Non-linear analytical model of composites based on basalt textile reinforced mortar under uniaxial tension

Else ie Edi o ial Sys em( m) o Composi es Pa B Manusc ip D a Manusc ip Numbe : Ti le: NON-LINEAR ANALYTICAL MODEL OF COMPOSITES BASED ON BASALT TEXTILE REINFORCED MORTAR UNDER UNIAXIAL TENSION A icle Type: Full Leng h A icle Keywo ds: A. Fab ics/ ex iles; B. Mechanical p ope ies; C. Analy ical modelling; D. Mechanical es ing Co esponding Au ho : D . Pello La inaga Alonso, Ph. D. Co esponding Au ho 's Ins i u ion: TECNALIA Resea ch & Inno a ion Fi s Au ho : Pello La inaga Alonso, Ph. D. O de o Au ho s: Pello La inaga Alonso, Ph. D.; Ca los Chas e, Assis an P o esso ; José Tomás San- José, Assis an P o esso ; Lei e Ga mendia, PhD Indus ial Enginee Abs ac : The ecen de elopmen o ino ganic based composi es as low-cos ma e ials in ein o ced conc e e s uc u al s eng hening and p ecas hin-walled componen s, equi es he c ea ion o models ha p edic he mechanical beha iou o hese ma e ials. Tex ile Rein o ced Mo a (TRM) shows complex s ess-s ain beha iou in ension de i ed om he he e ogenei y o i s cons i uen ma e ials. This complexi y is mainly caused by he o ma ion o se e al c acks in he ino ganic ma ix. The mul iple c acking leads o a dec ease in s uc u al s i ness. Due o he se e e condi ions o he se iceabili y limi s a e in s uc u al elemen s, he p edic ion o he s ess-s ain cu e is essen ial o design and calcula ion pu poses. A e checking o he models, a nonlinea app oach, which is based on he c ack con ol exp ession included in he Eu ocode 2, is p oposed in his pape . Following his scope, his pape p esen s an expe imen al campaign ocused on hi y one TRM specimens ein o ced wi h ou di e en ein o cing a ios. The esul s a e analysed and sa is ac o ily con as ed wi h he p esen ed non-linea app oach. Sugges ed Re iewe s: Ami Si La bi Claude Be na d Uni e si y o Lyon 1, F ance ami .si-la bi@uni -lyon1. D . Si La bi has b oad expe ience in he ield o ib e-cemen i ious composi es, especially wi h Tex ile Rein o ced Conc e e (TRC), a composi e e y simila o he one included in his pape . Due o his esea ch ac i i y D . Si La bi has o deal wi h he analysis o TRC uniaxial ensile beha iou . Hence, I conside D . Si La bi a sui able e iso o his pape . Heidi Cuype s PhD Ci il Enginee V ije Uni e si ei B ussel heidi.cuype s@ ub.ac.be D . Cuype s has b oad expe ience in he ield o ino ganic based composi es, especially he s udy o ma ix c acking and i s du abili y. Thus, I conside D . Cuype s a sui able e iso o he p esen ed a icle. This is he accep manusc ip o he ollowing a icle ha appea ed in inal o m in Composi es Pa B: Enginee ing 55: 518-527 (2013),which has been published in inal o m a h ps://doi.o g/10.1016/j.composi esb.2013.06.043.Copy igh © 2013 Else ie L d. unde CC BY-NC-ND licence (h ps://c ea i ecommons.o g/licenses/by-nc-nd/4.0/) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 1 NON-LINEAR ANALYTICAL MODEL OF COMPOSITES BASED ON BASALT TEXTILE REINFORCED MORTAR UNDER UNIAXIAL TENSION Pello La inaga a, * , Ca los Chas e b, José T. San-José c, Lei e Ga mendia a a TECNALIA. c/Geldo, Ed. 700, Pa que Tecnológico de Bizkaia, 48160, De io, Spain b UNIC, Faculdade de Ciências e Tecnologia, Uni e sidade No a de Lisboa, 2829-516 Capa ica – Po ugal c UPV/EHU, Depa men o Enginee ing o Ma e ials. c/Alameda U quijo s/n, 48013 Bilbao, Spain Abs ac The ecen de elopmen o ino