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Textile Research Journal

0(00) 1–13

Study on the tensile modulus of ! The Author(s) 2019

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seamless fabric and tight compression DOI: 10.1177/0040517519859931
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finite element modeling

Jiahong Wu1, Zimin Jin1 , Jing Jin2, Yuxiu Yan1 and Jianwei Tao3

Abstract
Tight compression garments are able to exert pressure on the surface of the human body, helping to relieve muscle
fatigue and accelerate recovery. In order to study the effect of the tensile property on fabric pressure on the human
body, by response surface methodology, in this paper 13 seamless knitting fabrics were designed with various knitting
parameters, including the linear density of bare elastic yarn (33.3, 55.6 and 77.8 dtex), yarn feed tension (0.015, 0.030 and
0.045 cN/dtex) and fabric structure (1  1 mock rib, cross-float and plain stitch). Through tensile testing, the tensile
moduli of 13 fabrics were measured and the effect of knitting parameters was analyzed. In addition, a finite element
method was used to simulate the tight pressure on the human thigh of fabrics with different tensile moduli with ANSYS
workbench 19.0. Furthermore, an actual pressure experiment was designed to prove the accuracy and validation of the
simulation. The result showed that the effect of yarn feed tension on the elasticity modulus was the least significant, while
linear density and structure had a great influence. A quadratic response surface regression model of the elasticity
modulus was created, which could calculate a bare elastic yarn knitting fabric by using its parameters. It was proved
that the finite element model was able to predict pressure accurately. Through the pressure numerical simulation of
three fabric samples with different tensile moduli (0.111, 0.253 and 0.523 MPa), it was indicated that for fabric with a low
tensile modulus, its tight compression merely changed as elongation increased; however, for fabric with a high tensile
modulus, tight compression was promoted as elongation increased.

Keywords
seamless technology, knitting parameters, tight compression, elasticity modulus, finite element modeling response, sur-
face methodology

Tight-fitting sportswear can apply gentle firming pres- curvature of the human body surface will also have
sure to specific parts of the body through its own elas- an impact on the pressure. Malgorzata et al.6 used the
ticity and stretch recovery performance.1 After intense I-scan system to evaluate two knitting fabrics of differ-
exercise, it helps athletes as well as fitness enthusiasts to ent structures, and their pressure exerted on an actual
relieve muscle fatigue and accelerate recovery of muscle human body and a manikin was tested. It was found
capacity, so as to strengthen their sports performance.2 that the pressure was related to the fabric structure and
Tight compression is an important factor affecting the the pressure on the actual human body was lower than
functionality and comfort of tight-fitting sportswear.3
A reasonable level of pressure can negate negative
effects, such as causing discomfort, obstructing exer-
cise, increasing exercise load, etc.4 1
Zhejiang Sci-Tech University, China
2
There are numerous tight-fitting sports products on Hangzhou Vocational & Technical College, China
3
Zhejiang Bangjie Digital Knitting Co., Ltd, China
the market currently; however, the effect of their tight
pressure cannot be measured by a unified standard or Corresponding author:
method.5 Actually, the factors are very complicated. Zimin Jin, Zhejiang Sci-Tech University, Hangzhou, China.
Apart from the tensile properties of the fabric, the Email: kivenjin@163.com
2 Textile Research Journal 0(00)

