a ions analysed a e shown in Table 4. Fu he mo e, o
compa e he impac pe o mance o asymme ical and symme ical lamina es, he esul s a e jux aposed wi h hose ob ained o
he symme ic lamina e sequence [0
8
], alida ed in Sec ion 3.
The nume ically p edic ed o ce- ime and o ce-displacemen cu es o he s acking sequences p esen ed in Table 4 a e
depic ed in Fig. 3. Fo all he con igu a ions analysed, i is possible o obse e a esponse ha is ypical o cu ed lamina es when
subjec ed o low- eloci y impac loads. To be mo e speci ic, he p o ile o he cu es is cha ac e ized by an inc ease in o ce up o a
maximum alue, P
max
, a e which he e is a mo e o less ab up d op. The P
max
alue, which is s ongly in luenced by he impac
ene gy, es ablishes he maximum load ha a composi e lamina e can esis be o e being se iously damaged. The beha iou
desc ibed abo e is pe ec ly in line wi h ha obse ed in o he s udies epo ed in he li e a u e [23, 25, 42-44], whe e he oscilla ions
seen in he cu es a e caused by he elas ic wa e and he ib a ions o he samples [45, 46]. Fu he mo e, because he impac o
cons an ly e u ns, he impac ene gy is insu icien o encou age ull pene a ion and, in his con ex , all he lamina es we e
a ec ed by a non-pe o a ing impac . Figu e 4 con i ms his highligh , whe e he loss o con ac be ween he s ike and he sample
co esponds o he beginning o he cu e's pla eau [47]. This ene gy co esponds o he ene gy abso bed by he specimen, and he
elas ic ene gy ( es o ed ene gy) can be es ima ed as he di e ence be ween he abso bed ene gy and he ene gy a peak load [48].
The e o e, o a clea e unde s anding o he placemen o he 0° o 45° laye s in he op/bo om hal o he composi e shells,
Fig. 5 di ec ly compa es con igu a ions [0
4
,45
4
] and [45
4
,0
4
], while Table 5 summa izes he esul s o all con igu a ions.
In gene al, he o e all impac esponses o all lamina es a e qui e simila , which is in line wi h he s udy de eloped by Sasikuma
e al. [22]. Howe e , a mo e de ailed analysis shows ha , in e ms o maximum impac o ce, i dec eases as he numbe o laye s
a 0 inc eases and when hey a e placed in he uppe hal o he cu ed lamina e. Fo example, he maximum impac o ce
dec eases by a ound 11.3% when compa ing he alues ob ained be ween [0
4
,45
4
] and [0
7
,45
1
]. On he o he hand, cu ed lamina es
wi h he op laye s in a 45 di ec ion a e cha ac e ized by a luc ua ion in he maximum impac o ce a ound an a e age alue o
2.03 kN, bu when he [45
4
,0
4
] con igu a ion is compa ed wi h he simila 0 con igu a ion ([0
4
,45
4
]), he impac o ce is 6% highe .
The e o e, acco ding o Sasikuma e al. [22], di e en delamina ion h eshold loads a e expec ed and, consequen ly, damages o
di e en se e i y.
(a) (b)
Fig. 2. Valida ion o he nume ical model o a [0]8 composi e shell: (a) Expe imen al and nume ical o ce and ene gy his o ies, (b) To al ene gy,
in e nal ene gy, and a i icial s ain ene gy his o ies.

Cha ac e iza ion o Low-Veloci y Impac Damage in Asymme ic Composi e Shells
103
Jou nal o Applied and Compu a ional Mechanics, Vol. 11, No. 1, (2025), 98-109
Fig. 3. Nume ical p edic ed o ce- ime and o ce-displacemen esul s o he asymme ic s acking sequences.
Fig. 4. Nume ical p edic ed ene gy- ime esul s o he asymme ic s acking sequences.
(a) (b)
Fig. 5. Nume ical p edic ed o ce- ime and o ce-displacemen esul s o he asymme ic s acking sequences [04,454] and [454,04].
104
L.M. Fe ei a e al., Vol. 11, No. 1, 2025
Jou nal o Applied and Compu a ional Mechanics, Vol. 11, No. 1, (2025), 98-109
Table 5. Maximum o ce, maximum displacemen , con ac ime and abso bed ene gy o he analysed s acking sequences.