ganic based composi es as low-cos ma e ials in ein o ced conc e e s uc u al s eng hening and p ecas hin-walled componen s, equi es he c ea ion o models ha p edic he mechanical beha iou o hese ma e ials. Tex ile Rein o ced Mo a (TRM) shows complex s ess-s ain beha iou in ension de i ed om he he e ogenei y o i s cons i uen ma e ials. This complexi y is mainly caused by he o ma ion o se e al c acks in he ino ganic ma ix. The mul iple c acking leads o a dec ease in s uc u al s i ness. Due o he se e e condi ions o he se iceabili y limi s a e in s uc u al elemen s, he p edic ion o he s ess-s ain cu e is essen ial o design and calcula ion pu poses. A e checking o he models, a nonlinea app oach, which is based on he c ack con ol exp ession included in he Eu ocode 2, is p oposed in his pape . Following his scope, his pape p esen s an expe imen al campaign ocused on hi y one TRM specimens ein o ced wi h ou di e en ein o cing a ios. The esul s a e analysed and sa is ac o ily con as ed wi h he p esen ed non-linea app oach. Keywo ds: A. Fab ics/ ex iles; B. Mechanical p ope ies; C. Analy ical modelling; D. Mechanical es ing; 1. In oduc ion By means o se e al esea ch p ojec s, he mechanical possibili ies and ad an ages o Tex ile Rein o ced Mo a ha e been p o en, bo h as s eng hening ma e ial and as p ecas ma e ial (in his ield his composi e is also called Tex ile Rein o ced Conc e e) [1-5]. Howe e , i s implemen a ion as a egula echnique is s ill a . One impo an s ep o each his objec i e is modelling he mechanical beha iou o TRM o u u e applica ions in eal si ua ions. As TRM usually bea s ensile loads, i is e y ele an o * Co esponding au ho . Tel: +34 667 178 992/946 430 850; ax: +34 946 460 900 E-mail add ess: p[email p o ec ed]m *Manusc ip Click he e o iew linked Re e ences 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 2 model he beha iou o his ma e ial unde pu e ensile loads, i.e. o de ine i s s ess- s ain ela ionship. In he bibliog aphy, he e is b oad in o ma ion e e ed o nume ical o analy ical TRM models which show excellen esul s [6-9]. Ne e heless, mos o hese analyses equi e he use o speci ic so wa es [9] o a e cos ly in e ms o ime. Mo eo e , in some cases addi ional in o ma ion is equi ed, which in ol es he de elopmen o addi ional es s [7,8]. Fo hese easons, i is con enien o p oduce simple and easy- o-implemen models. S ess-s ain ma hema ical exp essions a e usually p oposed o model he ma e ials, bo h o linea and non-linea analysis. These exp essions a e based on expe imen al da a and can be used as cons i u i e equa ions in simple nume ical models. Conc e e and s eel a e ob ious examples o s ess modelling by means o ma hema ical exp essions, in ac , bo h ma e ials a e modelled in design codes as he Eu ocode 2. A nonlinea app oach is p esen ed in his pape o de ine he s ess-s ain ela ionship o Basal Tex ile Rein o ced Mo a (BTRM) unde uniaxial ensile loads. The model is based on he conc e e c ack con ol exp ession included in he Eu ocode 2 [10]. The de eloped exp ession is calib a ed empi ically wi h expe imen al da a included in he a icle, he esul s o hi y one TRM specimens subjec ed o uniaxial ensile loads. 