on the manikin. Lee et al.7 developed a tight-fitting parameters on the tensile property of the fabric, with
trouser that enhances the stability of the lower limbs, a mathematical model between the process parameters
which was combined with kinematics. In addition to the and elastic modulus established. Then, combined with
physical pressure test method, many scholars have also the elastic moduli of different fabrics, their tight pres-
studied the pressure by finite element simulation.8 In a sure was simulated by a finite element method. Finally,
study of pressure gloves for the treatment of prolifera- the numerical results of the finite element pressure
tive scars,9 Yu et al. used ABAQUS finite element soft- simulation are verified by the physical tight pressure
ware to simulate the fabric pressure on the dorsum of test to ensure the accuracy and validity of the finite
the hand. However, the finite element model could only element model.
simulate the pressure when fabric was stretched by
10%. Only two fabrics were used in the study.
Therefore, the conclusions had limitations, and the Fabric elastic modulus modeling by
finite element model needs further improvement. response surface methodology
The elastic modulus E refers to the fabric unit
deformation under external force, which is used to
Fabric sample design and knitting
measure the tensile properties of the fabric, and the The fabric samples were all knitted by an Italian
larger the value, the smaller the elastic deformation SANTONI SM8-TOP2 single-sided seamless knitting
occurs. Seamless knitting technology has been widely machine with a machine diameter of 13 inches and a
used in the manufacture of tight-fitting sportswear.10 needle count of 1152 needles, which can be used to
Currently, the production of seamless knitting products produce underwear, sportswear, swimwear, medical
with specific tensile properties and pressure effects usu- equipment, etc.
ally relies on the technical level and production experi- The main knitting parameters of seamless fabric
ence of engineers. Due to the different requirements of include the linear density of spandex yarn (factor A),
tensile properties and comfort of the product, it is often its feeding tension (factor B) and the structure of the
necessary to continuously adjust the knitting param- fabric (factor C). These three knitting parameters affect
eters and repeatedly produce the sample to achieve the tensile properties of the fabric.11 According to the
the desired effect. If yarn breakage occurs during knit- BBD (Box–Behnken Design) response surface experi-
ting, the product can only be scrapped.11 Elastic yarn mental design method, three factors and their levels
needs to be fed into the knitting zone through an exter- were set and coded as –1, 0 and 1 in the Design
nal active feeder, which could easily cause problems, expert software (as shown in Table 1).
including yarn breakage, retreat, reverse yarn, etc.12 The fabric samples were knitted by two yarns,
Not only is it inefficient and affects the quality of the wherein the plating yarn was nylon filament (78 dtex/
product, but it also wastes resources and increases pro- 68 f) and the spandex yarn was ground yarn. The linear
duction costs. densities were 33.3 dtex (30 D), 55.6 dtex (50 D) and
In order to improve the efficiency of product devel- 77.8 dtex (70 D), which are commonly used for seamless
opment and promote the innovation of product func- elastic fabric. The unit yarn feeding tension was set to
tionality, it is necessary to conduct research on the three levels of 0.015, 0.030 and 0.045 cN/dtex, and the
knitting parameters of seamless knitted fabric and its actual yarn tension of the spandex yarn was the prod-
tight pressure. Much research has been devoted to the uct of the unit feed tension and the linear density of the
study of the relationship between process parameters elastic yarn. The yarn feed tension needs to be compat-
and fabric properties. El-Ghezal et al.13 studied the ible with the linear density of the spandex filament so as
relationship between spandex content and the finishing to meet the quality requirements of the production.
properties of elastic denim fabrics; Cuden et al.14 con- Three different structures were applied in the paper,
ducted research with the variance analysis of the loop namely plain stitch, cross-float and 1  2 mockrib,
length of single-sided elastic knitted fabrics to investi- which are commonly used in seamless knitting
gate the influence of yarn type, structure and the relax-
ation structure; Maqsood et al.15 analyzed the influence
Table 1. Fabric sample factors and levels
of the linear density of the spandex and the length of
the float on a bi-stretch woven fabric, and a regression Level
equation for tensile and recovery properties was estab-
lished to help rationally set weaving parameters. The Factor 1 0 1
ideas and methods of these studies have provided some A (dtex) 33.3 55.6 77.8
reference for further research. B (cN/dtex) 0.015 0.030 0.045
In this paper, the Box–Behnken response surface
C (loops) 1 2 3
method is used to explore the influence of knitting
Wu et al. 3

(as shown in Figure 1). The tensile properties of seam- atmospheric standard specified in ISO 3696 for
less elastic fabrics are mainly determined by the span- 24 hours. All fabric samples were cut into rectangles
dex ground yarn. In order to quantify the structure of of 200 mm  50 mm for the test, horizontally and verti-
the fabric, the number of columns in one complete cally, according to ISO 13934-1:2014.
organization that the spandex yarn stitched into a The sample was clamped with a tension of 1 N, the
loop was used to characterize the different structures. clamping length was (100  1) mm, the moving speed of
According to the BBD response surface experimen- the holder was constant at 100 mm/min, the return
tal design method, the knitting parameters of the fabric speed was 50 mm/min and the accuracy was 2%.
samples are as shown in Table 2. There were a total of Before testing, the ends of the length direction of the
13 different fabric samples, of which samples 6, 9, 11, 15 sample were flatly fastened in the holder. Then, the
and 16 were all fabrics of the same specification. instrument was actuated and a pre-tension of 1 N was
According to the requirements of response surface applied to stretch the fabric to a predetermined elong-
data analysis, repeated tests were required, but the ation value. Finally, the instrument would automatic-
experimental data was recorded separately. ally record the tensile force value. The result of each
fabric sample was the average value of three tests.
Fabric tensile properties test and elastic Considering the tensile requirements of the spandex
seamless knitted fabric during the actual wearing pro-
modulus calculation
cess, the test sets the elongation " to 10%, 20%, 30%,
The tensile properties of all fabric samples were tested 40%, 50%, 60%, 70%, 80%, 90% and 100%
by an INSTRON 3365 universal material tester.
The fabric samples were all conditioned with the L1  L0 L
"¼  100% ¼  100% ð1Þ
L0 L0

