Mechanical properties measurement and comparison of polyurethane foam substitute

50 MECHANICAL PROPERTIES MEASUREMENT AND COMPARISON OF POLYURETHANE FOAM SUBSTITUTE Michal Pe ů *Ondřej No ák Technical Uni e si y o Libe ec Facul y o Mechanical Enginee ing Depa men o Design o Machine Elemen s and Mechanisms S uden ská 2, 461 17, Libe ec 1, Czech Republic michal.pe [email protected] Technical Uni e si y o Libe ec Facul y o Mechanical Enginee ing Depa men o Design o Machine Elemen s and Mechanisms S uden ská 2, 461 17, Libe ec 1, Czech Republic [email p o ec ed] Abs ac Cu en ly, g ea emphasis is placed on imp o ing and op imizing o si ing com o (ca sea s, chai s, so as, hospi al ma esses...). The com o is also ela ed o sa e y, quali y, ai pe meabili y and e gonomics, which all depend on he mechanical p ope ies o he used ma e ial. Polyu e hane oams (PU) a e mos widely used o com o laye s. PU oge he wi h uphols e y ab ics c ea es comple e com o laye s. Wi h he apid oil disappea ance and i s p ice g ow h he e a e e o s o ind new solu ions which allow eplacing PU oam wi h sui able ma e ials. P e e ably ecyclable ma e ials a e wan ed o ha pu pose. An expe imen al quasi-s a ic inden ing o a load body o a PU sample is he s a ing poin o simula ions. Ob ained expe imen al da a a e used as a compa ison o he model simula ed in FEM. An e alua ion c i e ion is essen ially he con ac p essu e o he es ed sample. 1 In oduc ion An iden i ica ion and cha ac e iza ion o ma e ial p ope ies o laye s o ming a com o able ill o he sea s, ma esses, e c. is e y impo an o op imize he si ing and lying com o [1], [4]. These pa ame e s a e e y impo an especially o people who a e in cons an con ac wi h a laye o com o such as p o essional d i e s o pa ien s in hospi als. In hese cases a isk o p essu e so es is high. Du ing he design o sea s and ma esses he expe imen al measu emen s and e alua ion o con ac p essu es is equi ed. The main objec i e o he a icle was o c ea e he FEM models o polyu e hane oam and ecyclable nonwo en wi h an uphols e y ab ic ha will show simila mechanical p ope ies like eal samples. Especially, he con ac p essu es o a ious ma e ials, wi hou using an expensi e expe imen al de ice (e.g. Xsenso ) can be measu ed, es ed and compa ed. The con ac p essu es measu ed expe imen ally be ween inden e and he sample will be compa ed wi h simula ion esul s. Cu en ly, he sui able eplacemen o he Polyu e hane (PU) oam wi h ecyclable ex ile is ound, he esul will be compa ed. The expe imen al da a om he es ed samples will be used o i ual simula ion o FEM, because FEM simula ion a e e y help ul ool o biomechanical applica ions and hei esul s can se e o he op imiza ion and ob aining o desi ed p ope ies. Fo example, da a which is non-measu eable can be ob ained (s ess and s ain in di e en di ec ions...). Fo compa ison o he con ac p essu es ob ained om FEM simula ions wi h eal con ac p essu es he p essu e mapping de ice XSenso was used. 51 2 Theo y Cha ac e is ic mechanical p ope ies o samples, especially PU oam, nonwo en S u o and uphols e y ab ic, a e s ongly nonlinea . The PU oam shows iscoelas ic beha iou [1]. The ex ile S u o, due o i s speci ic o ien a ion o ibe s (pe pendicula laiding), is aniso opic and has iscoelas ic beha iou , and he uphols e y ab ic has o ho opic p ope ies in indi idual di ec ion o s ess [2]. The e o e, o a complex simula ion o he mechanical p ope ies, he signi ican FEM so wa e PAM CRASH om he ESI G oups was selec ed. PAM CRASH is a high pe o mance so wa e ha allows simula ions o he aniso opic and iscoelas ic beha iou , which is de ined di ec ly om expe imen al measu emen s. The so wa e me hod uses H-con e gence [8]; he sol ing p ocesso is buil on an explici algo i hm [1], [3] [6]. The oam ma e ial model and S u o (Fig.2) is de ined o Solid elemen s (ma e ial ype 45 - Gene al Nonlinea S ain Ra e Dependen Foam Ene gy Abso p ion wi h Op ional), based on a hypo he ical modi ied Kel in model (Fig.1), which is de ined by ela ion (1). F ig. 1 Kel in model used in PAM CRASH Fig. 2 Ma e ial 45 allows o de ine a dependence o s ess and s ain σε ε =⋅+⋅ E d d C (1) Whe e: C is New on membe (damping) and E is Hook membe (s i ness), σ is S ess and ε is s ain. The ma e ial model o he uphols e y ab ic (ma e ial ype 151 - Fab ic Memb ane Elemen wi h Nonlinea Fibe s) allows o de ine he di e en beha iou o memb ane componen s in di e en di ec ions o loading; i is based on cons i u i e ela ions o a con inuum mechanics - he ma e ial model is based on an ene gy conjuga ed pai o a G een-Lag ange de o ma ion enso (2) and 2.Piola-Ki chho s ess enso (3). () IFFE TG −⋅= 2 1 (2) T FJFS )( 11 −− = Σ (3) Whe e: G E is G een-Lag ange de o ma ion enso , S is 2. Piola-Ki chho s ess enso , F is ma e ial de o ma ion g adien , ,2,1, 0= ∂ ∂ =ji x x F j i (4) 52 1− Fis spa ial de o ma ion g adien , ,2,1, 0 1= ∂ ∂ = −ji x x F j i (5) I is iden i y ma ix, , 10 01 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ =I (6) Jis Jacobian o de o ma ion, ,de FJ = (7) Σ is Cauchy s ess enso in ma ix no a ion (8) . ij σ Σ = The loading body (Inden o ) was made o he polyamide, acco ding o ou own design om he CAD da a. The inden o was de ined in so wa e as a Rigid Body c ea ed om SHELL elemen s (ma e ial ype 101 - Elas ic - Plas ic Fo Shell Elemen s). The elas ic beha iou o his ma e ial model is de ined by he shea modulus G (9) and he bulk modulus K (10), 2(1 2 ) E G µ =+, (9) 3(1 2 ) E K µ =−. (10) Cha ac e is ic p ope ies o he inden o ma e ial model a e in he able 1. Tab. 1 Mechanical p ope ies o he inden o Pa Ma e ial model Densi y ρ [kg/m^3] Young's modulus E [GPa] Poisson numbe µ [-] Shea modulus G [GPa] Bulk modulus K [-] Inden o Elas ic - plas ic 1140 3.6 0.41 0.989 6,666 3 Expe imen and simula ion measu emen 3.1 Expe imen al measu emen The expe imen al samples o he oam and S u o we e pu o he expe imen al de ice. Each sample consis ed o ou laye s. The o al dimension o he PU sample was 500x500x100 mm; in he case o he S u o sample i was 500x500x93 mm (Fig.3, 4). 53 F ig. 3 Sample o PU oam Fig. 4 Sample o S u o The expe imen al de ice enables a p e-loading o he uphols e y ab ic in bo h di ec ions (X, Y) a an ini ial p eload o 60 N, which is con olled by load cells (Fig.3). The dimensions o he uphols e y ab ic we e 500x500x0, 799. Subsequen ly, he sample was quasi-s a ically pushed wi h he inden o in Z-di ec ion 30 mm deep in o he sample. The applied speed o mo emen was 50mm/min. Fo he measu emen and e alua ion o con ac p essu es XSenso de ice was applied. This de ice can measu e he con ac p essu es be ween he inden o and sample. Because his de ice is an addi ional laye , i s mechanical p ope ies mus secu e only minimal inc easing o con ac p essu es. The comple e a angemen o he expe imen is seen in Fig.5 and 6. F ig. 5 P es ess o UF on 60 N Fig. 6 Comple e es ing de ice 3.2 Simula ion measu e A i ual model o a ma ess sample (Fig.7, 8) o he same geome ical dimensions was c ea ed in he PAM CRASH so wa e. This so wa e is e y sui able o he simula ion o ma e ials wi h s ong nonlinea beha iou [6]. A ini e elemen mesh o he simula ion model o indi idual pa s ( ab ic, PU oam, and inden o ) was c ea ed in a special p e-p ocesso Hype mesh Al ai [7]. Ma e ial p ope ies o uphols e y ab ic model we e de ined by [2] and he ab ic was loaded in X and Y di ec ions on he alue o p e ension 60N as well as in expe imen al measu e. Subsequen ly, he inden o was pushed o he sample o he dep h o 30mm. Fo his pu