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Jerzy Smardzewski1, Silvana Prekrat2, Stjepan Pervan2

Research of Contact
Stresses between Seat
Cushion and Human Body
Istraživanje kontaktnih naprezanja između
ojastučenja sjedala i korisnikova tijela
Original scientiﬁc paper • Izvorni znanstveni rad
Received – prispjelo: 17. 2. 2010.
Accepted – prihvaćeno: 17. 5. 2010.
UDK: 630*836.1; 674.23
ABSTRACT • Design optimization of seat cushions is associated with the need to investigate their softness using,for this purpose, various kinds of loading pads. The aim of the investigation was: to determine seat cushion stiffness of a chair selected from a set of dining-room furniture, to determine values and distributions of contact strainson the seat surface caused by loading pad of different hardness, numerical calculation of contact strains between
the seat cushion and the loading pad and to verify the results of these calculations with the results of laboratory
experiments. The performed tests showed that the assessment of the seat cushion stiffness and the evaluation ofcontact stresses on their surface should be carried out using an equally stiff loading pad. In numerical calculations, polyurethane foams should be modeled as hyperfoam bodies of σ=f(ε) characteristics determined in an axial
compression test. Contact stresses between the seat cushion and the user’s body should be reduced as a result of
application of a frictionless connection of thin layers of polyurethane foams with foam forming the proper elastic
layer of the seat.
Keywords: seat cushion, human body, contact stresses, numerical analysis

SAŽETAK • Optimizacija konstrukcije ojastučenja sjedala povezana je s potrebom istraživanja krutosti s
gledišta različitih vrsta podložaka. Svrha opisanog istraživanja bila je odrediti krutost ojastučenja sjedala izabranoga iz asortimana namještaja za objedovanje, odrediti vrijednosti i raspodjelu deformacija površine ojastučenja
sjedala s obzirom na podloške različite tvrdoće, numerički izračunati kontaktna naprezanja – deformacije između
ojastučenja sjedala i podloška, te provjeriti rezultate dobivene laboratorijskim ispitivanjem. Provedena ispitivanja
pokazuju da postizanje krutosti ojastučenja i procjena kontaktnih naprezanja na površini trebaju biti obavljeni
korištenjem podložaka istovrsne tvrdoće. U numeričkom proračunu poliuretanske pjene trebaju biti modelirane
kao potpuno upjenjena tijela kojima je čvrstoća funkcija naprezanja određena u aksijalnome kompresijskom testu
σ=f(ε). Kontaktna naprezanja između ojastučenja sjedala i korisnikova tijela trebala bi biti smanjena zbog primjene spojeva koji ne uzrokuju trenje između tankih slojeva poliuretanske pjene i pjene koja tvori odgovarajući
elastični sloj sjedala.
Ključne riječi: ojastučenje sjedala, ljudsko tijelo, kontaktno naprezanje, numerička analiza

1

The author is a professor at the Department of Furniture Design, Faculty of Wood Technology, Poznan University of Life Sciences, Poznań,Poland. 2The authors are assistant professor and associate professor at the Wood Technology Department, Faculty of Forestry, University ofZagreb, Croatia.
1
Autor je profesor u Zavodu za dizajn namještaja Fakulteta drvne tehnologije Sveučilišta u Poznanu, Poljska. 2Autori su docentica i izvanredni profesor Drvnotehnološkog odsjeka Šumarskog fakulteta Sveučilišta u Zagrebu, Hrvatska.