The elastic modulus is one of the important mech-

anical properties to measure the ability of a fabric to
resist deformation when subjected to an external force.
The stress–strain curve of each sample was drawn. The
elastic modulus E of each fabric sample was solved by
Figure 1. Notations of fabric samples.
curve fitting. The value was the ratio of the stress of the
material to the corresponding strain. The calculation
formula was as follows
Table 2. Experimental design for fabric samples  F  L0
E¼ ¼ ð2Þ
" A  L
Factor
Sample where L0 is the original length of the sample (100 mm);
number A B C L1 is the length of the sample after stretching; 4L is the
1 77.8 0.045 2 tensile displacement of the sample; A is the cross-sec-
2 33.3 0.015 2
tional area of the sample; F is the tensile load; r is the
tensile stress.
3 33.3 0.030 1
4 77.8 0.030 1
5 55.6 0.015 3 Modeling of the fabric elastic modulus
6 55.6 0.030 2 Response surface methodology (RSM) is often used to
7 33.3 0.045 2 solve problems affected by multiple factors.16 Through
8 77.8 0.030 3 regression fitting, the mathematics between each factor
9 55.6 0.030 2 and response value is shown by the response surface
10 33.3 0.030 3 and contour mapping.
11 55.6 0.030 2 In this paper, three knitting parameters were taken
12 77.8 0.015 2 as the main impact factors; the mathematical relation-
13 55.6 0.015 1 ship between the fabric elastic modulus and these par-
14 55.6 0.045 1 ameters was established. The formula was as follows
15 55.6 0.030 2
X
3 X
3 X
16 55.6 0.030 2 R ¼ 0 þ i xi þ ii x2i þ ij xi xj ð3Þ
17 55.6 0.045 3 i¼1 i¼1 i5j
4 Textile Research Journal 0(00)

where R is the response value, the tensile modulus of knitted into loops, the spandex yarn would bounce
the fabric sample (N/mm2); x1 is the linear density of back as tension was eliminated, and the nylon yarn
the spandex yarn; x2 is the spandex yarn feed tension; was arched on the front side of the fabric, thereby
x3 is the number of columns in one complete organiza- increasing the thickness of the fabric.
tion that the spandex yarn stitched into a loop; 0 is a The stress–strain curves of each fabric sample were
constant; 1, 2 and 3 are linear coefficients; ii and ij drawn according to the experimental data. The elastic
are mixed quadratic coefficients. modulus (N/mm2) of each fabric sample was solved by
curve fitting. The coursewise tensile modulus and wale-
wise tensile modulus of the fabric samples are shown in
Analysis of basic performances and tensile properties Table 3. It was indicated that coursewise tensile modu-
The dry weight and thickness of 13 fabric samples were lus was larger than the walewise tensile modulus, that
measured according to ISO 3801:1977 and ISO is, the coursewise tensile stress was larger than walewise
5084:1996. The test results are shown in Table 3. tensile stress for each fabric when the elongation was
With the increase of linear density of the spandex constant, so fabrics were more likely to be deformed in
yarn and its feed tension, the square meter weight grad- the wale direction. Particularly for fabrics of plain
ually increased. Among all the fabric samples, sample jersey and cross-float, the tensile modulus differed
17 was the heaviest at 370.8 g, while the weight of greatly in coursewise with walewise, and the ratio of
sample 3 was only 241.2 g/m2. In the range of the span- the coursewise and walewise elastic modulus was up
dex linear density and the feeding tension in this experi- to 1.583. For 1  1 mockrib fabrics, however, the cour-
ment, the fabric weights of plain stitch were about sewise and walewise tensile properties were consistent,
240–320 g/m2, the cross-float about 260–340 g/m2 and with a mean ratio of 1.185.
1  2 mockrib about 280–380 g/m2.
According to the structure of the fabric, the thick- Response surface equation of the coursewise
ness of the fabric was ordered as 1  1 mockrib > cross-
float > plain jersey. For fabrics of 1  1 mockrib and
elastic modulus
cross-float, in some loops, the nylon yarn did not The tight-fitting trousers are mainly subjected to lateral
form loops but existed as float, while the spandex stretching to generate pressure on the thighs, so the
yarn was knitted into loops. In the knitting process, coursewise elastic moduli of the 13 spandex elastic
the spandex yarn was stretched under tension. After knitted fabric samples were analyzed.
The interaction on the coursewise elastic modulus of
the fabric between the linear density of the spandex
Table 3. Basic properties and elastic moduli of samples yarn and the yarn tension is shown in Figure 2. It sug-
gested that the effect of spandex yarn tension on the
Loop Tensile modulus (N/mm2) elastic modulus of fabric samples was the least signifi-
Weight Thickness density cant, that is, the coursewise elastic modulus of the
No. (g/m2) (mm) (loops/cm2) Coursewise Walewise fabric did not changed significantly as the feeding ten-
1 350.7 0.633 1196.82 0.426 0.408 sion increased; however, the linear density of the span-
2 242.2 0.780 1062.84 0.168 0.119 dex yarn and fabric structure did have a significant
3 241.2 0.587 910.53 0.153 0.124 effect on the elastic modulus of the fabric, while the
elastic modulus of the fabric increased as the linear
4 291.9 0.547 872.71 0.381 0.324
density of the spandex yarn increased.
5 299.7 0.747 1230.34 0.274 0.222
Based on the seamless knitting process, the elastic
6 309.5 0.643 1226.22 0.253 0.166
modulus of the fabric mainly depends on the spandex
7 307.0 0.853 1364.27 0.127 0.111 yarn, and the elastic modulus of the spandex yarn is
8 356.6 0.733 1295.91 0.523 0.453 proportional to its linear density, so the elastic modulus
9 309.2 0.641 1229.8 0.252 0.163 of the fabric increases as the linear density of the span-
10 314.4 1.117 1471.08 0.111 0.095 dex yarn increases. Fabric samples were sorted by ten-
11 309.6 0.645 1221.94 0.259 0.172 sile moduli from large to small as follows: 1  1
12 315.1 0.610 1029.21 0.466 0.449 mockrib > cross-float > plain jersey. The difference
13 251.6 0.530 840.45 0.223 0.151 among the three structures was the float. Fabrics of
14 302.9 0.613 1032.22 0.203 0.128 1  1 mockrib had the most float. Therefore, increasing
15 306.7 0.637 1211.14 0.251 0.161 the float in fabric can help to improve the elastic modu-
lus of the fabric, so that the fabric has better resistance
16 309.1 0.641 1220.49 0.252 0.164
to deformation and resilience. In actual production,
17 370.8 1.020 1668.24 0.183 0.155
due to good tensile properties, mockrib is usually
Wu et al. 5

