E alua ing ailu e modes h ough ene gy dissipa ion mechanisms
in hyb id composi es unde bending loads
J.M. Pa en e
a
, L.M. Fe ei a
b,c,*
, P.N.B. Reis
d
a
C-MAST, Cen e o Mechanical and Ae ospace Science and Technologies, Uni e sidade da Bei a In e io , Rua Ma quˆ
es d’A ila e Bolama 6201-
001 Co ilh˜
a, Po ugal
b
G upo de Elas icidad y Resis encia de Ma e iales, Escuela T´
ecnica Supe io de Ingenie ía, Uni e sidad de Se illa, Camino Descub imien os, S/N,
Se illa 41092, Spain
c
Escuela Poli ´
ecnica Supe io , Uni e sidad de Se illa, C/ Vi gen de ´
A ica, 7, Se illa 41011, Spain
d
Depa men o Mechanical Enginee ing, CEMMPRE, ARISE, Uni e si y o Coimb a 3030-788 Coimb a, Po ugal
ARTICLE INFO
Keywo ds:
Polyme ma ix composi es (PMCs)
Hyb idiza ion e ec
Bending esponse
Damage mechanisms
Nume ical analysis
Ene gy balance
ABSTRACT
Unde s anding he bending beha iou o composi e ma e ials is essen ial o e ec i e design,
pa icula ly wi h he inc easing use o complex componen s wi h mul iple bends. Ca bon ib es
a e o en p e e ed in such applica ions due o hei supe io ensile p ope ies; howe e , gi en
hei limi ed comp essi e pe o mance, hyb idiza ion wi h glass ib es is commonly used. In his
con ex , his s udy analyses he ene gy con ibu ions o in alamina and in e lamina damage
mechanisms leading o ailu e in hyb id ca bon/glass ab ic- ein o ced lamina es unde bending
loads. Di e en hyb idiza ion a ios and con igu a ions, speci ically he posi ioning o glass and
ca bon ab ic ein o cemen s ela i e o he load applica ion, a e e alua ed expe imen ally and
nume ically. The expe imen al esul s show ha he bending pe o mance o hyb id lamina es
alls be ween hose o non-hyb id ca bon (8C) and glass (8G) lamina es, wi h a clea dependence
on he hyb idisa ion a io. When glass ib es a e posi ioned in he comp ession egion, he hyb id
lamina es exhibi sligh ly highe o ce and displacemen alues. No ably, he 3G/5C con igu a ion
(glass on he comp ession side) achie es a o ce and a displacemen o 255.1 N and 4.23 mm,
espec i ely, ep esen ing inc eases o app oxima ely 5.9% and 13.1% compa ed o he 5C/3G
con igu a ion, which eaches 240.9 N and 3.74 mm. Nume ical models show a good ag eemen
wi h he expe imen al da a, wi h o ce e o s p edominan ly wi hin ±5.3% and displacemen
e o s wi hin ±6.8%. Non-hyb id con igu a ions demons a e a mo e p edic able damage p o-
g ession, whe eas hyb id lamina es in oduce a iabili y due o di e ences in ibe ype and
placemen , in luencing o e all ene gy dissipa ion and s uc u al pe o mance. Addi ionally, he
ene gy analysis e eals ha in alamina damage is he dominan ene gy dissipa ion mechanism,
ollowed by delamina ion and ic ion.
* Co esponding au ho a : G upo de Elas icidad y Resis encia de Ma e iales, Escuela T´
ecnica Supe io de Ingenie ía, Uni e sidad de Se illa,
Camino Descub imien os, S/N, Se illa 41092, Spain.
E-mail add ess: [email p o ec ed] (L.M. Fe ei a).
Con en s lis s a ailable a ScienceDi ec
Enginee ing F ac u e Mechanics
jou nal homepage: www.else ie .com/loca e/eng acmech
h ps://doi.o g/10.1016/j.eng acmech.2025.110855
Recei ed 26 Oc obe 2024; Recei ed in e ised o m 20 Decembe 2024; Accep ed 20 Janua y 2025
Enginee ing F ac u e Mechanics 316 (2025) 110855
A ailable online 21 Janua y 2025
0013-7944/© 2025 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY license
( h p://c ea i ecommons.o g/licenses/by/4.0/ ).
1. In oduc ion
The e a e inc easing challenges o enginee s o use ligh e and mo e e icien ma e ials wi hou comp omising hei mechanical
pe o mance. I is in his con ex ha composi e ma e ials eme ge as he a p omising subs i u e o adi ional me al-based ma e ials
[1,2]. In addi ion o a polyme -based ma ix, hey can use a ious ib es as ein o cing elemen s, aking ad an age o hei in insic
p ope ies [3,4]. In he case o ein o cemen , he aim is o p o ide s eng h and s i ness o wi hs and he applied load [5], while he
ma ix ac s as a s ess dis ibu o be ween he ein o cing ib es, as well as p o ec ing he ein o cing ib es om ex e nal ac o s (i.e.
mois u e, co osion, chemicals, e c.) [6,7].