2. Ma e ials. Basal ex ile and mo a cha ac e iza ion. Basal appea s o be a ma e ial which can o e in e es ing oppo uni ies in he u u e o he cons uc ion indus y [11]. Recen s udies ha e included basal ab ics as ein o cemen in FRP composi es [11,12] and basal ex ile as TRM in e nal co e [13,14]. The basal ex ile used in his s udy consis s o o ings wo en in he wo p incipal di ec ions, i.e. a bidi ec ional mesh which geome y is de ailed in Table 1. Basal o ings a e co e ed by a bi umen coa in o de o imp o e he bond be ween he mo a ma ix and he ex ile. In addi ion, he coa imp o es he ex ile pe o mance due o i s capaci y o ans e load di ec ly o mo e o ing ilamen s [15,16]. Table 1 Basal ex ile geome y Acco ding o se e al p e ious s udies, he e is a conside able gap be ween he main mechanical p ope ies - ensile s eng h, ul ima e s ain and Young’s modulus - o a single ib e o ilamen and hose o he ex ile mesh [17]. Fo his eason, he mechanical cha ac e is ics o he ex ile we e expe imen ally de e mined in ensile es s on specimens which leng h was 600mm. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 3 ASTM D 5034 [18] s anda d, used as a e e ence, sugges s a s ain a e o 300mm/min. Howe e , in o de o ca y ou a sui able da a acquisi ion, a speed o 1mm/min was selec ed o he p esen es . In o al, se en ex ile specimens o ou o ings we e es ed. The esul s a e summa ised in Table 2. Table 2 A e age esul s o basal ex ile unde pu e ensile load The di e ence be ween he da a gi en by he manu ac u e and he expe imen al esul s is caused by se e al ac o s, mainly he load ans e be ween ilamen s and he di icul y o exe an iden ical ini ial leng h and s ain o all he s ands o he specimens [13,17]. Hence, i was impossible o achie e a simul aneous up u e o all he o ings, so he expe imen al alues o ul ima e ensile s eng h and ul ima e ensile s ain can no be conside ed as e e ence da a. Howe e , as he es ed ex ile p esen s linea beha iou un il up u e, he ensile Young’s modulus alues ob ained in his es can be easily calcula ed [14] and i will be conside ed o he model p esen ed in his pape . Mo eo e , despi e he di icul ies de i ed in his kind o es s, he ob ained esul s p esen ed low sca e ing. A non-comme cial cemen -based mo a was used as TRM ma ix. The pe o mance o any ex e nally bonded s eng hening sys em is clea ly in luenced by he in e ac ion be ween he ma ix and he inne ein o cemen and he capaci y o he composi e- subs a e in e ace [15]. The maximum g ain size o he sand used in he mo a was 0.6mm. This ac o enhances he wo kabili y o he esh mix u e and acili a es i s in e ac ion wi h he ex ile mesh. The amoun o edispe sable esins was lowe han 5%, in o de o achie e a i e-p oo mo a . As can be obse ed in Table 3, he e a e no inno a i e p oduc s in he mo a composi ion because he idea is o p esen he TRM as a compe i i e ma e ial. Howe e , special a en ion was paid o i s composi ion so as o achie e app op ia e wo kabili y, cu ing ime and i e esis ance. Table 3 Mo a dosage by weigh (%) Ma ix mo a was mechanically cha ac e ized acco ding o. A e 28-day cu ing, 40x40x160mm p isms we e es ed o de e mine mo a mechanical p ope ies acco ding o UNE-EN 1015.11:1999 [19]. Comp essi e s eng h is 19.8MPa while ensile lexu al s eng h is 7.2MPa. 3. Uniaxial ensile es 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 4 The expe imen al campaign included in his pape is o med by hi y one uniaxial ensile specimens. Fou se ies, om one o ou ex ile laye s, o se en specimens each one we e de ined. The e ec o ein o cing a io was he e o e analysed. Specimens we e agged as TBX, whe e he X ep esen s he numbe o in e nal ein o cemen laye s, i.e. in