Figure 2. Response surface and contour map of the fabric coursewise elastic modulus in different structures: (a) plain jersey;
(b) cross-float; (c) 1  1 mockrib.

applied to sections that are easily deformed, such as the The F-value was 181.1921 and the p-value was less than
waist, cuff, hem, etc. 0.05, indicating that the nonlinear relationship between
The results of the variance analysis and significance the factors and the response values expressed by the
test of the regression equation are shown in Table 4. model was very significant, that is, the model could
6 Textile Research Journal 0(00)

Table 4. Regression equation coefficient significance test and analysis of variance

Sum of squares df Mean square F-value P-value

Model 0.22299 9 0.024777 181.1921 <0.0001 Significant

A 0.191147 1 0.191147 1397.862 <0.0001
B 0.004571 1 0.004571 33.42641 0.0007
C 0.002163 1 0.002163 15.82123 0.0053
AB 1.14E-07 1 1.14E-07 0.000837 0.9777
AC 0.008338 1 0.008338 60.97495 0.0001
BC 0.001261 1 0.001261 9.220164 0.0189
A2 0.014192 1 0.014192 103.7897 <0.0001
B2 0.000756 1 0.000756 5.525671 0.051
C2 0.001361 1 0.001361 9.956467 0.016
Residual 0.000957 7 0.000137
Lack of fit 0.00095 3 0.000317 186.1315 <0.0001 Significant
Pure error 6.81E-06 4 1.70E-06
Total 0.223948 16

accurately express the numerical relationship between structure, such as tights. Firstly, the geometric model of
the knitting parameters and the coursewise elastic the thigh and tights was built. Then, the material prop-
modulus of the fabric. The specific formula was as erties of these two objects were determine, including the
follows elastic modulus, etc. After meshing, the initial and
boundary conditions were determined. The software
EC ¼ 0:275  0:010  A þ 4:318  B þ 0:010  C then started to calculate according to the set program
þ 0:001  A  B instructions, and finally simulated the corresponding
ð4Þ pressure magnitude and distribution on the thigh.
þ 0:002  A  C  1:184  B  C
In addition, the accuracy of the finite element simula-
þ 0:0001  A2  59:538  B2  0:018  C2 tion would be verified by an actual human body
pressure test.
where EC is the coursewise tensile modulus of the
fabric; A is the linear density of spandex yarn; B is
the spandex yarn feed tension; C is the structure of
Creation of geometric models of the thigh and tights
the fabric. Geometric model of the thigh. A healthy female college
student (25 years old, 165 cm, 53 kg) participated in
Finite element numerical simulation of this study. By using a three-dimensional (3D) human
body scanner ([TC]2, USA), rasterized 3D point cloud
fabric tightness pressure data of the human thigh were obtained. Combined with
In the above, the elastic modulus of the fabric has been reverse engineering software Imageware and 3D soft-
tested. The influence of different knitting parameters on ware SolidWorks, the thigh 3D point cloud data was
the elastic modulus of the fabric has been analyzed, and converted into a thigh entity for finite element
the secondary response surface equation has been simulation.
established. In order to continue to study the pressure Firstly, the human body 3D point cloud data was
effect of fabrics of different elastic moduli, the finite imported into the software NY Imageware 13 with data
element numerical simulation of pressure was carried of the thigh part captured, which is shown in Figure 3.
out by using ANSYS Workbench 19.0 software. After creation of the section point cloud and curve fit-
This paper mainly studied the pressure effect of tight ting of each section, the curves of the thigh section
sports pants on human thighs. The problem could be curve were drawn, as shown in Figure 3. Wherein,
simplified as the contact problem between the thigh when creating a section point cloud, the distance
solid and the tights shell. The solid refers to a solid between each section was set to 1 cm; using tolerance-
substance in which external forces is distributed based curve fitting, the closed curve of the section was
throughout its whole volume, such as the human fitted according to the section point cloud, and the
thigh; the shell substance usually refers to a layered maximum deviation of the curve was controlled
structure, and external forces act on the surface of the within 0.05, which made it possible to realistically
Wu et al. 7