F om his pe spec i e, ca bon ib es a e p e e ed o many enginee ing applica ions, p ima ily due o hei excellen ensile
p ope ies. Howe e , hei poo pe o mance unde comp essi e loads ep esen s a signi ican limi a ion, educing hei b oade
applica ion. Fo example, his d awback is pa icula ly e iden in ca bon ib e- ein o ced composi es used in s uc u al elemen s
subjec ed o bending loads, a loading mode ha is gaining impo ance wi h he de elopmen o inc easingly complex componen s wi h
mul iple bends, designed o minimize welding and assembly equi emen s. In his con ex , he e is in e es in combining a ious ypes
o ib es (hyb idiza ion) o imp o e he mechanical pe o mance o composi e lamina es. Fo example, hyb idiza ion can inc ease
damage ole ance by combining ib es ha p omo e s eng h wi h o he s ha ha e highe duc ili y and, consequen ly, be e impac
pe o mance [8–11], o simply o ensu e a wide ange o applica ions, whe e ib es wi h highe mechanical pe o mance can be
combined wi h mo e economical ones o achie e a balance be ween mechanical p ope ies and cos [10,12]. These ad an ages
ansla e in o signi ican ad ancemen s ac oss a ious sec o s [13–16]. In au omo i e applica ions, o example, hyb id composi es can
enable he p oduc ion o ligh e and s onge componen s such as bumpe s and body panels [17,18]. In e ms o ma ine indus y, hey
can con ibu e o mo e du able and cos -e ec i e boa hulls [19–21], while in he ae ospace sec o , hey b ing ad an ages in he
Nomencla u e
Abb e ia ion Desc ip ion
VG
Glass ib e olume ic ac ion
VC
Ca bon ib e olume ic ac ion
VmMa ix olume ic ac ion
Thickness o he lamina e
ρ
Densi y
E1+,−Tensile/comp essi e Young’s modulus along ib e di ec ion 1
E2+,−Tensile/comp essi e Young’s modulus along ib e di ec ion 2
G12 In-plane shea modulus
ν
12 In-plane Poisson’s a io
X1+,−Tensile/comp essi e s eng h along di ec ion 1
X2+,−Tensile/comp essi e s eng h along di ec ion 2
S12 In-plane shea s eng h
G1,2
In alamina ac u e oughness along di ec ion 1 and 2
dmax
12 Maximum shea damage
σ
y0Ini ial e ec i e shea yield s ess
CCoe icien in ha dening equa ion
pPowe e m in ha dening equa ion
knElas ic no mal in e lamina s i ness
ksElas ic shea in e lamina s i ness
k Elas ic angen ial in e lamina s i ness
τ
0
nMaximum no mal con ac s ess
τ
0
sMaximum 1
s
shea con ac s ess
τ
0
Maximum 2
nd
shea con ac s ess
GIc In e lamina no mal ac u e oughness
GIIc In e lamina 1
s
shea ac u e oughness
GIIIc In e lamina 2
nd
shea ac u e oughness
η
Benzeggagh-Kenane exponen
CdDila a ional wa e speed
Lmin Smalles cha ac e is ic leng h o he elemen
Δ Time inc emen
FE Fini e Elemen
3PB 3-Poin Bending
CDM Con inuum Damage Mechanics
SbCB Su ace-based Cohesi e Beha iou
J.M. Pa en e e al.
Enginee ing F ac u e Mechanics 316 (2025) 110855
2
manu ac u e o ligh weigh and high-s eng h ai c a componen s, such as wings and uselage panels [22–24]. Fu he mo e, hyb id
composi es also ha e se e al ad an ageous applica ions in he enewable ene gy sec o , such as wind u bine blades o inc ease hei
imp o ed s eng h- o-weigh a io and, consequen ly, inc ease ene gy cap u e e iciency [25–27].
Howe e , o in eg a e his ype o ma e ial in o indus ial applica ions, equi es he e alua ion o i s s a ic, a igue, and iscoelas ic
pe o mance. This da a is c ucial o he design o sa e, eliable, and e icien composi e s uc u es. Bending es s a e widely conside ed
as an essen ial me hod o e alua e he mechanical p ope ies o composi e ma e ials. These es s p o ide key pa ame e s such as
bending modulus, bending s eng h, and ac u e oughness, which a e used o p edic he ma e ial beha iou unde se ice condi-
ions. Mo eo e , he aniso opic and he e ogeneous na u e o composi e ma e ials leads o he de elopmen o a ious ailu e
mechanisms, such as ensile and comp essi e ib e ac u e, enclosed o side-opened delamina ions (in e lamina shea ), and localized
c ushing unde he c osshead, which can be s udied h ough bending es s [28–31].