his pape om TB1 o TB4. Besides, h ee addi ional specimens we e also manu ac u ed wi hou ein o cing ma e ial. 3.1.Specimens geome y and manu ac u ing p ocess TRM has a ac ed a en ion o he las en yea s. The e has been a conside able inc ease in esea ch p ojec s and publica ions ela ed o his inno a i e composi e. Howe e , no s anda d cha ac e iza ion es s a e a ailable in he bibliog aphy. Thus, se e al es p oposals ha e al eady been made [6,15,20,21] by di e en au ho s. They di e p ima ily in: he shape and geome y o he specimens, he connec ion wi h he es machine clamps, he s ain a e and he ins umen a ion. Fig. 1. Uniaxial ensile TRM specimen geome y. The ec angula pa allelepiped specimen is easy o manu ac u e and implemen . Fo he p esen s udy i was decided o manu ac u e specimens wi h a 100x10mm c oss- sec ional a ea and 600mm in leng h. Samples we e p epa ed in plywood o mwo ks. In o de o p omo e he ailu e o he specimen in i s middle hi d po ion, bo h ends o each specimen we e ex a- ein o ced wi h wo laye s o 200x100mm ex ile (Figu e 1). The in e nal ein o cemen o co e laye s (800x100mm) we e always uni o mly posi ioned wi hin he c oss sec ion. In he pa icula case o he un ein o ced specimens, only he addi ional ein o cemen was ins alled a bo h ends. (a) (b) Fig. 2. Two s eps o he TRM ensile specimens manu ac u ing. Specimens we e cu ed in a sa u a ed a mosphe e o se en days, and, hen, hey we e s o ed o 21 days a oom empe a u e (18ºC and 60%RH). Tes s we e ca ied ou be ween 28 and 34 days a e he specimens we e manu ac u ed. 3.2.Tes Se up TRM ensile specimens we e es ed in a Schenk 100kN p ess which was p og ammed o exe a de o ma ion a e o 0.5mm/min [15]. Tensile o ce was applied wi h specially designed me allic clamps, in o de o a oid any s ess concen a ion poin , which would cause p ema u e b i le ailu e wi hou eaching he ul ima e ensile load. Fig. 3. Uniaxial ensile o he es se up. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 5 As he o ma ion o c acks is p omo ed in he specimen cen al hi d pa , wo displacemen ansduce s (LVDTs) we e placed on each side o he specimen o measu e he elonga ion o ha a ea. The measu ed e e ence leng h, as can be obse ed in Figu e 3, was 210mm. All he da a was compiled by a da a logge a a equency o 5Hz. 3.3.Expe imen al esul s The pu pose o es ing un ein o ced specimens was o cha ac e ize he beha iou o he mo a unde pu e ensile loads. As i was expec ed, only one c ack was o med in he un ein o ced specimens. The a e age esul s o he h ee specimens a e displayed in Table 4. Table 4 A e age esul s o un ein o ced specimens The load-s ain cu es o 28 TRM es s wi h 1-4 laye s a e shown g aphically in Figu e 4. The esul s show good epea abili y in con as wi h he cha ac e is ic sca e ing o his kind o ma e ials. Th ee s ages a e clea ly di e enced in each cu e. This beha iou is ypical in ino ganic composi es subjec ed o uniaxial ensile load [22], ein o ced abo e he c i ical olume ac ion. These s ages a e: - S age I. P e-c acking s a e. - S age II. Mul ic acking p ocess. - S age III. S abilized c ack pa e n. Only he ib es ca y load. Fig. 4. Load-s ain cu es o TRM specimens. Table 5 includes he a e age main alues o each se ies: ul ima e ensile o ce and s ess, he Young’s modulus o s age III, and he inal s ain a each s age. The ensile s ess o he specimens is calcula ed di iding measu ed load by he a ea o in e nal ein o cemen : b· ·n; whe e b is he wid h o he specimen (100mm), is he design hickness (0.0349mm) and n is he numbe o ex ile laye s ins alled as in e nal ein o cemen . Table 5 A e age esul s o each TRM se ies The analysis o he esul s p oduces in e es ing in e p e a ions. Acco ding o he bibliog aphy, he s i ness o he hi d s age E ,III is sligh ly lowe han he Young’s modulus o he ex ile ein o cemen E (see Table 2). In h ee o he ou se ies E ,III emained close o 60GPa, while he basal ex ile Young’s modulus is 67GPa, i.e. 9% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 6 highe . This educ ion has been quan i ied (10-30%) by o he au ho s [22,23]. Likewise, he e was good co ela ion in se ies TB2, TB3 and TB4 in e ms o ensile s eng h and ul ima e s ain. The main di e ence be ween hese h ee se ies is he leng h o he S age II (see Table 5). The mul iple c acking s ain ε ,II was educed wi h a highe numbe o ein o cemen laye s [24]. Ne e heless, se ies TB1 showed a signi ican disc epancy when compa ed wi h he o he esul s. The a e age alue o E ,III was equal o 43GPa. The low amoun o in e nal ein o cemen in se ies TB1 can explain his disc epancy; one laye may no be enough o achie e a monoli hic ma e ial which could be conside ed as a composi e. Acco ding o Peled and Ben ou [16] he c i ical olume con en o ib es in cemen composi e is abou 1-3%. A a ios abo e his le el he beha iou load is cha ac e ized by mul iple c acking and he TRM is able o ca y he addi ional load applied a e he ma ix has c acked. Howe e , Se ies TB2 p esen s a olume con en o 0.7% and he specimens showed mul iple c acking and beha ed as he es o he se ies wi h highe ib e con en . These s a emen s can be con as ed wi h he s ess-s ain esul s included in Figu e 5. While se ies TB2, TB3 and TB4 p esen ed simila beha iou a e mul iple-c acking, se ies TB1 de eloped a di e en slope a hi d s age. Fig. 5. Di ec compa ison be ween specimens o di e en se ies. The analysis o he c ack pa e n also p o ides in e es ing in o ma ion. Fi s ly, i is no iceable how he numbe o c acks ises when he numbe o ex ile laye s inc eases (see Figu e 6). Mo eo e , he dis ance be ween c acks is educed when mo e in e nal ein o cemen is used. A se ies TB1 only one o h ee c acks we e o med, being an e idence o i s incapabili y o de eloping mul iple c acking and beha e as an ino ganic based composi e. Finally, as he ib e con en inc eases, he c ack pa e n ends o s anda dize. (a) (b) (c) (d) Fig. 6. C ack pa e n de elopmen . F om up-le o down igh : TB1, TB2, TB3 and TB4. In he ollowing sec ion a non-linea analy ical model is p esen ed. The ob ained expe imen al esul s will be compa ed wi h hose ob ained in he model in o de o check i s alidi y. 4. TRM modelling 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 7 The p oposed model is based on he c ack con ol exp ession included in he “Eu ocode 2: Design o conc e e s uc u es. Pa 1-1” and he A es on-Coope -Kelly heo y. This well-known heo y was he i s sa is ac o y explana ion o mul iple c acking. Fo his eason, he au ho s would like o e ise he ACK heo y and compa e i s esul s wi h he expe imen al da a. 4.1. ACK-Theo y This heo y de ines a heo e ical i-linea s ess-s ain beha iou o a composi e wi h a b i le ma ix, in which i is assumed ha he ib es a e held in he ma ix solely by he p esence o ic ion, and ha axial sliding along a ib e-ma ix in e ace would occu unde a c i ical, limi ing alue o longi