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1 INTRODUCTION
1. UVOD
Scientiﬁc development in the ﬁeld of analysis of
the sitting position and adjusting furniture to the user’s
physiological features began with Staffel’s (1884) statement that “chairs are almost exclusively designed forthe eye, for their beautiful form rather than for theback”. These investigations showed that factors affecting sitting comfort included: the value of contact stresses between the seat cushion and the user’s body, stresses inside soft tissues, period of utilization of a given
piece of furniture, anatomic construction of the user’s
body, size and gender of the user, temperature of the
body and seat, predisposition to secrete and absorb
sweat, air circulation as well as the way of sitting (Carison, 1995; Deﬂoor and Grypdonck, 1999; Dzięgielewski and Smardzewski, 1995; Gefen, 2005; Guzik, 2001;
Kapica, 1993; Kapica and Smardzewski, 2001; Kernozek, 2002; Kokate et al, 1995; Krutul, 2004; LinderGanz and Gefen, 2004; McCormick, 1957; Nachemson, 1976; Nowak, 1993; Slavikova, 1988; Smardzewski
et al, 2006; Smardzewski and Wiaderek, 2006; Smardzewski, 2008; Stępowski, 1973; Stinson, 2003; Wang
and Lakes, 2002).
Furthermore, the above studies clearly show thatcompression forces caused by maintaining the sitting
position should not lead to constrained circulation in
the surface cardiovascular system. Each pressure
exceeding 32 mm/Hg may result in closing the veinand next the artery lumen slowing down or even stopping blood circulation leading to localized ischaemia(Krutul, 2004; Stinson, 2003).
The value of stresses between the user and theseat cushion increases proportionally to the user’s bodyweight and is closely related with the stiffness of theused materials. For these reasons, attempts have been
made, so far unsuccessful, to ﬁnd materials with properties similar to the stiffness of the human soft tissue(Smardzewski et al, 2006; Linder-Ganz and Gefen,
2004; Wang and Lasek, 2002). That is why more research is necessary to ﬁnd new ways of optimizing design and certiﬁcation of anthropo-technical systems
such as furniture for sitting.
It is evident from the performed review of thecurrent state of knowledge in the area of cushion modeling of furniture for sitting that so far research has
been focussed on: the determination of anthropometricproperties of individual Polish and European group populations, determination of elastic properties of the soft
tissues of the human body, gels and porous polyurethane foams, property modeling of hyper-elastic bodies
and systems made up of traditional cylinder or conicalsprings as well as modeling of contact phenomena
between two hyper-elastic bodies. In addition, basic
research is also being conducted in the ﬁeld of property
modeling of auxetic materials and ways of their practical application.
However, in literature on the subject, there is alack of research results in the area of interactions
between: ecology, ergonomics, anthropometry, con96.......

struction, technology, functionality, mechanics, biomechanics, strength and durability of furniture utilization
important for an impeccable design. There is also alack of research on design optimization of seat cushions, including reasons for testing seat softness,using for this purpose loading pads of various stiffness.
It is not quite clear whether the widespread use of hardloading pads instead of soft ones modeled to the shapeand anatomically resembling parts of human body ismethodologically justiﬁed.
The objective of investigations was: to determine
seat cushion stiffness of a chair selected from a set of
dining-room furniture, to determine values and distributions of contact strains on the seat cushion surface
caused by loading pad of different hardness, numericalcalculation of contact strains between the seat cushionand the loading pad and to verify the results of thesecalculations with the results of laboratory experiments.
2 MATERIAL AND METHODS
2. MATERIJALI I METODE
The object of experiments was a chair from a setof dining-room furniture. The seat measuring 400 mm
x 400 mm was made of several materials forming four
layers, Figure 1. The base layer was a 16 mm particleboard onto which 40 mm thick T4060 polyurethane
foam was glued. The seat was covered with upholstery
fabric lined with nonwoven fabric in order to ensure
minimum friction with the polyurethane foam and desired visual effect.
The seat was loaded using a loading pad with ashape and dimensions corresponding to the appropriate
standard (PN-EN 1728:2000). The hard loading pad
was made of oak wood, Figure 2a, whereas the softloading pad was prepared by covering the hard one
with 30 mm thick T4060 polyurethane foam, Figure
2b. Bearing in mind the need to represent the contact
phenomenon between the two parts, the foam was notglued to wood and, additionally, the chair seat was loaded with a volunteer student, 183 cm tall and weighing
74 kg, corresponding to male anthropometric traits of
50 % of European population.

Figure 1 Structure of the seat used in experiments: 1)
upholstery fabric (1.5 mm thick), 2) cotton wool 120 g/m2, 3)
T4060 polyurethane foam (40 mm thick), 4) particleboard(16 mm thick)Slika 1. Konstrukcija (prikaz slojeva) sjedala korištenoga ueksperimentu 1 – tkanina debljine 1,5 mm, 2 – pamučna vunagustoće 120 g/m2, 3 – T4060 poliuretanska pjena debljine 40
mm, 4 – iverica debljine 16 mm

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F

F

Wood
drvo
a)

T2520

b)