Nume ical simula ions, can p o ide an excellen ool o imp o e he unde s anding o he ma e ial’s esponse, he eby con ibu ing
o he de elopmen o sa e , mo e e icien , and inno a i e composi e s uc u es. The e o e, nume ous s udies in he li e a u e ha e
employed Fini e Elemen (FE) models o in es iga e he bending beha iou o hyb id composi es. Fo example, Dong e al. [32–37]
ocused on modelling he bending esponse o hyb id composi es ein o ced wi h ca bon and glass ib es. They concluded ha he
op imal a io o glass o ca bon ib e is 0.125 [34] and ha glass and ca bon ib e con igu a ion in luences he ailu e beha iou o he
lamina es [33]. These au ho s also ound ha placing glass ib es on he comp essi e side can imp o e he bending p ope ies o he
hyb id composi e compa ed o an all-ca bon composi e, while hei placemen on he ensile side has a nega i e e ec [33,36]. Jiang
e al. [38] ca ied ou an expe imen al and nume ical s udy o in es iga e he in e ac i e ailu e o a hyb id composi e comp ising
ca bon, Ke la ®, and glass ib es. They concluded ha he hyb id ca bon/Ke la ® and ca bon/glass/Ke la ® composi es exhibi ed
supe io ene gy abso p ion capabili ies compa ed o ca bon ib e and Ke la ® only composi es. Fu he mo e, he au ho s epo ed ha
he mechanical p ope ies can be imp o ed h ough he in e play be ween b i le and duc ile ailu e mechanisms. Bu gani e al.
analysed he bending ailu e o a ca bon ib e- ein o ced composi e by compa ing expe imen al and nume ical esul s [39]. They
ound ha he Ho man and Tsai-Wu c i e ia we e he mos accu a e in p edic ing he onse o bending ailu e. Addi ionally, he s udy
e ealed ha he ype o ca bon ib e and esin used could in luence he composi e’s ailu e mechanisms. Massa wa e al. [40]
employed FE models o s udy he ailu e beha iou o a hyb id composi e composed o glass and ca bon ib es. They obse ed ha he
posi ioning o he ca bon laye s ela i e o he neu al axis signi ican ly in luenced he bending modulus. Fu he mo e, damage
ini ia ion occu ed in he comp essi e ou e laye s and hen p opaga ed h oughou he specimen. Rega ding he ene gy dissipa ion
capabili ies o composi e ma e ials, he s udies conduc ed by Jiang e al. [41], and Jiang and Ren [42], demons a ed he impo ance o
enginee ed in e aces in enhancing he pe o mance o CFRP composi es. Th ough he inco po a ion o mic o- and nano ille s and he
applica ion o echniques such as CNT-modi ied esin p e-coa ing, hese in e aces can be ailo ed o p omo e speci ic ailu e mech-
anisms ha maximize ene gy abso p ion.
F om he a ailable li e a u e, i is possible o conclude ha mos s udies ocus on he nume ical eplica ion o expe imen al da a
and, in some cases, on analysing he mo phology o he esul ing damage. While hese s udies ha e signi ican ly ad anced he un-
de s anding o he o e all beha iou o hyb id ib e- ein o ced composi es, some aspec s emain unde explo ed, pa icula ly ega ding
he cha ac e iza ion o he ini ia ion and p og ession o damage. Mo eo e , o he bes o he au ho s’ knowledge, no s udy has
sys ema ically quan i ied he ene ge ic con ibu ions o damage mechanisms a he in a- and in e lamina le el, speci ically in hyb id
ab ic- ein o ced composi es. To add ess hese gaps, he p esen s udy in es iga es he bending esponse o hyb id ab ic- ein o ced
composi e lamina es wi h a ious hyb idiza ion a ios and ib e posi ioning, ocusing on nume ically p edic ing he ene gy dissipa-
ion con ibu ions o ib e ailu e and ma ix c acking (in alamina damage), delamina ion (in e lamina damage), and ic ion. Fo
his pu pose, and conside ing ha FE modelling p o ides a obus ool o analysing he complex in e ac ions be ween di e en ab ic
ein o cemen ypes and hei a angemen , 3D FE models we e de eloped using ABAQUS®/Explici [43]. These 3D FE models
in eg a e a Con inuum Damage Mechanics (CDM) model o simula ing in alamina damage in ab ic- ein o ced composi es and a
Su ace-based Cohesi e Beha iou (SbCB) model o in e lamina damage. I is impo an o acknowledge ha while 3D FE models
ha e p o en o be highly e ec i e in cha ac e ising he mechanical esponse o composi e lamina es [44], he e a e s ill some chal-
lenges. These include, o example, he sensi i i y o he simula ion esul s o ma e ial p ope y a ia ions and FE disc e iza ion, and
he complexi y o accu a ely modelling pos - ailu e beha iou . In his way, o ensu e he eliabili y o he simula ions, he de eloped
3D FE models we e alida ed agains he expe imen al o ce–displacemen cu es and he pos - ailu e damage mechanisms obse ed
in bo h hyb id and non-hyb id composi e lamina es. A o al o eigh con igu a ions we e analysed, including wo non-hyb id con-
igu a ions (a ca bon and a glass ab ic- ein o ced composi e lamina e) and six hyb id con igu a ions, p o iding a obus assessmen o
he p edic i e accu acy o he 3D FE models.
Fig. 1. Lay-up con igu a ions o he hyb id and non-hyb id composi e lamina es employed.
J.M. Pa en e e al.
Enginee ing F ac u e Mechanics 316 (2025) 110855
3
A de ailed unde s anding o hese mechanisms is undamen al o op imizing he design o hyb id composi es o imp o ed me-
chanical pe o mance and eliabili y. The nume ical app oach and esul s p esen ed in his s udy aim o con ibu e o he op imiza ion
o hyb idiza ion a ios and ib e a angemen s o speci ic applica ions, educing dependency on ex ensi e expe imen al es ing.