udinal shea s ess [25,26]. The ib e debonding deg ee and c ack spacing a e closely linked o he maximum shea s ess a he ib e- ma ix in e ace. Se e al models o b i le ma ix composi es ha e al eady been modelled conside ing he ACK heo y, e.g. [27,28]. Basic assump ions, employed in i s de elopmen , a e [24]: - The ib es a e only capable o ca ying load along hei longi udinal axis. - The ma ix- ib e bond is weak. - Once he ma ix and he ib e a e debonded, a pu e ic ional shea s ess η eplaces he p e iously exis ing adhesion shea s ess ηa. This ic ional in e ace shea s ess η is cons an along he debonded in e ace. - Poisson e ec s o he ib e and ma ix a e neglec ed. - Global load sha ing is assumed o he ib es. - No mal ma ix s esses, ans e sal o he loading di ec ion, a e uni o m in a c oss sec ion. As i has been expe imen ally s a ed, TRM ensile beha iou could be di ided in h ee di e en , bu complemen a y, s ages. The ACK heo y consis s on h ee s aigh lines which supe imposes he expe imen al s ess-s ain cu e (see Figu e 7). Fig. 7. Typical s ess-s ain cu e o TRM in ension (in black) and ACK linea iza ion (in do ed g ey) Acco ding o ACK heo y, a he i s s age, he composi e obeys he law o mix u es: mm c VEVEE  1 (1) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 8 whe e Ec1 is he composi e s i ness, E ep esen s he ensile Young’s modulus o he ib es, Em is he ma ix one, and V and Vm a e he olume ic ac ion o ib es and ma ix, espec i ely. A he i s s age, he ma ix- ib e in e ace shea beha iou is assumed o be elas ic. S age I inishes when he ma ix eaches i s ensile ailu e s ess ζmc. Ma ix ensile ailu e s ess, ζmu, (and i s co esponding s ain εmu) has a di ec in luence on ζmc: m muc mc E E   1  (2) A his alue, he composi e p esen s mul iple c acking, i.e. successi e c acks a e o med as he composi e s ain inc eases. As has been s a ed, when a c ack appea s in he ma ix and eaches a ib e, debonding o he ma ix- ib e in e ace occu s due o weakness o he bond. Then, a cons an ic ional in e ace shea s ess η is conside ed. This shea s ess p o ides no mal s ess ans e om ib es o he ino ganic ma ix. The leng h o he debonded in e ace δ can be w i en by exp essing he o ce equilib ium along he loading (longi udinal) axis o he ib es [25]:    2 mum V V  (3) whe e, is he ib e adius and η ep esen s he ic ional shea s ess a he ma ix- ib e in e ace. A he mul iple c acking s age, dis ances be ween c acks a e no smalle han δ and no la ge han 2δ. The spa ial in oduc ion o c acks occu s andomly un il no space emains o new c acks, in a simila way o he geome ical ca pa king p oblem. Widom [29] de e mined ha he a e age dis ance be ween c acks equals X=1.337δ. By means o his alue i is possible o de e mine he composi e s ain (εmc) when he mul iple c acking s ops: m mu emc E   )666.01(  (4) whe e: mm eVE VE   (5) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 15 o in e nal ein o cemen and gene a es a cu e ha shows conside able di e ences wi h he expe imen al ones (se ies TB1). The p oposed simula ion p esen s op imum esul s o he mul iple c acking s ain εmc, so he e a e no signi ican disc epancies be ween he analy ical and expe imen al da a on his key poin . The beha iou o he model a s age III is sa is ac o y due o he in oduced non-linea i y which imp o es he model’s pe o mance a he end o his s age. The C acking Model has been success ully p o en by he au ho s wi h o he ein o cing ma e ials such as glass, ca bon and s eel wi e [14]. This ac enhances he e sa ili y o he C acking Model o ma e ials ha could be used as TRM ein o cing co e. Mo eo e , his model has al eady been employed as a cons i u i e equa ion in nume ical models de eloped o simula e he beha iou o ein o ced conc e e beams s eng hened in lexu e using Tex ile Rein o ced Mo a [14]. 