Applied Mechanics and Materials
ISSN: 1662-7482, Vol. 461, pp 213-219
doi:10.4028/www.scientific.net/AMM.461.213
© 2014 Trans Tech Publications, Switzerland
Online: 2013-11-21
Finite Element Analysis in the Characteristics of Ostrich Foot Toenail
Traveling on Sand
Rui Zhang, Haibao Liu, Sihua Zhang, Guiyin Zeng, Jianqiao Li
Key Laboratory of Bionic Engineering, Ministry of Education, Jilin University, Changchun, 130022,
China
Corresponding author: Rui Zhang E-mail: [email protected] Telephone: +8613504419232
Keywords: ostrich foot toenail, reverse engineering, model reconstruction, finite element simulation,
sand fixation and flow limitation.
Abstract: The ostrich foot toenail plays a crucial role in the process of ostrich foot traveling on
sand. 3D laser scanner was used to measure the three-dimensional point clouds of ostrich foot
toenail surface morphology, and the three-dimensional model of ostrich foot toenail was
reconstructed by using reverse engineering technology. The finite element analysis in the
interactions between ostrich foot toenail and sand was implemented by Abaqus and Hypermesh.
The quasi-static analytical results of ostrich foot toenail inserting the sands showed that the groove
structure of the toenail had a better sand fixation effects, the tiptoe structure was beneficial to insert
into the sands, and the inverted triangular structure of the toenail had the weak disturbance on the
sands which produced the less resistance of the toenail inserting the sands. According to the velocity
and the stress fields in the process of the ostrich foot toenail dynamically traveling on sand, ostrich
foot toenail tiptoe could help to improve the thrust of traveling on sand, the groove area of the
toenail played the effects of sand fixation and flow limitation in the process of ostrich foot toenail
traveling on sand.
1. Introduction
China has a large area of the desert and the Gobi regions, where reserve the abundant of
minerals, oils and gases resources. At the same time, these regions are the treasured places for
developing agriculture, forestry and energy. Because the special environments of the regions, it is
unsuitable to use the conventional wheeled or tracked walking devices, due to the flow of sand
under the wheels, the large slip subsidence and the difficulty in providing a larger traction. The
conventional exploratory and carrying vehicles are often difficult to drive in loose sand, or even lost
the travelling performance [1]. In order to improve the performances of the vehicle in the desert
region, the scholars have done a lot of studies and obtained a series of important research results.
However, the improvement of travelling capacity on sand is still limited, which cannot satisfy the
demands for the development of desert resources. The animals living in the desert have the inherent
ability of travelling on the sand. Research on the mechanism of the key parts traveling on sand of
the animals living in the desert, and according to the principle of bionic engineering, the new
theoretical foundations and the research methods for studying the vehicles and the operating
equipment in the desert can be provided [2].
African ostrich (Struthio camelus) (hereinafter referred to as ostrich) is the largest cursorial
ratite living in the desert, who is capable of remarkable speed, exceptional endurance and steady
locomotion. Fig. 1 shows ostrich running in the desert. An adult ostrich can span 3.5 to 7 meters
every stride, the continuous running speed reaches 50~60 km/h and maintains about 30 minutes
without feeling tired, and the sprint speed over 70 km / h. Ostrich is the fastest two-legged animals
on the land. The excellent performance of ostrich traveling on sand is the result of the combined
actions by the various factors [3, 4]. Ostrich feet carry the weight of the ostrich, and participate in
locomotion on sand directly, which play a crucial role in the process of ostrich traveling on sand[5].
Each ostrich foot only has two toes (the 3rd and the 4th toe), the inner toe (the 3rd toe), has a large
and hard toenail, the toenail of the outer toe (the 4th toe) has degenerated and disappeared. Through
observing ostrich in the process of walking or running in desert, the toenail of the 3rd toe is similar
to a spike, which can effectively improve the traction performance and the resistance to subsidence
[6]
. The mechanism of ostrich foot toenail traveling on sand is difficult to obtain accurately by the
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actual experiment in vivo. It is possible to gain the mechanical and the kinematic laws of ostrich
foot toenail traveling on sand by use of reverse engineering and finite element analysis. Through
analyzing the processes of ostrich foot toenail traveling on sand under the quasi-static state and the
dynamic travelling state respectively, the interactions between ostrich foot toenail and sand were
studied and the mechanism of ostrich foot toenail traveling on sand was explored.
2. Structural characteristics of ostrich foot toenail
Ostrich belongs to Ratitae, Struthioniformes and Struthionidae[7]. Ostrich is native to the
African the Arab desert areas. Ostrich mainly lives in the open desert areas, or the dry and treeless
prairie. Ostrich is the only existing bird with didactyl foot in the world. Due to the long-term natural
evolution, the 1st toe and the 2nd toe of ostrich foot have completely degenerated, only two toes
were reserved. They are the 3rd toe and the 4th toe from inside to outside. The 3rd toe is strong and
more developed. One developed and hard toenail exists at the end of the 3rd toe. The 4th toe is thin
and short, whose length is approximately as one half as that of the 3rd toe. The toenail of the 4th toe
has disappeared or very small [8]. One ostrich left foot is shown in Fig. 2.
The structures of ostrich foot are shown in Fig. 3. In Fig. 3, A is tarsometatarsal bone, B is
toenail, C is digital cushion, D is phalangeal pad, E is metatarsal phalangeal pad and P1-4 is
phalangeal bones. Bones of ostrich foot are connected by joints. The motions between the various
parts of ostrich foot are controlled by the ligaments and the skin adhered to each bone. The 3rd toe
and the 4th toe have four phalanges respectively. The phalanges of the 4th toe (especially the end
phalanx) have seriously degenerated. In addition, there are unique surface morphology and papillary
group at the bottom of ostrich foot.