S acking sequence Maximum Con ac Time (ms) Abso bed Ene gy (J)
Fo ce (kN) Displacemen (mm)
[04,454] 2.03 4.33 8.15 3.37
[06,452] 1.92 4.23 8.51 3.60
[07,451] 1.80 4.27 8.73 3.76
[454,04] 2.15 4.02 7.61 3.67
[456,02] 1.89 4.17 7.61 3.52
[457,01] 2.05 4.15 7.20 3.32
[08] 1.80 4.27 8.73 3.76
Rega ding he impac displacemen , bo h con igu a ions luc ua e a ound di e en a e age alues, which a e abou 4.28 mm
o cu ed lamina es wi h a 0 o ien a ion placed on he op laye s and 4.11 mm when he op laye s a e a 45. Howe e , all
con igu a ions wi h he 45 o ien a ion a he op ha e lowe displacemen alues han hose wi h he 0 o ien a ion. Fo example,
he displacemen is a ound 7.2% lowe when compa ing he alues ob ained be ween [0
4
,45
4
] and [45
4
,0
4
]. Conside ing he es ima ed
con ac ime, i is highe o he cu ed lamina es wi h he 0di ec ion a he op, eaching a di e ence o 7.1% be ween [0
4
,45
4
] and
[45
4
,0
4
]. On he o he hand, while inc easing he laye s a 0 a he op o cu ed lamina es leads o an inc ease in con ac ime, he
opposi e occu s o lamina es a 45. I is obse ed ha be ween [0
4
,45
4
] and [0
7
,45
1
] he inc ease is a ound 7.2%, while be ween
[45
4
,0
4
] and [45
7
,0
1
] he dec ease is abou 5.4%.
Finally, he end obse ed o he abso bed ene gy is simila o ha o he con ac ime, bu when compa ing he con igu a ions
[0
4
,45
4
] and [45
4
,0
4
] he abso bed ene gy in he i s case is a ound 8.2% lowe . In his case, he inc ease be ween [0
4
,45
4
] and [0
7
,45
1
]
is a ound 11.6%, while be ween [45
4
,0
4
] and [45
7
,0
1
] he dec ease is a ound 9.5%, wi h he pa icula i y o he abso bed ene gy being
e y simila be ween he con igu a ions [0
4
,45
4
] and [45
7
,0
1
]. The e o e, because he abso bed ene gy is ela ed o he se e i y o he
damage [47,49], and acco ding o Sasikuma e al. [20] his ype o lamina es has se e al delamina ed in e aces, al hough one is
dominan ( he one ha go e ns he o al delamina ion p o ile and plays a dominan ole in he damage ole ance o he s uc u e),
a de ailed analysis o he damage mechanisms will be de eloped o each lamina e and ela ed o he abso bed/dissipa ed ene gy.
Fo his pu pose, an analysis o he ene gy abso p ion/dissipa ion mechanisms linked o low- eloci y impac s on asymme ic
semicylind ical composi e shells is p esen ed. In con as o unlike expe imen al es s, he gene a ed FE models o e he capabili y
o quan i y ene gy abso p ion ac oss mul iple mechanisms. These mechanisms encompass he in alamina damage, accoun ing
o ene gy dissipa ion esul ing om ib e damage, in e lamina damage, e lec ing he ene gy dissipa ion due o delamina ion,
and ic ion which encompasses a ious in e ac ions, including hose be ween he igid impac o and he composi e shell, as well
as in e ac ions wi hin he delamina ed laye s. The con ibu ion o each o he ene gy-abso p ion mechanisms o he a ious
asymme ic s acking sequences and he symme ic [0
8
] s acking sequence a e p esen ed in Fig. 6. No ice ha he ene gy dissipa ion
mechanisms we e iden i ied by analysing speci ic ABAQUS ou pu s: in alamina damage ( ep esen ed as ALLPD – Plas ic
dissipa ion), in e lamina damage (ALLDMD – Damage dissipa ion), and ic ional e ec s (ALLFD - F ic ional dissipa ion).
O e all, a clea pa e n eme ges whe e mos o he ene gy abso p ion occu s h ough in alamina damage (comp ising 48.7%
o 57.5%), ollowed by delamina ion ( anging om 32.8% o 38.4%), and ic ion ( alling wi hin he 7.1% o 15.5% ange). These esul s
a e consis en wi h he nume ical p edic ions o he low- eloci y impac esponse o asymme ic composi es p esen ed by
Sasikuma e al. [20]. These au ho s also iden i ied ib e ailu e (in alamina damage) as he main ene gy dissipa ion mechanism.