5. Conclusions Bo h as new cons uc ion ma e ial o as s uc u al s eng hening solu ion, ino ganic- based composi es, mainly TRM and TRC, ha e inc eased hei ele ance wi hin he cons uc ion a ea and a e cu en ly ocusing he e o s o se e al esea ch g oups. Fo his eason, i is impo an o s anda dize he use o he TRM. Cha ac e iza ion es , manu ac u ing and applica ion guides o analy ical models a e among he aspec s ha should be no malized. The e a e s udies ha ha e de eloped analy ical and nume ical models wi h sa is ac o y esul s. Howe e , mos o hem a e e y sophis ica ed and hei applica ion could be expensi e in e ms o ime and budge . The e o e, i is necessa y o de elop models easy- o-apply. TRM, as s eng hening ma e ial, usually wo ks unde ensile loads which a e ans e ed by adhe ence om he s eng hened elemen . I is essen ial o s udy he ensile beha iou o TRM o de ine i s possibili ies and ailu e modes. Especially a e s a ing ha hese ailu e modes ha e di e en na u e compa ed o hose obse ed in o he ex e nally bonded s eng hening sys ems. Tex ile Rein o ced Mo a is a composi e wi h a e y complex ma e ial beha iou . In addi ion, i s s uc u al ele ance asks o accu a e model wi h no signi ican disc epancies wi h he eal beha iou . A non-linea model is p esen ed in his pape o desc ibe he s ess-s ain beha iou o TRM unde uniaxial ensile loading. The model is based on he RC c ack con ol exp ession included in he Eu ocode 2, bu akes in o accoun he na u e o he composi e cons i uen ma e ials. The goal o his s udy is o e i y he simula ion, called C acking Model, con as ing i s esul s wi h hose ob ained in an expe imen al campaign also included in his pape . In addi ion, a well-known model as ACK heo y is 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 16 also discusses in his documen and i s simula ions compa ed wi h he expe imen al esul s. Due o he good i be ween he calcula ed and he expe imen al alues, he C acking Model migh be employed in nume ical models as TRM cons i u i e equa ions. Ne e heless, due o he na u e and he ho oughness o he s uc u al calculus wi hin cons uc ion sec o , i is necessa y o suppo his model by means o mo e expe imen al da a. Fu u e esea ch lines a e ocused on es ing new ein o cing ma e ials, mo e e ec i e ma ices and di e en ein o cing a es. Acknowledgmen s This esea ch wo k was unded h ough he esea ch p ojec s DFB 7-12-TK-2009-10 and BIA2010-20789-C04-03/04; and he schola ship p og amme o he Iñaki Goenaga Founda ion. Re e ences [1] Omb es L. Flexu al analysis o ein o ced conc e e beams s eng hened wi h a cemen based high s eng h composi e ma e ials. Composi e S uc u es, 94, pp. 143-155. 2011. [2] Si La bi A, Con amine R, Hamelin P. TRC and hyb id solu ions o epai ing and/o s eng hening ein o ced conc e e beams. Enginee ing S uc u es, 45, pp.12-20. 2012. [3] La inaga P, San-José JT, Ga cía D, Ga mendia L, Díez J. Expe imen al s udy o he lexu al beha iou o low pe o mance c beams s eng hened wi h Tex ile Rein o ced Mo a . P oceedings o he In e na ional RILEM Con e ence on Ma e ial Science (Ma Sci). Aachen, Ge many. Vol. 1, pp. 235-244. 