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