I is wo h no ing ha he con ibu ion o a i icial s ain ene gy dissipa ion emains minimal and consis en ly below 2% o he
o al impac ene gy ac oss all s acking sequences. This consis ency unde sco es ha he esul s emain una ec ed by his ac o
[30].
Acco ding o Fig. 6, in s acking sequences whe e he uppe laye s a e o ien ed a 45, he e is a ma ginally g ea e ene gy
dissipa ion a ibu ed o ib e ailu e (in alamina damage) and delamina ion when compa ed o hose wi h a 0 o ien a ion. In
he i s se o con igu a ions ([45
4
,0
4
], [45
6
,0
2
] and [45
7
,0
1
]), in alamina damage accoun s o a ange o 48.7% o 51.1%, while
delamina ion cons i u es be ween 37.9% o 32.8% o he o e all ene gy dissipa ion. Con e sely, o he second se ([0
4
,45
4
], [0
6
,45
2
]
and [0
7
,45
1
]), he alues exhibi a ia ions be ween 53.2% and 57.5% o in alamina damage, and 32.8% o 38.4% o delamina ion.
Fu he mo e, i can be obse ed ha ene gy dissipa ed by hese damage mechanisms (in alamina damage and delamina ion) a e
no subs an ially a ec ed by he changes in he s acking sequence in he lowe hal o he s acking sequence.
Fig. 6. Con ibu ion o a ious ene gy-abso p ion mechanisms: in alamina damage, delamina ion, and ic ion.
Cha ac e iza ion o Low-Veloci y Impac Damage in Asymme ic Composi e Shells
105
Jou nal o Applied and Compu a ional Mechanics, Vol. 11, No. 1, (2025), 98-109
The [45
7
,0
1
] con igu a ion exhibi s a no ewo hy inc ease in in alamina damage and a co esponding dec ease in in e lamina
damage compa ed o o he con igu a ions. Acco ding o Classical Lamina e Theo y, any al e a ion in he ib e o ien a ion angle
induces a ia ions in he lamina e's appa en in-plane s i ness p ope ies. Speci ically, he inc ease o 45 laminas in he lamina e
con igu a ion leads o a educ ion o he in-plane elas ic modulus and an inc ease o he in-plane shea modulus, he eby
in luencing he impac esponse o he lamina es and subsequen ly he mechanisms go e ning ene gy dissipa ion [13]. This
phenomenon may elucida e he obse ed inc ease in in alamina damage pe cen age and dec ease in in e lamina damage o
he [45
7
,0
1
] con igu a ion. Fu he mo e, a supplemen a y s udy e ealed ha i a s acking sequence wi h [45
8
] is conside ed, he e
is a sligh inc ease in he pe cen age o ene gy abso bed by in alamina damage and a co esponding sligh dec ease in
in e lamina damage compa ed o he la e con igu a ion. This unde sco es he impac o appa en in-plane s i ness p ope ies
on he impac pe o mance o composi e shells.
F ic ion accoun s o he lowes ene gy dissipa ion among he mechanisms. Ne e heless, i s signi icance should no be
unde s a ed, as i s ill cons i u es up o abou 15% o he o al dissipa ed ene gy. This alue is in good ag eemen wi h he indings
p esen ed by Lopes e al. [50]. These au ho s de eloped a nume ical analysis o low- eloci y impac damage in dispe sed s acking
sequence composi e lamina es, and hei s udy simila ly indica ed ha ic ion cons i u es he mechanism wi h he leas ene gy
dissipa ion, accoun ing o app oxima ely 15% o he o al impac ene gy. Fu he mo e, i is e iden ha ic ional dissipa ion is
mo e p onounced in asymme ic lamina es wi h he uppe laye s aligned a 0, wi h alues anging om 12.9% o 15.5%. On he
o he hand, o s acking sequences wi h he uppe laye s aligned a 45, he ic ional dissipa ion alues ange om 7.1% o 8.2%.
Once again, i is appa en ha al e ing he alignmen o he bo om laye s has a negligible impac on he ene gy dissipa ed h ough
ic ion.
