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International Journal of Engineering & Technology, 7 (4.26) (2018) 245-250
International Journal of Engineering & Technology
Quantifying Tensile Properties of Bamboo Silicone Biocomposite
using Yeoh Model
Kamarul Nizam Hassan1, Jamaluddin Mahmud2*, Anwar P.P. Abdul Majeed3, Mohd Azman Yahaya4
1Faculty of Mechanical Engineering, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia
2Innovative Manufacturing, Mechatronics and Sports Laboratory, Faculty of Manufacturing Engineering, Universiti Malaysia Pahang,
26600 Pekan, Pahang, Malaysia
*Corresponding author E-mail: email@example.com
The utilisation of bamboo has the potential of improving the properties of silicone. However, a thorough investigation has yet to be re-
ported on the mechanical properties of bamboo silicone biocomposite. This study was carried out with the aim to quantify the tensile
properties and assess the tensile behaviour of bamboo silicone biocomposite using Yeoh hyperelastic constitutive function. The speci-
mens were prepared from the mix of bamboo particulate and pure silicone at various fibre composition ratio (0wt%, 1wt%, 3wt% and
5wt%) cured overnight at room temperature. A uniaxial tensile test was carried out by adopting the ASTM D412 testing standard. The
Coefficient of Variation, CV, and the Coefficient of Determination, r2, were determined to assess the reliability of the experimental data
and fitting model. The results of the determined Yeoh material constants for 5wt% specimen is found to be C1 = 12.0603×10-3 MPa, C2 =
8.7353×10-5 MPa and C3 = -11.6165×10-8 MPa, compared to pure silicone (0wt%) C1 = 5.6087×10-3 MPa, C2 = 8.6639×10-5 MPa and C3
= -7.6510×10-8 MPa. The results indicate that the bamboo fibre improves the stiffness of the silicone rubber by 115 percent. A low vari-
ance was exhibited by the experimental data with a CV value of less than 8 percent. The Yeoh Model demonstrated an excellent predic-
tion of the elastic behaviour of bamboo silicone biocomposite with a fitting accuracy of more than 99.93 percent.
Keywords: Bamboo fibres; Hyperelastic; Tensile properties; Yeoh Model; Coefficient of Variation
The exploitation of natural fibers as reinforcement material has led
to a massive development of biocomposite for various applica-
tions. The transition towards sustainable products is in tandem
with one of the seventeen United Nation’s Sustainable
Development Goals that contribute towards a sustainable future.
Lignocellulosic fibres possess an advantage over other natural
fibres due to its massive annual production which reflected from
substantial agriculture activities across the tropical continents
especially in China, India and South East Asia [1-3]. These mate-
rials are favoured for their notable strength–to–density ratio and
have been extensively utilised in the production of high–elastic–
resistance and weight–reduced components for automobiles,
aircraft, marines and buildings [4-11]. The integration can also be
seen in the exploratory works of rubberlike composites, although
the employment greatly accentuated on high–strength fibres such
as jute and hemp [12-14]. The limitation, however, resulted in the
diversity towards the exploration of alternative resources with
comparable properties and yet, provide facile accessibility and less
In Malaysia, bamboo offers considerable potential, primarily due
to its large cultivation area and relatively cost-effective [16, 17]. It
is worth to note that bamboo has identical performance to major
timber species  and have been exploited in numerous form to
cater for different industrial applications [19, 20]. Bamboo fibres
are mostly incorporated into polymeric composites i.e. polyvinyl
chloride (PVC) and high–density polyethylene (HDPE) where the
addition enhances the stiffness and flexural strength of the ma-
trixes [21, 22]. The integration was also found to improve the
tensile modulus of natural rubber in [23, 24]. It is worth noting
that the amount of fibre used was between 2.5 to 45 weight
percent of the matrix. Though, the effect from the embedded fibre
on elastomeric response has yet to be thoroughly reported in the
previous work of rubber composites.