2010. [4] T ian a illou TC, Papanicolau CG. Shea s eng hening o RC membe s wi h Tex ile Rein o ced Mo a (TRM) jacke s. Ma e ials and S uc u es, 39, pp.85-93. 2007. [5] Bou nas D, Lon ou P, Papanicolau CG, T ian a illou TC. Tex ile-Rein o ced Mo a (TRM) e sus FRP con inemen in ein o ced conc e e columns. ACI S uc u al Jou nal, 104(6), pp. 740-748. 2007. [6] Haüßle -Combe U, Ha ig J. Bond and ailu e mechanism o Tex ile Rein o ced Conc e e (TRC) unde uniaxial ensile loading. Cemen & Conc e e Composi es, 29, pp. 279-289. 2007. [7] Ri che M, Zas au BW. On he nonlinea elas ic p ope ies o ex ile ein o ced conc e e unde ensile loading including damage and c acking. Ma e ials Science and Enginee ing A, 422, pp. 278-284. 2006. [8] Chudoba R, Kon ad M, Schlese M, Meskou is K, Reisgen U. Pa ame ic s udy o ensile esponse o TRC specimens ein o ced wi h epoxy-pene a ed mul i. ilamen ya ns. P oceedings o he 4 h Colloquium on Tex ile Rein o ced S uc u es, CTRS4, D esden, Ge many. pp. 87-98. 2006. [9] Chudoba R, Vořecho ský M, Kon ad M. S ochas ic modelling o mul i- ilamen ya ns. I. Random p ope ies wi hin he c oss-sec ion and size e ec . 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Table 1 Basal ex ile geome y Design hickness, 0.0349 mm Opening size 25x25 mm Weigh o he d y shee 233 g/m2 Densi y 2.75 g/cm3 Table 2 A e age esul s o basal ex ile unde pu e ensile load Filamen - Gi en by he manu ac u e Tex ile – Expe imen al* Ul ima e ensile s eng h, σ u [MPa] 2100 1160 (0.025) Young’s Modulus, E [GPa] 89 67 (0.054) Ul ima e ensile s ain, ε [%] 3.14 1.82 (0.054) *COV be ween b acke s Table 3 Mo a dosage by weigh (%) W/C a io 0.2 Sand (g ain size < 0.6mm) 60-70 G ey cemen ype II 42.5R 30-40 Polyme ic chopped ib es 3-5 Redispe sable esins 1-3 Table 4 A e age esul s o un ein o ced specimens Fmu [N] σmu 1 [MPa] εmu [%] Em [GPa] 2480 2.48 0.03 8.25 1 σmu = Fmu / (10·100) Table 5 A e age esul s o each TRM se ies Se ies F (N) σ 1 (MPa) E ,III (GPa) ε ,I (%) ε ,II (%) ε ,III (%) TB1 3797 1088 43 0.034 0.40 2.15 TB2 8772 1256 59 0.041 0.29 1.96 TB3 12515 1195 57 0.028 0.21 2.10 TB4 16679 1194 61 0.028 0.15 2.07 1 σ = F / (0.0349·100·n) Table Table 6 ACK Theo y esul s Se ies Vm [-] V [-] Ec1 [GPa] σmc [MPa] εmc [%] TB1 0.9965 0.0035 8.46 2.54 0.734 TB2 0.9930 0.0070 8.66 2.60 0.381 TB3 0.9895 0.0105 8.87 2.67 0.263 TB4 0.9860 0.0140 9.07 2.73 0.204 Table 7 C acking Model da a and esul s Se ies Vm [-] V [-] Ec1 [GPa] σmc [MPa] εmc [%] TB1 0.9965 0.0035 8.46 2.54 0.896 TB2 0.9930 0.0070 8.66 2.60 0.473 TB3 0.9895 0.0105 8.87 2.67 0.332 TB4 0.9860 0.0140 9.07 2.73 0.261 Figu e1 Click he e o download high esolu ion image Figu e2a Click he e o download high esolu ion image Figu e2b Click he e o download high esolu ion image Figu e3 Click he e o download high esolu ion image Figu e7 Click he e o download high esolu ion image Figu e8 Click he e o download high esolu ion image Figu e9 Click he e o download high esolu ion image Figu e10 Click he e o download high esolu ion image Figu e11 Click he e o download high esolu ion image Figu e12a Click he e o download high esolu ion image Figu e12b Click he e o download high esolu ion image Figu e13 Click he e o download high esolu ion image Figu e14 Click he e o download high esolu ion image Figu e15 Click he e o download high esolu ion image Figu e22 Click he e o download high esolu ion image