As i is possible o app ecia e in Table 5, he esul s highligh a simila i y in he p edic ed impac beha iou be ween he
symme ic lamina e [0
8
] and he asymme ic lamina e [0
7
,45
1
], in e ms o maximum o ce, maximum displacemen , con ac ime,
and abso bed ene gy. Addi ionally, i was obse ed ha he con ibu ions o he ene gy abso p ion mechanisms (in alamina
damage, delamina ion, and ic ion) o hese wo lamina e con igu a ions a e also compa able, as illus a ed in Fig. 6. This simila i y
ein o ces he p e ious discussed indings in which, o he analysed s acking sequences and load condi ions, he o ien a ion o
he bo om laye s has a negligible e ec on he lamina e's pe o mance.
Conside ing ha in alamina damage accoun s o he mos subs an ial po ion o ene gy dissipa ion, an analysis was ca ied
ou o de e mine he laye s ha con ibu e he mos o his dissipa ion. Consequen ly, he ene gy dissipa ed by in alamina
damage o each laye wi hin a ious asymme ic s acking sequences and he symme ic [0
8
] s acking sequence a e p esen ed in
Fig. 7.
The esul s show ha he amoun o ene gy dissipa ed by in alamina damage dec eases, s eadily in gene al, om he op o
he bo om laye s ac oss all conside ed s acking sequences, ag eeing wi h wha was obse ed by Sasikuma e al. [20]. These esul s
we e expec ed, as when he e is no punc u ing in he specimens, ib e damage p edominan ly occu s in laye s ha a e in close
con ac wi h he impac o [23]. I is possible o obse e ha he i s laye o s acking sequences [45
4
,0
4
] and [0
4
,45
4
] exhibi s he
highes (18.8%) and lowes (15.3%) ene gy dissipa ion, espec i ely. Mo eo e , he op ou laye s o s acking sequence [45
4
,0
4
]
dissipa e abou 17.3% mo e ene gy han hei coun e pa s in [0
4
,45
4
]. On he o he hand, he opposi e end eme ges o he bo om
ou laye s, wi h [0
4
,45
4
] demons a ing app oxima ely 30% g ea e ene gy dissipa ion han [45
4
,0
4
]. A signi ican d op in ene gy
dissipa ion in s acking sequence [45
4
,0
4
] is pa icula ly e iden be ween laye 4 and 5, co esponding o he shi in he wo en
ab ic's alignmen om 45 o 0. These esul s unde sco e ha he dis ibu ion o ene gy dissipa ed by in alamina damage is
in luenced by laye posi ioning and o ien a ion. Placing laye s o ien ed a 45 ei he in he uppe o lowe hal o he specimen
esul s in inc eased ene gy dissipa ion compa ed o hose o ien ed a 0. While as men ioned be o e, he gene al end ac oss all
con igu a ions indica es a dec ease in he ene gy dissipa ed by in alamina damage om op o bo om laye s, ce ain s acking
sequences exhibi a sligh de ia ion. No ably, some con igu a ions show an inc ease in ene gy dissipa ion a posi ions 6 and 8. Fo
ins ance, in Fig. 7, laye 6 o s acking sequence [0
4
,45
4
] he pe cen age o ene gy dissipa ed by in alamina damage ises om 12.7%
a laye 5 o 14% a laye 6. The e appea s o be no disce nible co ela ion be ween laye o ien a ions and hei posi ions ha could
explain his sub le ye sudden inc ease. Fu he in es iga ion is wa an ed o elucida e he unde lying ac o s con ibu ing o his
phenomenon.
In he case o he emaining asymme ic s acking sequences, whe e he numbe o laye s o ien ed a 0 and 45 g adually
inc eases wi hin he lowe hal o he lamina e hickness, he esul s e eal a mo e uni o m decline in ene gy dissipa ion when
compa ed wi h [45
4
,0
4
] and [0
4
,45
4
]. Fu he mo e, no end eme ges om he change in he laye ’s o ien a ion, as he s acking
sequences exhibi compa able dis ibu ions o ene gy dissipa ed by in alamina damage. As depic ed in Fig. 7, he ene gy
dissipa ion caused by in alamina damage in each laye exhibi s a consis en pa e n ac oss bo h he asymme ic s acking
sequence [0
7
,45
1
] and he symme ic s acking sequence [0
8
].
Fig. 7. Ene gy dissipa ed by in alamina damage in each laye o he analysed s acking sequences.