The characteristics of rubber, in contrary to bamboo fibre, are
induced by the elastic behaviour of the material , hence, the
need for nonlinear elastic models to quantify their properties is
essential. Hyperelastic polynomial relations such as Neo–Hookean
and Mooney–Rivlin are among the commonly used quantification
models [26-30] owing to their lower degree of intricacy to be as-
sessed as compared to exponential prediction models [31, 32].
However, the precision of the invariant–based models is limited
by the presence of insufficient terms thus brought to the estab-
lishment of the extended polynomial hyperelastic models such as
Yeoh and third order deformation approximation . Yeoh
model has been employed in many studies to quantify tensile ,
compressive  and shear  properties of rubberlike materials.
The model was found to provide a reasonably accurate prediction
of the experimental values with a relatively low error .
Therefore, this work attempts to quantify and assess the tensile
properties of a novel bamboo silicone biocomposite using Yeoh
hyperelastic constitutive equation. Low fibre loading was used to
prevent the tendency for large size agglomerates to develop in the
mixture . The study also employed two different statistical
indicators, namely, Coefficient of Variation, CV, and Coefficient
of Determination, r2 to assess the reliability of the attained ex-
perimental results and the prediction model respectively. More-
over, since silicone rubber is favoured in many applications, i.e.
International Journal of Engineering & Technology
biomedical and automotive, amongst others for its excellent mate-
rial properties [30, 39, 40], thus interpreting its elastic response is
of critical importance for design optimization.
2.1. Specimen Formulation and Compounding
Bamboo acquired is of Dendrocalamus pendulus species with an
initial moisture content of 36.5 percent. The culm was cut into
sections before peeled and dried in an oven at 80⁰C for 24 h.
Dried mid culm was then crushed using ball mill at a speed of 300
rpm for 2 h. The produced powder was ground using a 100 μm
screen. Next, bamboo particulate and pure silicone (Ecoflex 0030)
were mixed at a fibre composition ratio of 0, 1, 3 and 5 weight
percentage to the matrix and left to cure overnight at room tem-
perature. Specimens were labelled as BS00, BS01, BS03 and
BS05 where the number represents the respective fibre composi-
tion. Composed specimens were considered to be homogeneous
throughout the structure.
2.2. Tensile Test
The uniaxial tensile test was carried out using Shimadzu Auto-
graph AG-X 5kN (Fig. 1), by employing the ASTM D412 testing
standard . A total of 20 specimens was tested; 5 specimens for
every composition of bamboo particulate. Attained results were
presented in the form of mean engineering stress–stretch relation.
Fig. 1: Tensile test in progress
2.3. Determining the Yeoh Material Constants
Mechanical properties of the composed material were determined
numerically through the manipulation of Yeoh hyperelastic consti-
tutive model to the experimental data. The general form of strain
energy function is given by :
W = C10(I1 – 3) + C20(I1 – 3)2 + C30(I1 – 3)3 (1)
where C10, C20 and C30 are the material constants of the tested
specimen. For the case of incompressible material, the Green de-
formation tensor relation, I1, reduces to:
I1 = λ2 + 2λ-1 (2)
where λ is the principle extension ratio. Considering Piola
Kirchhoff stress theory, engineering stress–stretch relation can be
derived from Eq. (1):
σe = 2(λ – λ-2)(C10 + 2C20(λ2 + 2λ-1 – 3) + 3C30(λ2 + 2λ-1 – 3)2) (3)
Material constants were computed using the derivative of the
polynomial regression method, which is represented by the fol-
lowing relation :
Sr = Σ(σ(λ)i, exp – σ(λ)i, model)2 (4)
This method has been employed in various studies due to its effec-
tiveness in solving multiple–constant polynomial equation [43,
2.4. Statistical Analysis
The precision of the experimental results was measured by the
evaluation of data extendibility using Coefficient of Variation
CV = [Σ(λi – λmean)2 / (n – 1)]1/2 / |λmean| (5)
where n is the number of specimens. In general, the value of CV
represents the ratio of sample standard deviation relative to its
absolute mean, λmean at predetermined stress magnitude. A dataset
of high precision scattered at low variance, contributed to the
small CV value vice versa [46, 47].