Figure 2 Construction of the sensor used in investigations:a) hard, b) soft with 30 mm thick T4060 polyurethane foam
Slika 2. Konstrukcija podloška upotrijebljena u istraživanju:a) tvrdi, b) meki, obložen s 30 mm debelom T4060 poliuretanskom pjenom

Laboratory experiments were carried out on threedifferent research stands. The ﬁrst experiment of seatcushion stiffness using a hard loading pad was performed on a special testing machine developed for furniture certiﬁcation, Figure 3a. As recommended by PNEN 1728:2000, PN-EN 1729-2:2006 standards, thepressure was exerted with a F force of 1300 N. Consecutive experiments were carried out on the ZWICK
1445 testing machine using both hard and soft loading
pads pressed into the seat with the maximum force of
760 N, Figure 3b. The ﬁnal laboratory test consisted inloading the seat with a volunteer exerting the force of
740 N, Figure 3c. In order to measure contact stresses
between the sensor/volunteer and the seat cushion, an
FSA sensor mat was used consisting of 32 x 32 sensors
arranged in the form of a 900 x 900 mm sheet. The mat
guaranteed measurements of stresses in the 0-200mmHg interval with 3% accuracy. Results of thesemeasurements were collected and collated in the formof a diagram and maps of stress distribution. The seatcushion stiffness was determined on the basis of themeasurement results of values of F loads and their corresponding dL displacements illustrating the dependencies on the F=f (dL) chart.
Numerical calculations of the contact between
the loading pad as the model of a human body and theseat cushion were carried out in the ABAQUS systema)b)environment using the ﬁnite element method (FEM)
algorithm. Three and four-nodal envelope elements in
ﬂat state of stress were used for modeling. All component elements of the model were 400 mm thick corresponding to the length of the loading pad and the seat.
Calculations were carried out for two static schemes.
The ﬁrst scheme corresponded to driving in the hardloading pad into the T4060 foam with the force of 760
N, Figure 4a. The second scheme represented forcing
in the soft loading pad with the same force into theidentical foam, Figure 4b. Bearing in mind the seat,loading pad and load symmetry, the calculation model
was reduced to the symmetrical, right half of the system. The model was supported in a way that ensured
freedom of the vertical play of the loading pad which
was loaded with a pressure q of 5.9375·10-6 kPa value
corresponding to the force of 760 N. When modelingthe contact between two bodies, it was assumed that in
the case of the model with the hard loading pad the‘master’ and ‘slave’ type surfaces would occur, respectively, on the surfaces of the loading pad and the T4060
foam, Figure 4a. For the model with the soft loading
pad, two pairs of surface were formed. The ﬁrst pair ofthe ‘master’ and ‘slave’ type surfaces occurred between
the hard loading pad and the T2520 foam, while thesecond pair of surfaces, between the T2530 and T4060
foams, Figure 4b.
When preparing the developed model for numerical calculations, it was necessary to determine elastic
properties of the applied materials. The wooden part ofthe loading pad was assigned elastic properties of oak
wood as an isotropic material of the Young modulus of
E=15 GPa and Poisson coefﬁcient of 0.3. Polyurethane
foams belong to hyper-elastic materials (Smardzewski,
2008; Smardzewski et al, 2008) and some of them caneven be considered auxetic materials (Leaks, 1986,
1991, 1992, 1993, 1996). That is why their elastic properties were determined in a single axis compression
test (Smardzewski, 2008), Figure 5. The obtained characteristics in the form of a dataset σ=f (ε) were fed
into the ABAQUS system using a hyperfoam type model for these bodies.

c)Figure 3 Stands for seat cushion stiffness tests and contact pressures on their surface: a) a special testing machine developed
for furniture certiﬁcation, b) ZWICK 1445 testing machine, c) volunteer weighing 74 kg
Slika 3. Uzorci za testiranje krutosti sjedala i kontaktnog tlaka na površini: a) specijalni uređaj razvijen za ispitivanje namještaja
prema normama, b) ZWICK 1445 uređaj za testiranje, c) ispitanik mase 74 kg

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Wood
drvo

q=5.9375E-6 kPa
Contact surface – masterkontaktna površina – podložak
Contact surface – slave
kontaktna površina – sjedalo.......

q=5.9375E-6 kPa
Contact surface – master and slave
kontaktna površina – podložak i sjedalo

T4060

Wood
drvo
T2520
T4060

a)

b)