106
L.M. Fe ei a e al., Vol. 11, No. 1, 2025
Jou nal o Applied and Compu a ional Mechanics, Vol. 11, No. 1, (2025), 98-109
To complemen he p eceding indings, Fig. 8 p esen s he in alamina damage p edic ed by he nume ical models. I is
impo an o obse e ha he depic ed damage esul s om he in e play o ensile and comp essi e ib e ailu es along bo h
di ec ions o he wo en ab ic, as well as shea damage. The di e se o ien a ions o he ailed ib es a e dis inc ly disce nible ac oss
he semicylind ical composi e shells, aligning wi h he asymme ic s acking sequences o he lamina es.
In e ms o in alamina damage dissipa ion, i becomes e iden ha s acking sequences wi h he uppe laye s ( he impac side)
o ien ed a 45, as depic ed in Fig. 6, exhibi highe le els o damage. This obse a ion sugges s ha hese lamina e con igu a ions
expe ience a mo e ex ensi e deg ee o damage esul ing om ib e ailu e. I 's impo an o no e ha hese di e ences in damage
ex en among he asymme ic s acking sequences a e no easily disce nible in Fig. 8. Howe e , a dis inc pa e n eme ges when
conside ing he p ojec ed in alamina damaged a ea in ela ion o he s acking sequence. Fo ins ance, when examining s acking
sequences [45
4
,0
4
], [45
6
,0
2
] and [45
7
,0
1
], i is no iceable ha he p edic ed in alamina damaged egion dec eases as he numbe o
laye s a 45 inc ease. Howe e , he ene gy dissipa ed by his mechanism sligh ly inc eases, as shown in Fig. 6. These esul s imply
ha inc easing he numbe o laye s a 45 does no necessa ily educe he o e all amoun o in alamina damage. Ins ead, i
con ibu es o cons aining he ex en o he p ojec ed in alamina damaged a ea a ound he impac poin . Fo s acking sequences
wi h he uppe laye s o ien ed a 0, ha is [0
4
,45
4
], [0
6
,45
2
] and [0
7
,45
1
], a simila end is disce nible. Inc easing he numbe o laye s
o ien ed a 45 in hese sequences se es o diminish he p ojec ed damaged a ea su ounding he impac poin .
To demons a e his e idence, Fig. 9 p o ides a isual ep esen a ion o he delamina ed a eas wi hin he asymme ic s acking
sequences. I 's wo h no ing ha hese esul s speci ically pe ain o ully delamina ed in e ace nodes, which a e nodes whe e he
CSMG ou pu has eached a alue o 1. The delamina ed a ea alues shown in Fig. 9 a e a cumula i e sum o delamina ed in e ace
a eas, and hey do no e lec he p ojec ed a ea.
In all he s acking sequences, a ypical low- eloci y impac damage mo phology is obse ed. This mo phology is cha ac e ized
by a spi al s ai case delamina ion pa e n, whe e he delamina ions a e mo e ex ensi e in he lowe in e aces and diminish
owa ds he uppe in e aces (side o impac ) [29, 51, 52]. This pa e n a ises due o bending o he composi e shell du ing he impac
e en , which consequen ly causes highe in e lamina shea s esses o appea on he lowe in e aces. Ne e heless, i can be
app ecia ed ha he choice o s acking sequence can exe a signi ican in luence on he o al delamina ed a ea, wi h di e ences
eaching up o app oxima ely 25.4%. This dispa i y is especially e iden when compa ing [45
4
,0
4
] and [45
7
,0
1
]. A no able educ ion in
he delamina ed a ea is e iden when compa ing s acking sequences [45
6
,0
2
] o [45
7
,0
1
]. This can be a ibu ed o highe in e lamina
shea s esses de eloping on he lowe in e aces and an inc ease in he numbe o laye s a 45, which cause an augmen a ion o
he in-plane shea modulus o he lamina e. The e o e, con ibu ing o he educ ion o delamina ion in he laye s mos a ec ed by
i . This dual e ec unde sco es he complex in e play be ween lamina e con igu a ion, in e lamina s esses, and ma e ial
p ope ies in in luencing delamina ion beha iou .
Fig. 8. In alamina damage o he asymme ic s acking sequences.
Fig. 9. Delamina ed a eas o he asymme ic s acking sequences.