Figure 3. Human thigh point cloud data and section curve fitting.

restore the geometry of the thigh and ensure the accur-

acy of the simulation.
In the SolidWorks software, the lofting tool was
used to complete the conversion of the thigh section
curve to the solid, as shown in Figure 4, where the
green curves are the fitting curves of the thigh sections
and the gray cylinder is the middle section of the thigh
that complete the entity transformation. As the main
part of the pressure control of the tights, this paper
selected the middle section of the thigh for the finite
element simulation.

Geometric model of tights. The tights shell model was

drawn using the SolidWorks software. As shown in
Figure 5, the height of the shell was the same as the
height of the thigh body. The circumference of the
upper (lower) side of the tights was the circumference
of the upper (lower) side of the thigh body multiplied
by the elongation of the fabric. In this paper, the finite
element simulation of the tight pressure of the fabric
was carried out under the three commonly used elong-
ations (10%, 20% and 30%).

Model assembly. In the SolidWorks software, the tights Figure 4. Creation of the geometric model of the thigh solid.
shell model and the thigh solid model were assembled, (Color online only.)
as shown in Figure 4, where the boss A was designed as
the sliding track of the tights. In the process of simula-
tion, the tights shell would move up along the surface of
Attribute definition of fabric and thigh
the boss A and finally slide onto the thigh. Since
the circumference of the tights was smaller than the The finite element model consisted mainly of two
circumference of the thigh, the tights shell could not materials, the thigh and tights. In the ANSYS
be directly attached to the thigh solid if the boss was Workbench 19.0 software, their elastic moduli would
not used as a reference. The height of the boss and the be set. The thigh was assumed to be a homogenized,
size of its lower bottom surface need to be adjusted isotropic linear elastomer. Based on a study of human
according to the simulated fabric elongation. The body mechanical properties, the elastic modulus and
larger the fabric elongation was, the larger the height Poisson’s ratio of the human thigh were assumed to
of the boss and the smaller size of the lower bottom be 177 kPa and 0.4, respectively, and the boss applied
surface would be. the same material properties as the human thigh.
8 Textile Research Journal 0(00)

Figure 5. Finite element simulation model assembly.

According to the response surface formula of

the elastic modulus above, the elastic moduli of
the fabric simulated were calculated and set up in the
Figure 6. Finite element simulation model meshing result.
software. In this paper, three fabric samples were
selected for finite element simulation. These were
fabric samples 10 (33.3 dtex, 0.030 cN/dtex, 1  2 mock-
rib), 12 (77.8 dtex, 0.015 cN/dtex, cross-float) and
14 (55.6 dtex, 0.045 cN/dtex, plain jersey), numbered
sequentially as A, B and C, which respectively repre-
sented the minimum value of the elastic modulus
of the fabric (0.111 N/mm2), the maximum value
(0.466 N/mm2) and the intermediate value (0.203 N/mm2).