Moreover, the accuracy of the fitted curves was determined using
the Coefficient of Determination (COD) relation :
r2 = 1 – Σ(σ(λ)i, exp – σ(λ)i, model)2 / Σ(σ(λ)i, exp – σ(λ)mean)2 (6)
Mainly, the higher coefficient value indicates higher accuracy is
achieved by the prediction model to the original uncertainties of
experimental data [48, 49].
3. Results and Discussion
Fig. 2 shows the uniaxial elastic behaviour of bamboo silicone
biocomposite at various fibre–to–matrix ratio. All curves display
nonlinear characteristic in which similar to the profile of silicone
rubber composites reported in [30, 50].
Fig. 2: Mean stress–stretch behaviour of specimens BS00 (○); BS01 (●);
BS03 (●); and BS05 (●).
It is interesting to note the transition of the curvilinear trend across
the axes. It could be observed that the addition of bamboo filler
into the silicone rubber matrix affects the elasticity properties of
International Journal of Engineering & Technology
the developed biocomposite. This is apparent with the decrease in
the elongation of 6 percent. A similar trend was also portrayed in
 where the relative strain reduces with the increase of fibre
content. The poor elasticity behaviour is resulted from the pro-
gression of strain energy, which leads to a higher degree of resis-
tance of the structure towards large deformation state.
Furthermore, it could also be observed that along the deformation
range 2 ≤ λ ≤ 7, gradual increment transpired to the slope of the
curves which suggested that stiffening effect is highly intensified
at lower stress range (20 kPa ≤ σ ≤ 300 kPa). The presence of
more fillers provides a larger surface area, allowing higher load
transfer to take place due to the significant interaction occurs be-
tween matrix and fibres [39, 51]. The increase in stiffness is re-
flected by the upsurge trend of constant C1 in Table 1. The
stiffness of the silicone rubber was found to enhance by 115
percent with the incorporation of 5 wt% bamboo fibres. The elon-
gation profile also tends to be less nonlinear in which conveyed by
the decreasing value of constant C3. However, no changes tran-
spired to the behaviour of the stress–stretch curve beyond the
aforesaid range, probably due to the greater matrix crosslinking
effect as compared to the fibre reinforcing . Such occurrence
can be related to the unvarying trend of the constant C2 in the
Table 1: Yeoh material constants determined at various composition
Material Constants (MPa)
Fig. 3 shows the CV value of the experimental data at various
mean stretch. High CV value was found to appear in the range of 2
≤ λ ≤ 7 which concentred at 200 percent stretch for all specimens.
The emergence of the peak value is brought by the abrupt data
distribution exhibited by the specimens within the stress value of
0.02 to 0.03 MPa (refer Fig. 4). However, as the exerted load in-
creases, the transpired elongation becomes closer to the sample
mean, that in turn resulted in the less deviation of the error bar.
Despite the broad data distribution exhibited in Fig. 4(c) and 4(d),
low variance data appeared in the stress–stretch diagram of speci-
mens BS00 and BS01 with a CV value of less than 3 percent (Fig.
4(a) and 4(b)).
In terms of reinforcing mechanism, such development might be
associated to the disproportionate tensile strength exhibited by the
distinctive specimens as a result from the presence of the large and
poor dispersion of agglomerates throughout the matrix [52-54].