2. Ma e ials and Me hods
A wo-componen epoxy esin, SR8100 and SD8824 supplied by Sicomin, was used as he ma ix, while ein o cemen s in ol ed
combina ions o wo en bidi ec ional ca bon ab ic 195 T (196 g/m
2
) and wo en bidi ec ional glass ab ic 1195P (195 g/m
2
), bo h
supplied by Rebelco. Acco ding o he supplie , he hicknesses o he indi idual ca bon and glass ab ic ein o cemen s a e 0.25 mm
and 0.21 mm, espec i ely. A o al o eigh lay-up con igu a ions we e p oduced wi h he ollowing combina ions: “1G/7C”, “7C/1G”,
“2G/6C”, “6C/2C”, “3G/5C”, “5C/3G”, “8C”, and “8G”, as illus a ed in Fig. 1. The numbe s ep esen he quan i ies o laye s, while
he le e s ep esen he ype o ein o cemen , i.e. “C” o ca bon ib es and “G” o glass ib es. I should be no ed ha hese an i-
symme ic con igu a ions we e used o s udy he damage mechanisms and hei p opaga ion un il inal ailu e, aiming o op imize he
bending esponse o hyb id composi es in ol ing glass and ca bon ib es.
The esin and ha dene we e mixed using a mechanical s i e a 300 pm o i e minu es, ollowed by he emo al o any ai
bubbles in a acuum chambe . This mix u e was hen used o ab ica e he composi e lamina es using hand lay-up echnique. The
lamina es we e placed in acuum bags and comp essed in a hyd aulic p ess wi h a load o 2.5 kN o 24 hou s o ensu e a cons an ib e
olume ac ion and uni o m hickness. Du ing he ini ial 30 minu es, he acuum bag was connec ed o a acuum pump o emo e any
ai bubbles ha may ha e been in oduced du ing he manu ac u ing p ocess. Finally, he lamina es unde wen pos -cu ing a 40◦C o
ou hou s. The co esponding ib e olume ac ions, de e mined by he bu n-o es in acco dance wi h ASTM D2584-11 s anda d
[45], a e shown in Table 1. The ib e olume ac ions o he ca bon and glass ab ic ein o cemen s a e ep esen ed as VC
and VG
,
espec i ely, whe eas he ma ix olume ac ion is deno ed as Vm.
Specimens wi h dimensions o 60 ×10 × mm
3
we e p epa ed o he s a ic es s, whe e “ ” ep esen s he lamina e hickness: 1.4
mm o he “8C” con igu a ion, 1.52 mm o “8G”, 1.50 mm o “1G/7C” and “7C/1G”, 1.49 mm o “2G/6C” and “6C/2G”, and 1.49
mm o “3G/5C” and “5C/3G”. These specimens we e hen subjec ed o 3-poin bending es s (3PB) in acco dance wi h he ISO
178–2019 s anda d [46]. The es s we e ca ied ou using a Shimadzu AG-X uni e sal es ing machine equipped wi h a 10 kN load cell.
The displacemen a e was se a 2 mm/min, and he span be ween he suppo s was 35 mm, ensu ing compliance wi h he s anda d o
all lamina e con igu a ions. Fo each condi ion, eigh specimens we e es ed o ensu e s a is ical signi icance and he accu acy o he
es esul s. The expe imen al se up used o he 3PB es s is shown in Fig. 2.
3. Expe imen al esul s
The expe imen al s a ic bending esponse o bo h hyb id and non-hyb id composi e lamina es, ep esen ed by o ce–displacemen
cu es o all s udied con igu a ions is shown in Fig. 3. These ep esen a i e cu es we e selec ed because hey closely e lec he
a e age esponse o he eigh es s. Mo eo e , i should be no ed ha he expe imen al bending esul s p esen ed a low a ia ion, wi h
he s anda d de ia ion o he a e age o ce anging om 2% o 15%, and o he a e age displacemen , anging om 2.5% o 12%.
A quasi-b i le beha iou is obse ed ac oss all composi es, cha ac e ized by a nea ly linea inc ease in o ce wi h displacemen up
o a peak alue, a e which he o ce d ops ab up ly. I is no iced ha some o he cu es exhibi a no iceable zigzag pa e n in he
egion o maximum o ce, a ibu ed o he sequen ial ailu e o di e en ib es. This beha iou is pa icula ly no iceable in hyb id
composi es wi h ca bon ib es on he comp ession side (“7C/1G”, “6C/2G”, and “5C/3G”) because he high comp essi e s ess con-
cen a ion in he c osshead load con ac egion, combined wi h he low comp essi e s eng h o he ib es, p omo es ib e b eakage
leading o he zigzag pa e n obse ed [47–49]. No ably, he highes o ce was achie ed by he non-hyb id ca bon ab ic- ein o ced
lamina es “8C”, while he non-hyb id glass ab ic- ein o ced lamina es “8G” exhibi ed he lowes . This end is e e sed when
conside ing displacemen a maximum load. The hyb id composi e lamina es, showing a s ong dependence on he hyb idiza ion a io,
all be ween hese o ce and displacemen alues.