Meshing
The mesh of the thigh solid and the tights shell adopted
a high-order unit, that is, a linear tetrahedral unit of
four nodes, which made the calculation easier to con-
verge. The mesh unit size of the thigh body was 10 mm
and the mesh unit size of the tights shell was 5 mm. The
meshing result is shown in Figure 6.
Figure 7. Boundary condition setting.
Finite element simulation
In the ANSYS Workbench 19.0 software, the contact
method of the fabric and the thigh was set. The inner the tights were free to deform and displaced in the posi-
surface of the tights was regarded as the contact face, tive direction of the Y-axis, the distance of which
while the outer surface of the thigh body and boss A was the height of the boss A, as shown in Figure 7.
were regarded as the target faces. The solution to the During the simulation, the tights shell would slide
problem was based on the augmented Lagrangian algo- along the surface of the boss A, and finally slide onto
rithm. The contact was set to the method of Gaussian the thigh body to form a wrap around the thigh with a
integral point contact detection. The thickness of the tight compression effect. After several trials of simula-
tights fabric was also considered in the simulation. The tions, the speed of the computational simulation
friction between the thigh and the tights was negligible. was determined to be 1 mm/s, and the initial step was
Then the boundary condition of the model was set. 200 steps.
The upper surface of the thigh body was provided with Through the settings of the above boundary condi-
no friction support, and the lower surface of the boss A tions, the software would calculate according to the
was loaded with full constraint, thereby preventing the program instructions. During the simulation process,
model from shifting during the simulation. the calculation status needs to be checked in real
The upper edge of the tights was defined as the dis- time. If the calculation failed to converge, the adjust-
placement constraint. In the X and Z-axes directions, ment could be made in time.
Wu et al. 9

height. The maximum value of the cross-section cir-

Validation cumference was 513.27 mm in the upper thigh.
In order to verify the simulated predicted pressure In the Imageware software, the curvature changes of
values, the actual human thigh pressure test was per- the thigh sections were measured (the results are shown
formed on the above fabric samples and experimental in Figure 9), taking the middle section of the thigh as an
data was compared with the finite element simulation example. In the picture, the outer circle of data indi-
prediction values. Each fabric was tested in three dif- cates the angular position of the point; the inner circle
ferent elongations of 10%, 20% and 30%, respectively. of data indicates the curvature radius value of the point
The MFF multi-point film test system and the position; and the length of the straight line indicates the
TracerDAQ software were used to test the contact curvature magnitude. The curvature and the radius of
pressure between the thigh and the fabric of tights. A curvature were inversely related to each other, so the
total of four pressure test points were set around the larger the curvature, the smaller the radius. Statistical
middle thigh, including the medial, anterior, medial and analysis was performed on the curvature and radius of
posterior medial, numbered 1, 2, 3 and 4, respectively. all 28 thigh sections, as shown in Table 5, which were
The pressure value was the average value of the data
collected for 10 seconds. The human body was in an
erect static state during data measurement and
acquisition.

Results and analysis

Human thigh geometry analysis
Through reverse engineering modeling, the 3D scanned
human thigh point cloud data was converted into a
thigh entity. Using the measurement function of the
SolidWorks software, the circumference of each thigh
section was measured with an average value of
434.45 mm. As shown in Figure 8, the circumferences
of the thigh sections showed a good linear relationship
with the height of the section. The line was a fitting
curve (R2 ¼ 0.995). The circumference of the thigh sec-
tion gradually increased with the increase of the section
Figure 9. Analysis of the curvature and radius of curvature of
the middle section of the thigh.

Table 5. Statistical analysis of the radius of curvature of the

thigh cross-section (mm)

Angle Minimum Maximum Mean

60 48.55 149.80 56.2861

0 (360 ) 28.45 608.90 75.2879
330 48.23 227.20 78.2200
270 14.97 281.40 80.6954
240 31.66 207.00 84.6786
210 32.66 220.60 85.6893
150 22.53 441.20 87.0489
30 29.77 297.40 90.4918
120 35.13 662.40 109.0068
180 28.55 1100.00 134.8882
90 15.85 1331.00 143.4175
300 44.77 3247.00 212.8143
Figure 8. Thigh section circumference statistics.
10 Textile Research Journal 0(00)

arranged in ascending order of the mean value of the the fat layer made the skin on the surface of the muscle
radius of curvature. The mean radiuses of curvature of part slacker, and thus the curvature changed greatly.
the 330 , 0 and 60 positions were relatively small,
while the 300 position (the lateral thigh, corresponding
Finite element simulation of the pressure of tights
to the lateral thigh muscle) had the largest mean radius.
So, the curvature of the human thigh was very compli- The finite element pressure simulations were carried out
cated. In conclusion, the radius of curvature of the for fabrics 10, 12 and 14, respectively, and each fabric
thigh cross-section gradually increased from bottom was stretched at 10%, 20% and 30%, respectively.
to top, and the difference in curvature at different Taking the fabric sample 10 as an example, after mul-
angles increased as well, that is, the shape of the section tiple solving and post-processing, the model was able to
tended to be more irregular. finally obtain the solution convergence. Figure 12
A comparative analysis of the curvature changes of shows the visualization result of the finite element pres-
the thigh was conducted from both front and side sure simulation, including the deformation cloud dia-
views. Figure 10 shows the curvature change of the gram of the leg shell and the overall contact pressure
thigh in the front view, which indicates that the curva- distribution on the surface of the thigh. The pressure is
ture of the curve on the outer side of the thigh was
relatively uniform, while the inner side of the curvature
changed greatly, and the curvature reached the max-
imum near the root of the thigh. Figure 11 shows the
curvature change of the side view of the thigh. From
the perspective of sports anatomy, the front side of the
thigh is mainly composed of the quadriceps muscles,
including the rectus femoris, the medial femoral
muscle, the lateral femoral muscle and the medial fem-
oral muscle. This explained why the curvature of the
front side of the thigh changed little. Meanwhile, the
curvature of the back of the thigh was more significant,
especially in the upper middle part. In general, the pos-
ition near the root of the thigh, including the medial
and posterior sides, was a place where fat is easily accu-
mulated. In addition, the increase in the thickness of

Figure 11. Curvature of the front and back of the thigh.