The development of the filler network during low deformation is
highly related to the higher surface interaction between fibre and
matrix . However, as the concentration of filler increases, the
matrix–filler interaction tends to become weaker due to the reduc-
tion of specific surface area transpired from the agglomeration of
fibres . Large agglomerates act as a stress concentrator in a
matrix  and it is unfavoured for its low transverse stiffness
. Agglomerates with a size larger than the flaw size of matrix
contribute to poor dispersion [57, 58] and deteriorate the mechani-
cal properties .
Fig. 3: Coefficient of variation of dataset attribute to specimens BS00 (○);
BS01 (●); BS03 (●); and BS05 (●) at various mean stretch
Though, less variation was found to appear to the data set beyond
700 percent stretch range with a CV value of less than 2 percent.
At large strain, filler network tends to be weak due to amplifica-
tion of local strain which causes rubber chains between crosslinks
to greatly extend . The development of rubber crosslinking
reduces the inconsistency of reinforcing effect thus resulted in the
homogeneous deformation of the specimens. All the data attained
from the experiment are distributed within 95 percent of the
Fig. 4: Mean stress–stretch behaviour of specimens (a) BS00; (b) BS01; (c)
BS03; and (d) and BS05 focusing specifically on deformation region of 1
≤ λ ≤ 7 with 2 standard deviation error bar.
The stress–stretch curve for each variation is separated into Fig.
5(a), Fig. 5(b), Fig 5(c) and Fig 5(d) to explicitly highlight the
behaviour of the prediction curve (Yeoh Model) with respect to
the experimental value. Predicted hyperelastic profiles are de-
picted by the dashed curve lines. The fitted curves are almost con-
sistent with the experimental data value (denoted by markers) with
International Journal of Engineering & Technology
a standard error of less than 1 percent. The high value of r2 ob-
tained indicates the adequacy of the Yeoh Model on representing
the experimental results. The outcome shows that there is a real
relation between stretch, λ, and stress, σ,  for all tested speci-
mens in present work.
Nevertheless, at lower stretch range (1 ≤ λ ≤ 3.25), a high discrep-
ancy occurs to the projections (Fig. 6(a) to 6(d)) due to the inher-
ent limitation of the model on depicting small strain behaviour of
large deformation material . Disassociation of invariant tensor
I2 has brought to such drawback . A relative error within the
range was found to be 31.38, 30.27, 34.09 and 56.42 percent
which attribute to the prediction model of specimen BS00, BS01,
BS03 and BS05 respectively. An inverse relation can be seen be-
tween relative error and coefficient of determination value – the
higher the error transpired, the lower the value of the coefficient
attained. At higher stretch range (3.25 < λ ≤ 14), transpired rela-
tive error is below 5 percent for all predicted value.
Fig. 5: Mean stress–stretch behaviour of specimens (a) BS00; (b) BS01; (c)
BS03; and (d) BS05 and respective Yeoh Model prediction curves.
Fig. 6: Mean stress–stretch behaviour of specimens (a) BS00; (b) BS01; (c)
BS03; and (d) BS05 in deformation region of 1 ≤ λ ≤ 3. The dashed line
represents the Yeoh Model prediction curve.
This paper reports the work related to the quantification of the
tensile properties of bamboo silicone biocomposite. The variation
of experimental data was found to be acceptable with the
distribution of less than 8 percent. It was observed that the stiff-
ness of bamboo silicone biocomposite is improved by 115 percent
through the reinforcement of 5 weight percent ratio of bamboo
fibres into silicone rubber. Moreover, an excellent prediction of
the elastic behaviour of tested specimens was demonstrated by the
Yeoh Model, suggesting its efficacy in predicting the behaviour of
the proposed biocomposite. Future works will involve the investi-
gation and the quantification of the compressive behaviour of
International Journal of Engineering & Technology
bamboo reinforced silicone biocomposite to provide further
insight on its potentiality and practical implications.
The authors gratefully acknowledge the financial support by the
Ministry of Higher Education Malaysia (MOHE) and Universiti
Teknologi MARA (UiTM). (Grant no: 600–RMI/FRGS 5/3
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