pose, he senso unc ion was used. Bounda y condi ions we e de ined o he mo emen o he uphols e y ab ic. Unloaded sides o ab ics we e ixed agains shi in all di ec ions. P es ess o UF o 60N Uphols e y ab ic (UF) XSenso Load cell 54 F ig. 7 Simula ion model in FEM Fig. 8 P es ess o UF in FEM The p es essing o uphols e y ab ic on p es ess 60N is shown in ig. 9. The e can be seen elonga ion o sample sides and a de o ma ion o he mesh. In he ig. 10 is seen he inden o pushed 30mm deep o he sample. F ig. 9 P es essed UF in FEM Fig.10 Pushing o inden o 4 Resul s The simula ion gi es lo s o esul s, bu o an e alua ion o com o quali y he con ac p essu e is mos impo an . The compa ison o he measu ed expe imen al da a om XSenso and ob ained om he simula ion a e shown in ab. 2. In ig. 13-16 a e displayed p essu e maps o bo h samples. Also g aphs ( ig.17,18) wi h dependence o he o ce on displacemen a e added. In hese g aphs i is possible o compa e he cou se o he expe imen al and simula ed cu e. P e ension 60 N o uphols e y ab ic in FEM Y=0 X =0 55 Tab. 2 Compa ison o expe imen al and simula ed con ac p essu e peaks Expe imen al measu e Simula ion measu e Sample Con ac P essu e in displacemen 30 mm [GPa] Con ac P essu e in displacemen 30 mm [GPa] PU oam wi h Fab ic 1.442E-5 1.492E-5 STRUTO wi h Fab ic 1.287E-5 1.236E-5 F ig. 11 FEM – Pushing o inden e o PU oam Fig. 12 FEM – Pushing o inden e o S u o F ig. 13 FEM –de ail Con ac p essu es o PU oam 56 Fig. 14 FEM –de ail Con ac p essu es o S u o F ig. 15 Con ac p essu es o PU oam expe imen al measu emen wi h XSenso Fig. 16 Con ac p essu es o S u o expe imen al measu emen wi h XSenso 57 F ig. 1 7 Dependence o ce – displacemen o PU oam sample Fig. 18 Dependence o ce – displacemen o S u o sample 5 Conclusion The a icle has shown he simula ion o mechanical p ope ies in FEM en i onmen . The main aim was o c ea e FEM models o polyu e hane oam and bulky nonwo en wi h nonlinea beha iou and p ope ies o eal samples. The e y impo an was he e alua ion o con ac p essu es be ween he modeled ma e ial and inden e . These con ac p essu es we e compa ed wi h con ac p essu es o eal samples. The esul s a e in close ag eemen wi h each o he (see ig. 13-16). Also s ain-s ess cu es o expe imen al and modeled ma e ials a e e y close ( ig. 17-18). Thus i can be concluded ha he FEM simula ions a e use ul ool o he op imizing and es ing o new ma e ials, because hey educe ime and he cos o e y expensi e expe imen al measu emen s. 58 Li e a u e [1] NOVAK,O.; PETRŮ, M.: SIMULATION OF MATTRESSES FOR IMMOBILE PATIENTS, Au ex 2009 Wo ld Tex ile Con e ence, ISBN 978-975-483-787-2, Izmi Tu key. [2] NOVAK,O.; PETRŮ, M.: SIMULATION OF NONLINEAR MATERIAL PROPERTIES OF UPHOLSTERY FABRICS, 16 h in e na ional con e ence S u ex, ISBN 978-80-7372-542-6, Libe ec, Czech epublic. [3] PETŘÍK, J.; PETRŮ,M.: SIMULATION OF THE TRANSMISSIBILITY OF THE NON- LINEAR MATERIALS, In: VIBROENGINEERING 2009, P oceedings o he 8 h In e na ional Con e ence, Klaipeda, Li huania, ISSN 1822-1622. [4] PETRŮ,M.; PETŘÍK,J.: SYSTEMS TO OPTIMIZE COMFORT AND DEVELOPMENTS OF CAR SEATS, ACTA TECHNICA CORVINIENSIS – Bulle in o Enginee ing, ANNALS o Facul y Enginee ing Hunedoa a, Romania, In e na ional Jou nal o Enginee ing – ascicule 4, ISSN 1584-2665. [5] PETŘÍK,J.; PETRŮ,M.: OPTIMALIZATION OF THE SEAT CUSHION COMFORT LAYER, 50. Con e ence o Depa men s o Pa s and Mechanism o Machines, Zilinska uni e zi a, Slo ensko, ISBN 978-80-554-0080-8. [6] PAM-CRASH/SAFE, Re e ence And Sol e No es Manuals, Ve sion 2005. [7] ALTAIR HYPERMESH 9.0, www.al ai .com/so wa e/hw_hm.h m. [8] BELYTSCHKO,T. ; LIU,W.K. ; MORAN, B.: Nonlinea Fini e Elemen s o Con inua and S uc u es. John Wiley, Chiches e , 2000. Ing. Michal Pe ů Ing. Ondřej No ák