Figure 12. Pressure cloud diagram of the tights shell.

Figure 10. Curvature of the inner and outer thigh. (Color online only.)
Wu et al. 11

represented by different colors, red indicating the high- different elongations, as shown in Figure 14. The loca-
est pressure value and blue indicating the lowest pres- tion of the test point had a significant influence on the
sure value. As shown in Figure 13, the pressure of the pressure value. The simulation results indicated that the
tights changed with displacement, in which the green contact pressures on the back side and the outer side of
line indicates the maximum pressure, the blue repre- the thigh were lower than the contact pressure on the
sents the pressure average value and the red represents front side and the inner side of the thigh. According to
the minimum pressure. When the tights started to the Laplace principle, the tight pressure on the surface
move, they do not come into contact with the boss A, of the human body was inversely proportional to the
so the fabric was not stretched. When the tights moved radius of curvature of the human body. When the
near to the middle of the tights, they began to make radius of curvature was larger, the human body
contact with the boss A and were gradually stretched. would undergo less pressure. According to the analysis
Finally, the leg moved up to coincide with the top edge of the thigh geometry described above, the curvatures
of the thigh, when the simulation finished. The pressure of the back side and the outer side of the thigh were
value at the end of time was the final simulation result. smaller than those of the front side and the inner side,
The average pressure was about 0.23 kPa, the max- that is, the radius of curvature was larger, which lead to
imum value was 0.31 kPa and the pressure of the lower pressure.
fabric showed a good linear trend during the stretching Apart from body curvature, the elastic modulus of
process. the fabric was also an important factor affecting the
According to statistical analysis, the pressure values tight pressure effect. The range and variation of the
of different test points in the middle thigh showed dif- pressure value had a relationship with the elastic modu-
ferences under various fabric elastic moduli and lus of the fabric. Under the same elongation, the fabric
with larger elastic modulus generated higher pressure
on the thigh. When the elastic modulus was small
(0.111 MPa), the pressure generated by the fabric
hardly changed as the elongation rate increased.
However, when the elastic modulus was large
(0.523 MPa), the pressure would be increased with the
increase of the elongation. In other words, the pressure
could be adjusted by the elongation when the fabric
possessed a higher elastic modulus, while it could not
for the fabric with low elastic modulus, and it could
undergo severe deformation by excessive stretching.

Validation
By comparing the predicted pressure value with the
actual measured pressure value, an error analysis of
the data was carried out to prove the accuracy of the
Figure 13. Equivalent pressure result. (Color online only.) finite element simulation pressure value. The finite

Figure 14. Pressures on different testing points of the thigh under different fabric elongations: (a) fabric 10 (0.111 MPa); (b) fabric 12
(0.253 MPa); (c) fabric 14 (0.523 MPa).
12 Textile Research Journal 0(00)

Figure 15. Actual pressure test results and simulated pressure results: (a) 10% elongation; (b) 20% elongation; (c) 30% elongation.