Contact surface – masterkontaktna površina – podložak
Contact surface – slave
kontaktna površina – sjedalo

Stress / naprezanje, kPa

Stress / naprezanje, kPa

Figure 4 Static load model of the chair seat cushion by: a) hard sensor, b) soft sensor
Slika 4. Model statičkog opterećenja ojastučenog sjedala stolice a) tvrdim podloškom b) mekim podloškom

Strain / deformacija

Strain / deformacijaa)b)Figure 5 Polyurethane foam stiffness: a) T4060 foam used on the chair seat, b) T2530 foam used as the loading pad cover
Slika 5. Krutost poliuretanske pjene: a) T4060 pjena upotrijebljena za sjedalo stolice, b) T2530 pjena upotrijebljena kao obloga
podloška

3 RESULTS
3. REZULTATI

Load / opterećenje, N

The stiffness of the seat cushion loaded with two
types of sensors is presented in Figure 6. It is clear
from this Figure that the use of the hard loading padcaused a signiﬁcantly smaller foam deﬂection thanwhen the soft loading pad was applied. For example,
for the same load of 400 N, the difference in the recor-

Displacement / pomaci, mm

Figure 6 Seat cushion stiffness: H_1300 – hard loading padloading up to 1300 N, H_760 – hard sensor, loading up to 760
N, S_760 - soft loading pad loading up to 760 N
Slika 6. Krutost ojastučenja sjedala: H_1300 – tvrdi podložak,opterećenje silom do 1300 N, H_760 – tvdi podložak, opterećenje silom do 760 N; S_760 – meki podložak, opterećenje
silom do 760 N
98

ded seat deﬂection amounted to 20 mm. This can be
attributed to the superposition of T2530 and T4060
foams which formed a serial system of elastic materials
whose resultant stiffness was smaller than the component stiffnesses.
Expressing seat cushion stiffness by k= dF/dL
quotient, seat stiffness can be calculated on the basis of
Figure 6. When the hard loading pad was applied, themean value of the seat cushion stiffness coefﬁcient k
reached 26.6 N/mm, whereas when the soft loading
pad was used the stiffness coefﬁcient of the same seatcushion ranged from 6.66 N/mm to 18.40 N/mm. Hence, objective seat cushion stiffness assessment should
be carried out exclusively using loading pad of identical hardness.
The impact of loading pad hardness on the distribution of stresses on the seat cushion surface is wellillustrated in Figure 7. Using a hard loading pad driven
into the seat with the force of 1300 N, the greatest contact surface was achieved as well as the highest stresses
reaching values of 120-130 mmHg, Figure 7a. Whenthe value of the pressure force was reduced and thesame hard sensor was used, values of contact stresses
were reduced proportionally to value changes of theload, Figure 7b. In this case, contact stresses did notexceed 51 mmHg. Additionally, it should be emphasized that chair seats are considered ergonomic and functional when the pressures exerted on the human body
do not exceed 32 mmHg. From this viewpoint, the examined seat cushion was too stiff and did not guarantee
sufﬁcient level of comfort during long hours of meetin-

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Measuring point / mjerna točka

Figure 8 Pressures in selected points of the sensor mat(fourth row from top)
Slika 8. Tlak prikazan u odabranim točkama prostirke(četvrti red odozgo)

Figure 7 Pressure distribution on the seat cushion surface in
mmHg caused by: a) hard loading pad at the load of 1300 N,b) hard loading pad at the load of 760 N, c) soft loading padat the load of 760 N, d) a volunteer of 74 kg weight
Slika 7. Raspodjela tlaka na površinu sjedala u mmHg
prouzročena: a) tvrdim podloškom pri sili od 1300 N, b) tvrdim podloškom pri sili od 760 N, c) mekim podloškom pri
760 N, d) tijelom ispitanika mase 74 kg