In mo e de ail, he highes a e age bending o ce was ob ained o he con igu a ion “8C” (366.6±27.7 N) and he lowes o “8G”
(219.6±5.5 N), while he displacemen a maximum o ce shows an in e se beha iou (2.58±0.2 mm and 5.96±0.18 mm, espec-
i ely). These di e ences a e app oxima ely 1.67 imes lowe o he bending o ce and 2.31 imes highe o he displacemen .
Rega ding he hyb id lamina es, he e ec o he glass ab ic ein o cemen posi ion on he bending esponse should be emphasized,
because when hey a e in he comp ession egion o he specimen lead o sligh ly highe esul s in e ms o o ce and displacemen .
Mo eo e , i can be obse ed ha ega dless o hei posi ion, a highe numbe o glass ab ic ein o cemen laye s dec eases he
Table 1
Fib e olume ac ion o he di e en lamina es ob ained by he bu n-o es .
Lamina es VG
(%)VC
(%)Vm(%)
3G/5C 16 38.07 45.93
2G/6C 10.28 44.03 45.69
1G/7C 5.16 51.62 43.22
8C −56.40 43.60
8G 55.91 −44.09
J.M. Pa en e e al.
Enginee ing F ac u e Mechanics 316 (2025) 110855
4
Fig. 2. Expe imen al se up o he 3PB es s acco ding o ISO 178-2019 [46].
Fig. 3. Fo ce-displacemen cu es o he ab ic- ein o ced composi e lamina es wi h: a) glass ab ic- ein o cemen placed in he comp essi e e-
gion; b) glass ab ic- ein o cemen placed in he ensile egion.
Fig. 4. Damage mechanisms obse ed in ab ic- ein o ced lamina es “8C”, “8G”, “3G/5C” and “5C/3G”.
J.M. Pa en e e al.
Enginee ing F ac u e Mechanics 316 (2025) 110855
5
bending o ce bu inc eases he bending displacemen . To cla i y he p e iously men ioned obse a ions, Fig. 4 p o ides a summa y o
he ypical damage mechanisms obse ed in he “8C”, “8G”, “3G/5C” and “5C/3G” con igu a ions, wi h he hyb id a angemen being
ep esen a i e example o he o he s.
Rega ding he non-hyb id lamina es, he “8C” con igu a ion p esen s ib e b eakage and delamina ions on he comp ession side,
while in he “8G” con igu a ion shows ib e b eakage on he ensile side, due o highe bending capaci y compa ed o he ca bon
lamina e, along wi h delamina ions in he c osshead load con ac egion caused by he s ess concen a ions in ha a ea. In he case o
“8G”, a mo e g adual ailu e p og ession was obse ed. These damage mechanisms a e consis en wi h he li e a u e [48,50–54], and
a e ela ed o he in insic p ope ies o he ib es. I should be no ed ha ca bon ib es a e ou imes s i e han glass ib es and ha e a
ensile s eng h 20%–50% g ea e [55–57], he glass ib es show highe s ains (a ound 650%) han ca bon ib es and, consequen ly,
highe oughness [58–60]. On he o he hand, he comp essi e s eng h o he ca bon ib e/ca bon ib e composi es is be ween 30% o
50% o he ensile s eng h [61], which means ha ca bon ib es a e much mo e sensi i e o comp ession loads han glass ib es [36].
Fo he hyb id con igu a ions “3G/5C” and “5C/3G”, he damage mechanisms a e simila o hose obse ed in he non-hyb id
con igu a ions. Fo ins ance, when ca bon ib es a e placed on he comp ession side, many o hem b eak, and delamina ions o m
a ound hem, while he glass ib es on he ensile side b eak punc ually. This p og ession o ib e ailu e in he comp ession egion
con ibu es o he zigzag pa e n obse ed in he o ce–displacemen cu es o he ca bon/glass con igu a ions [47–49]. On he o he
hand, when he glass ib es a e placed on he comp ession side, he damage is mo e ex ensi e. In addi ion o delamina ions, i includes
b eaking o he ca bon ib es in he ensile egion and glass ib es in he comp ession egion. This mo e se e e damage is esponsible o
he ab up d op in he o ce–displacemen cu es a e he peak load is eached. Fu he analysis o he damage e olu ion and i s
co ela ion wi h he o ce–displacemen cu es is p o ided in he ollowing sec ions.
4. Nume ical models
4.1. Damage models
Unde bending loading, composi e ma e ials expe ience ensile and comp essi e s esses ha can lead o in alamina damage,
ypically mani es ing as ma ix c acking and ib e b eakage. Addi ionally, in e lamina shea s esses, pa icula ly concen a ed nea
he loading poin and suppo s, can cause sepa a ion be ween he lamina e laye s, known as delamina ion. These damage mechanisms
con ibu e o a educ ion in he ma e ial’s s i ness and load-bea ing capaci y, making i essen ial o de elop FE models capable o
p edic ing he ma e ial’s beha iou . To simula e he damage mechanisms ha occu in he ab ic- ein o ced composi e lamina es
unde 3PB bending loading, wo damage models we e used: a Con inuum Damage Mechanics (CDM) model and a Su ace-based
Cohesi e Beha iou (SbCB) model, which accoun o in alamina damage and in e lamina damage, espec i ely.