element simulation prediction results and the experi- fabric has good elasticity and tensile recovery perform-
mental results are shown in Figure 15; they indicate ance, and is light and comfortable as well. This paper
that the pressure values simulated by the finite element mainly studied the elastic modulus and tightness pres-
method were similar to the actual measured pressure sure of seamless knitted fabrics, and proposed a finite
values, but overall, the simulated data were slightly element model for tight pressure simulation.
lower than the results of the actual test; in the outer Firstly, three knitting parameters, namely the linear
side and the back side of the thigh, the differences density of bare elastic yarn, yarn feed tension and the
between the simulated the actual pressure were more structure of fabric, were regarded as impact factors,
significant than those in the front side and the inner and by using the Box–Behnken RSM, the experimental
side of the thigh. The structure of actual human scheme of fabric samples was designed. The correlation
thighs was complicated, including skin, muscles, between elasticity modulus and all the impact factors
bones, tendons, blood vessels, nerves and so on, was tested and analyzed, and a response surface model
which was not homogenized or linear elastic, as for elasticity modulus prediction was built. Secondly, a
assumed in this paper. Human thighs were not only human thigh was taken as the experimental subject. By
geometrically irregular, but their material properties using a 3D body scanner, point cloud data of the
were also non-uniform. In addition, the distribution human thigh was collected. The human thigh was
of bones, muscles and fats would make the elastic reconstructed in two reverse engineering softwares –
modulus of different parts of the thighs different, Imageware and SolidWorks. Then it was imported to
which will also affect the actual pressure results. ANSYS workbench 19.0 for finite element simulation.
A non-parametric test of the paired samples was also When the computer finished the calculation, the pres-
carried out on the finite element simulated pressure sure distribution of the thigh entity was simulated, and
value and the actual test pressure value. By the two- the result was presented in both 3D animation and
pair sample symbol test and the Wilcoxon signed rank numerical forms. Finally, a validation experiment was
test of the two paired samples, it was observed whether designed to verify the result of numerical modeling to
there was a significant difference between the two kinds ensure its accuracy and validity.
of pressure values. Under different fabric elastic moduli It was found that the effect of yarn feed tension on
and elongation conditions, the actual tested pressure the elasticity modulus was the least significant, while
values were greater than the simulated pressure value, the linear density and structure maintained great influ-
but the cumulative probability of binomial distribution ence. The order of the highest fabric elastic modulus
on both sides is 0.183, which was greater than the sig- was as follows: 1  1 mockrib > cross-float > plain
nificance level of 0.05, so the original hypothesis could stitch. For cross-float and plain stitch, the horizontal
not be rejected. It is considered that there was no sig- elastic modulus was higher than the vertical elastic
nificant difference between the measured mean pressure modulus, whereas the elastic modulus of 1  1 mockrib
and the simulated mean pressure, so the effect of the performed equally. By the analysis of knitting param-
finite element simulation was satisfactory. eters, a quadratic response surface regression model of
the elasticity modulus was created, which could calcu-
late a bare elastic yarn knitting fabric by using its par-
Conclusion
ameters, then predict its tensile property and provide
The tight pressure of garments is a research hotspot in the basis for product development. It was proved that
the field of sports equipment. As one of the new mater- the finite element model was able to predict pressure
ials for tight-fitting sports garment, seamless knitted accurately. Through the pressure numerical simulation
Wu et al. 13

of three fabric samples with different tensile moduli 4. Engel F and Sperlich B. Compression garments in sports:
(0.111, 0.253 and 0.523 MPa), it was indicated that athletic performance and recovery. 1st ed. Switzerland:
pressure change via elongation varied. For fabric with Springer International Publishing, 2016, pp.2–23.
a low tensile modulus, its tight compression merely 5. Bera M, Chattopadhay R and Gupta D. Effect of linear
density of inlay yarns on the structural characteristics of
changed as elongation increased. However, for fabric
knitted fabric tube and pressure generation on cylinder.
with a high tensile modulus, tight compression was pro-
J Text Inst Proc Abstr 2015; 106: 8.
moted as elongation increased. 6. Malgorzata C, Karaszewska A, Ewa G, et al.
Via the tensile modulus numerical model and pres- Comparison of methods for measurement of the pressure
sure finite element simulation method, the fabric tensile exerted by knitted fabrics. Text Res J 2016; 87:
property could be predicted, according to its knitting 2117–2126.
parameters, and tight compression upon the thigh 7. Lee H, Hong K and Lee Y. Compression pants with dif-
could be simulated as well. This study has contributed ferential pressurization: kinetic and kinematical effects on
to the understanding of the tight compression mechan- stability. Text Res J 2016; 87: 1554–1564.
ism, and also provided the basis for the development of 8. Dan R, Fan X, Shi Z, et al. Study on the relationship
tight compression clothing. between pressure and stiffness coefficient, and elastic
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Declaration of conflicting interests
751–766.
The authors declared no potential conflicts of interest with 9. Yu A, Yick KL, Ng SP, et al. Numerical simulation of
respect to the research, authorship and/or publication of this pressure therapy glove by using finite element method.
article. Burns 2016; 42: 141–151.
10. Au KF. Advances in knitting technology. 1st ed.
Funding Cambridge: Woodhead Publishing Limited, 2011,
The authors disclosed receipt of the following financial sup- pp.171–192.
port for the research, authorship, and/or publication of this 11. Roshan S. Textiles for Sportswear. 1st ed. Cambridge:
article: This work was supported by the Program for Science Woodhead Publishing Limited, 2015, pp.53-76.
Technology Department of Zhejiang Province (2017D60SA 12. Duru SC, Candan C and Mugan A. Effect of yarn,
731795). machine and knitting process parameters on the dynam-
ics of the circular knitting needle. Text Res J 2015; 85:
ORCID iD 568–589.
13. El-Ghezal S, Babay A, Dhouib S, et al. Study of the
Zimin Jin https://orcid.org/0000-0003-2882-8267 impact of elastane’s ratio and finishing process on the
mechanical properties of stretch denim. J Text Inst
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