gs, talks and meals. However, when the kind of sensor
was changed to soft driven into the seat cushion withthe force of 760 N, the value of the obtained contactpressure was 36 mmHg, Figure 7c. Loading of thesame seat by a volunteer weighing 74 kg resulted in the
distribution of contact pressures different from thoseobtained using loading pad, Figure 7d. Pressure values
were also different with their upper value not exceeding 47 mmHg in the place where the sciatic tubers
were supported.
In order to better illustrate differences in the distribution of pressures on the seat surface caused by different loading pad as well as by the volunteer, Figure 8
shows the course of pressures in the same, fourth fromthe top, row of loading pad running along the width ofthe mat. It is clear from this Figure that the value of contact stresses is signiﬁcantly dependent on the loading
pad hardness. Nevertheless, making the construction of
the soft loading pad similar to the structure of the humanbody failed to guarantee similar stress values. On theother hand, similar stresses were obtained in the case of
application of the loading pad with the pressure of 760
N. It can be stated, on the basis of the performed experiments, that the hard loading pad better represents
working conditions of the seat cushion under operatingload and makes it possible to better assess the stiffness
and functionality of the examined chairs.
From the viewpoint of design of furniture for sitting and/or resting, it would be exceptionally advantageous to be able to carry out virtual quality assessmentof seats at the stage of their designing or modeling in
the CAD system environment. Creating block models,
it is relatively easy to subject them to numerical calculations that can verify: construction stiffness as well as
the strength of cross sections and connections.
Figure 9 presents distribution of reduced stresses
according to Mises caused by loads with the hard andsoft loading pad driven into the T4060 foams.

Figure 9 Reduced stresses according to Mises during loading of the seat cushion with the force of 760 N by: a) hard loading
pad, b) soft loading pad
Slika 9. Smanjenje naprezanja prema Misesu tijekom trajanja opterećenja na ojastučenje sjedala silom od 760 N i upotrebom:a) tvrdog podloška, b) mekog podloška

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Table 1 Contact stresses on the seat surface caused by loading pads of different hardness
Tablica 1. Kontaktna naprezanja na ojastučenje sjedala prouzročena podlošcima različite tvrdoće
Contact stress, kPa (mmHg)
Kontaktno naprezanje, kPa (mmHg)
Sensors mat / Senzorska prostirka Numerical calculations / Brojčani izračun
H_130013.99 (105)14.49 (108.7)
Hard / tvrdi
H_760
5.99 (45)6.63 (49.74)
Hard / tvrdi
S_760
2.66 (20)
2.68 (20.11)
Soft / meki
Volunteer / ispitanik Volunteer / ispitanik
4.79 (36)(-)
Loading pad type
Tip podloška

Designation
OznakaIt is evident from Figure 9 that the application ofan additional layer of soft T2520 polyurethane foam in
the construction of the loading pad caused a signiﬁcantreduction of pressure on the surface of the T4060 foam,
Figure 9b. In such situation, the strongest stresses wereconcentrated in the central layer causing simultaneously maximum stresses of 2.68 kPa on the surface of theseat. In the case of a uniform hard loading pad, contact
stresses on the seat surface amounted to 6.63 kPa. The
obtained results of numerical calculations were compared with the results of measurements taken using a sensor mat and they are collated in Table 1.
On the basis of this comparison, tt is possible todemonstrate that the results of the performed numerical calculations differ from measurement results in therange of 0.74% to 9.65% and always reach values higher than those obtained in the laboratory. The accuracy of the obtained results was achieved both thanks
to the quality of the elaborated numerical model, thequality of the introduced data about material characteristics as well as the calibration error of the sensor mat
and standard measurement inaccuracies resulting fromtechnical properties of the sensor mat. However, it
should be emphasized that the accuracy is satisfactoryand justiﬁes the use of numerical methods for anthropo-technical design and modeling of furniture for work,
meal consumption and rest.
4 CONCLUSION
4. ZAKLJUČAK
The following conclusions were drawn on the basis of the analysis of the obtained research results:
1. Seat cushion stiffness assessment should be carriedout using the identical loading pads of stiffness selected by the investigator.
2. Contact pressure distribution assessment on theseat cushion surface should be carried out with theassistance of a hard loading pad.
3. In the course of numerical calculations polyurethane foams should be modeled as hyperfoam bodies
of σ = f (ε) characteristics determined during theaxis compression test.
4. Contact stresses between the seat cushion and theuser’s body should be decreased as a result of application of a frictionless combination of thin layers ofpolyurethane foams with foams forming the proper
elastic layer of the seat.

100

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Corresponding address:
prof. dr hab. JERZY SMARDZEWSKI, Ph.D.
Poznan University of Life Sciences
Faculty of Wood Technology
Department of Furniture Design
ul. Wojska Polskiego 38/42
60-637 Poznań, Poland.
E-mail: jsmardzewski@up.poznan.pl101