To e alua e damage e olu ion a he in alamina le el in he es ed lamina es, which we e ein o ced wi h ca bon and/o glass
ab ics, he cons i u i e damage model o ab ic- ein o ced composi es a ailable in ABAQUS®/Explici was used [43]. This model,
implemen ed ia a VUMAT sub ou ine and accessed by de ining a use -de ined ma e ial wi h a s ing “ABQ_PLY_FABRIC”, is
compa ible exclusi ely wi h plane-s ess elemen s and conside s each laye a homogeneous o ho opic elas ic ma e ial. I accoun s o
s i ness deg ada ion esul ing om ib e ailu e, ma ix c acking, and plas ic de o ma ion unde shea loading. This CDM model
applies he maximum s ess ailu e c i e ion o iden i y he onse o ib e damage and uses a damage e olu ion app oach, go e ned by
ac u e ene gies, o con ol he educ ion in s i ness. Table 2 p esen s he VUMAT sub ou ine inpu s o he ca bon and glass ab ic-
ein o ced composi e laye s used in his s udy. The subsc ip s “+” and “-” deno e he ensile and comp essi e loading modes,
espec i ely, while “1” and “2” e e o he p incipal di ec ions o he laye . The elas ic and s eng h p ope ies, as well as he ac u e
ene gies o he non-hyb id composi e lamina es, we e ini ially es ima ed om he expe imen al da a. These alues we e hen e ined
h ough a pa ame ic s udy o achie e a good co ela ion wi h he expe imen al esul s, ensu ing an accu a e ep esen a ion o he
lamina e beha iou . The shea plas ici y da a was ob ained om [62–64].
The bond be ween he laye s was simula ed using he SbCB model. This app oach is sui able o in e aces wi h negligible hickness
and p o ides capabili ies simila o he cohesi e elemen s. The cohesi e beha iou was de ined as a su ace in e ac ion p ope y,
Table 2
In alamina p ope ies o he ca bon and glass ab ic- ein o ced composi e laye s.
P ope y Symbol Uni s Ca bon Fab ic Glass Fab ic
Value Value
Densi y
ρ
kg/m
3
1900 1600
S i ness p ope ies E1+,−=E2+,−GPa 40 9.5
G12 GPa 6 3
ν
12 −0.14 0.11
S eng h p ope ies X1+,−=X2+,−MPa 640 320
SMPa 120 40
F ac u e ene gy G1,2
N/mm 15,000 25,000
Shea plas ici y dmax
12 −1 1
σ
y0MPa 55 25
C−800 800
p−0.552 0.552
J.M. Pa en e e al.
Enginee ing F ac u e Mechanics 316 (2025) 110855
6
go e ned by a ac ion-sepa a ion cons i u i e model. Delamina ion onse was de e mined using he ou pu damage a iable
“CSQUADSCRT”, which co esponds o he s ess-based damage ini ia ion c i e ion o cohesi e su aces in gene al con ac wi hin
ABAQUS® FE code [43]. Once delamina ion ini ia es (i.e., when CSQUADSCRT=1), i s p og ession un il comple e debonding, was
cap u ed using he ou pu damage a iable “CSMDG” o cohesi e su aces. This a iable is con olled by he powe law ep esen ed in
Eq. (1), whe e comple e delamina ion is p edic ed when CSMDG eaches he alue o one.
(GI
GIc)
η
+(GII
GIIc)
η
+(GIII
GIIIc)
η
=1 (1)
The ma e ial in e lamina p ope ies used o de ine he SbCB model o his s udy a e de ailed in Table 3. These p ope ies we e
ob ained om he li e a u e and subsequen ly adjus ed o mee he speci ic equi emen s o he lamina e con igu a ions unde analysis.
The s i ness alues we e ob ained om [65], while he damage ini ia ion pa ame e s we e aken om [66]. Damage e olu ion
ene gies, which de ine he ma e ial’s esis ance o p og essi e delamina ion, we e ob ained om [67] and [68]. Finally, he in e -
ac ion pa ame e was de ined om [63]. The in alamina and in e lamina damage models used in his s udy a e ho oughly
explained in [43,69,70]. These models ha e been applied by he au ho s in se e al p e ious s udies [63,64,71,72] and ha e
demons a ed eliable pe o mance in p edic ing damage beha iou in ab ic- ein o ced composi e lamina es.
4.2. Fini e elemen model
Th ee-dimensional FE models eplica ing he expe imen al 3PB es s desc ibed in Sec ion 2 we e de eloped using ABAQUS® FE
code [73]. Acco dingly, he eigh di e en lamina e lay-up con igu a ions illus a ed in Fig. 1 we e gene a ed wi h he co esponding
geome ic pa ame e s. No ice ha he lamina e hickness, ep esen ed wi h he pa ame e “ ” in Fig. 2, was de ined based on he
speci ic dimensions o each lay-up con igu a ion.
The lamina e laye s we e simula ed using 8-node con inuum shell elemen s (SC8R), while he c osshead and suppo s we e
modelled wi h 4-node disc e e igid elemen s (R3D4). Gi en he negligible hickness o he laye ’s in e aces, cohesi e su aces we e
employed o model he bonding, elimina ing he need o elemen de ini ion. I should be no ed ha in SbCB models, he cohesi e zone
is ep esen ed as a ze o- hickness in e ace, cap u ing he mechanical beha iou o bonded su aces wi hou explici ly modelling he
ma e ial’s ini e hickness. The 3D FE mesh disc e iza ion employing quad ila e al-shaped elemen s is ep esen ed in Fig. 5.
Mesh e inemen was applied in he con ac egions wi h he c osshead and suppo s, whe e elemen s we e assigned a cha ac e is ic
leng h o 0.1 mm. This e inemen ensu es an accu a e ep esen a ion o s ess concen a ions and g adien s nea he loading poin and
suppo s, leading o a mo e p ecise p edic ion o ma e ial beha iou unde bending load. To eplica e he expe imen al se up, ixed
bounda y condi ions we e applied o bo h suppo s and a amped displacemen , u
y
, was imposed on he c osshead. To imp o e
compu a ional e iciency, only hal o he geome y was modelled, aking ad an age o he sys em’s symme y. In his way, symme y
bounda y condi ions we e imposed along he zy-plane. Fo e e ence, he de eloped 3D FE models a e composed o a o al 35,464
elemen s and 64,660 nodes. The penal y en o cemen con ac me hod was used o model he su ace- o-su ace in e ac ion be ween he
c osshead and he lamina e. This me hod was also applied a he laye s’ in e aces, o accoun o ic ion ha may de elop once
delamina ion occu s. A ic ion coe icien o 0.3 was assigned o he c osshead-composi e and suppo s-composi e in e ac ions, while
a coe icien o 0.5 was used o he laye s’ in e aces [64,72,74].
4.3. Quasi-s a ic analyses
E icien quasi-s a ic solu ions can be achie ed using he explici dynamics sol e in ABAQUS® [75]. This app oach is well-
documen ed in he li e a u e [67,76–78] and i in ol es inc easing he loading a e and employing mass scaling. To keep he
ine ia o ces negligible h oughou he analysis and ensu e he accu acy and eliabili y o he nume ical p edic ions, se e al gene al
ecommenda ions we e implemen ed. Fi s ly, he loading eloci y was limi ed o app oxima ely 1.2 m/s, which is less han 1% o he
ma e ial’s dila a ional wa e speed, Cd, which can be calcula ed o a linea elas ic ma e ial as,
Cd=
E
ρ
√(2)
whe e, E is he elas ic modulus and
ρ
he ma e ial densi y. No ice ha , acco ding o he li e a u e, he dila a ion wa e speed Cd o
Table 3
In e lamina p ope ies.
P ope y Symbol Uni s Value
S i ness kn=ks=k N/mm
3
10
6
Damage ini ia ion
τ
0
nMPa 50
τ
0
s=
τ
0
MPa 42
Damage e olu ion ene gies GIc J/m
2
0.5
GIIc =GIIIc J/m
2
2.0
In e ac ion pa ame e
η
−1.45
J.M. Pa en e e al.
Enginee ing F ac u e Mechanics 316 (2025) 110855
7
composi e ma e ials can ange om 2500–6500 m/s depending on he speci ic composi ion o he lamina e [79–82]. Secondly, he
s abili y limi in he explici dynamics’ p ocedu e, Δ , should ollow Eq. (3), whe e Lmin ep esen s he smalles cha ac e is ic elemen
leng h.
Δ ≤Lmin
Cd
(3)
Based on he ange o Cd alues o composi e ma e ials and knowing ha he de eloped 3D FE models ha e an Lmin o 0.1 mm, he
s able ime inc emen Δ was main ained below 1.5 ×10
–8
s h oughou he quasi-s a ic analysis. Las ly, o minimize s ess wa e
p opaga ion h oughou he model, a smoo h amp-up o he loading eloci y om ze o was applied.
To e alua e i he simula ions p o ide an app op ia e quasi-s a ic esponse, an ene gy balance was pe o med o all lamina e
con igu a ions. As an example, Fig. 6 shows he ene gy balance p edic ions o con igu a ion “8C”, whe e is excluded he con ibu ion
o he igid bodies (c osshead and suppo s). Fu he mo e, he esul s a e p esen ed o a 3D FE model wi h ixed mass scaling, applied
a he beginning o he s ep wi h a ac o o ou , and wi hou mass scaling. No ice ha i is ecommended ha he kine ic ene gy o he
de o ming ma e ial (ou pu a iable ALLKE) does no exceed 1%–5% o he in e nal ene gy (ou pu a iable ALLIE) o mos o he
quasi-s a ic analysis [75].
The esul s demons a e ha du ing he quasi-s a ic analysis, he kine ic ene gy emains negligible, ega dless o whe he he
model’s densi y is scaled by a ac o o ou . Ac oss all con igu a ions, he ALLKE/ALLIE a io consis en ly s ayed below 5% a e
app oxima ely 1.5 ms, which co esponds o 0.2 mm o c osshead displacemen . I is impo an o no e ha achie ing such balance in
Fig. 5. 3D FE model de eloped o analyse he di e en lamina e con igu a ions unde 3PB loading.
Fig. 6. Kine ic ene gy (ALLKE) and in e nal ene gy (ALLIE) ene gy wi h and wi hou mass scaling, h oughou he quasi-s a ic analysis o lamina e
con igu a ion “8C”.
J.M. Pa en e e al.
Enginee ing F ac u e Mechanics 316 (2025) 110855
8
he ea ly s ages o he analysis is gene ally no possible because he lamina e, as he only de o mable body, mo es be o e expe iencing
signi ican de o ma ion. Addi ionally, he use o mass scaling imp o ed he compu a ional ime o he solu ions by abou 50%. La ge
scale ac o s we e also conside ed; howe e , hey led o an inc ease in ine ia o ces, and wi hou any signi ican imp o emen in
compu a ional e iciency. O e all, hese esul s con i m ha he sys em p esen s no signi ican dynamic e ec s.
5. Nume ical esul s
5.1. Nume ical-Expe imen al co ela ion
The expe imen al o ce–displacemen cu es o all he lamina e con igu a ions p esen ed in Fig. 3, we e used o alida e he nu-
me ical p edic ions ob ained wi h he 3D FE models. As an example, he nume ical p edic ions and expe imen al esul s o he non-
hyb id con igu a ions “8C” and “8G”, and he hyb id con igu a ion “5C/3G” a e p esen ed in Fig. 7. Poin s A o D co espond o he
damage s ages illus a ed in Fig. 8, while poin s E and F ep esen hose shown in Fig. 9. A mo e de ailed analysis o all con igu a ions,
suppo ed by quan i a i e alues, is p o ided in Table 4.
The esul s show ha he nume ical models e ec i ely p edic he mechanical esponse o he hyb id and non-hyb id lamina e
con igu a ions unde 3PB loading. The nume ical and expe imen al o ce–displacemen cu es p esen a good co ela ion, wi h o ces
peaking a simila displacemen s. In he pos -peak egion, he expe imen al da a exhibi s mo e a iabili y compa ed o he smoo he
nume ical p edic ions, which a e ela ed o he complex damage mechanisms in lamina es a e yielding. When analysing he peak
o ce esul s o all con igu a ions in Table 4, i can be concluded ha he nume ical models end o sligh ly o e es ima e he
expe imen al mean alues, wi h e o s anging om +1.1% o +15.9%. Howe e , he nume ical p edic ions show pe cen age e o s
ha all wi hin he s anda d de ia ion obse ed in he expe imen al es s. The la ges disc epancy is obse ed in he “7C/1G”
con igu a ion, while “8G” shows an excellen ag eemen be ween nume ical and expe imen al da a. No ably, “7C/1G” also has he
highes a iabili y in he expe imen al esul s, which is e idenced by he g ea es s anda d de ia ion in peak o ce (39.8 N).
Displacemen a peak o ce p edic ions shows mo e a ia ion compa ed o o ce, wi h se e al con igu a ions unde es ima ing
displacemen , pa icula ly in “8G” (−4.7%), “2G/6C” (−6.8%), and “3G/5C” (−17.5%). Con e sely, “7C/1G” o e es ima es
displacemen by +8.7%.
5.2. Damage e olu ion
The implemen ed damage models allow he nume ical p edic ion o he in alamina and in e lamina damage mechanisms o he
ab ic- ein o ced lamina es unde he 3PB loading, as discussed in Sec ion 4.1. The p edic ed damage a wo di e en damage s ages,
peak o ce and delamina ion onse , o he non-hyb id con igu a ions “8C” and “8G”, and hyb id con igu a ions “5C/3G” and “3G/5C”,
a e p esen ed in Figs. 8 and 9, espec i ely. These s ages a e iden i ied in he nume ical o ce–displacemen cu es shown in Fig. 7. The
in alamina damage is ep esen ed as ensile and comp essi e damage along he ib e di ec ions, wi h ou pu a iables anging om
0.5 o 1, while delamina ion is cap u ed by he ou pu a iable “CSDMG” o comple e debonding be ween he laye s, ha is when
CSDMG=1. I should be no ed ha al hough only wo o he six hyb id composi e lamina es we e selec ed o de ailed analysis, he
damage e olu ion p edic ions o he emaining ou lamina es a e in ag eemen wi h he expe imen al esul s. The selec ion o
ep esen a i e esul s was made o p o ide a ocused and clea compa ison, ensu ing ha key ends we e e ec i ely highligh ed
wi hou comp omising he o e all consis ency o he indings.
In all he hyb id and non-hyb id con igu a ions, in alamina damage is he i s damage mode o be p edic ed. This damage is
con ined o he egions aligned wi h he c osshead axis, p ima ily in he uppe and bo om laye s whe e ensile and comp essi e
s esses a e he highes . I is subsequen ly ollowed by in alamina damage (delamina ion), which de elops in he a eas wi h he mos
Fig. 7. Nume ical p edic ions and expe imen al o ce–displacemen cu es o lamina e con igu a ions “8C”, “8G” and “5C/3G”.
J.M. Pa en e e al.
Enginee ing F ac u e Mechanics 316 (2025) 110855
9
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