Fig. 1 Ostrich running on sand
Fig. 2 Ostrich left foot
Fig. 3 The structure of ostrich foot
One high developed toenail with special structure exists at the end of the 3rd toe of ostrich
foot[9]. The studied ostrich foot toenail is obtained from Lu Sheng Garden Villa, Changchun City,
Jilin Province, China. The ostrich foot toenail comes from one adult male ostrich with the age of
one and a half year. The length of the ostrich foot toenail is approximately 4 cm. The structure of
ostrich foot toenail is shown in Fig. 4. In Fig. 4, (a) shows the outboard inverted triangle structure,
which is located on the back of the toenail, the structure seems to be one part of a triangular prism,
but it has some radian, (b) shows the inboard groove structure, (c) shows the side surface of the
toenail.
(a)
(b)
(c)
Fig. 4 The structure of ostrich foot toenail
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3. Model reconstruction of ostrich foot toenail
The ostrich foot toenail was cleaned by the ultrasonic cleaning machine, and then the ostrich
foot toenail surface was sprayed with the DPT-5 eikonogen. The three-dimensional scanner of
Rexcan III-0.8M series was used to obtain the point cloud data of the toenail. The resolution of the
Rexcan III-0.8M series scanner is 5 million pixels, and the accuracy of pixel can achieve 0.007mm.
The laser scanning process of ostrich foot toenail is shown in Fig. 5. Fig. 6 displays the scanning
result of ostrich foot toenail. Fig. 7 shows the original spatial point clouds of ostrich foot toenail.
Fig. 5 Scanning process of toenail
Fig. 6 Scanning result of toenail
Fig. 7 Point clouds of toenail
The point cloud data of ostrich foot toenail was imported into the reverse engineering
processing software, where the noise removal, the filter, and the smooth processing were performed.
The three-dimensional irregular surface of ostrich foot toenail is shown in Fig. 8. After the physical
reconstruction in Geomagic Studio and the mesh processing on the three-dimensional irregular
surface in Hypermesh, the 3D mesh model is obtained (Fig. 9), The mesh type of the 3D foot
toenail model is linear C3D4, the mesh size is 1×1×1 mm3, the total mesh number of the 3D foot
toenail model is 20902, this model can be used for the finite element analysis on the characteristics
of ostrich foot toenail traveling on sand.
Fig. 8 3D irregular surfaces of toenail
Fig. 9 3D mesh model of toenail
4. The toenail/sand interaction model and material properties
The finite element analysis in the interaction between ostrich foot toenail and sand was
performed by ABAQUS. The extended Drucker-Prager model was chosen as the constitutive model
of sand, this model is an elastoplastic constitutive model, it can effectively reflect the main
characteristics of sand in the loose desert [10]. The dry sand properties in Taklimakan desert was
selected as the material parameters of sand [11]. This paper focuses on the interactions between the
structure morphology of ostrich foot toenail and sand, the isotropic linear model was selected as the
model of ostrich foot toenail in order to simplify the calculation, the elastic modulus and Poisson's
ratio were obtained from the references[12, 13], the average density of ostrich foot toenail is obtained
from the experimental test. The material properties in the FEM analysis are shown in Table 1.
Table 1 The material properties in the FEM analysis
Density(g/cm ) Elasticity modulus (MPa) Poisson ratio Internal friction angle (°)
Toenail
0.98
1585
0.41
sand
1.54
47.199
0.4
42.2
The encastre constraint was imposed on four side faces and the bottom face of the sand model.
It seems like that the sand was put into a soil bin. The mesh size of the upper part of the sand model
is 2×2×2mm3 and the mesh size of the lower part is 4×2×2 mm3, the total mesh number of the
sand model is 30000, the linear C3D8R was selected as the element type, this element type is
suitable for large strain analysis.
3
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5. FEM analysis in the quasi-static process of ostrich foot toenail inserting into sand
5.1 Initial conditions of quasi-static process of ostrich foot toenail inserting into sand
At the start of ostrich foot toenail inserting sand during the quasi-static force analysis, the
toenail is set 5mm above the center of the sand-bin, the toenail will insert into sand with three
different postures as shown in Fig. 10, namely, (a) shows the posture of the groove touching sand
(the degree between the toenail axis and the perpendicular axis is anticlockwise 45°), (b) shows the
posture of the tiptoe touching sand (the toenail axis overlap the perpendicular axis) and (c) shows
the posture of the inverted triangle face touching sand (the degree between the toenail axis and the
perpendicular axis is clockwise 45°).
During the quasi-static process of ostrich foot toenail inserting into sand, the Z-axis is
perpendicular to the top surface of sand. Ostrich foot toenail inserts into sand at the velocity of
0.5m/s until the whole toenail contacts sand. The whole toenail has only one degree of freedom, the
linear velocity along the positive direction of the Z-axis. The loads and constraints of ostrich foot
toenail are shown in Fig. 11.
(a)
(b)
(c)
Fig. 11 The quasi-static loads and
Fig. 10 Three different postures of toenail inserting sand
constraints of toenail
5.2 The result analysis in the quasi-static process of ostrich toenail inserting into sand
The equivalent stress distributions of three different postures of toenail inserting into sand are
shown in Fig. 12. According to Fig. 12(a) under the posture of the groove touching sand, a stress
distribution of large area exists at the bottom of the toenail. This phenomenon shows that the sand at
the bottom of the toenail receives the greater forces, which is caused by the inboard groove
structure of ostrich foot toenail. The sands along the surface of the toenail groove forms an obvious
protuberance, which shows that toenail groove surface has sand fixation effects. According to Fig.
12(b) under the posture of toenail vertically touching sand, the sand stress at the bottom of the tiptoe
reaches the maximum value in all postures. The stress field mainly concentrates in the area below
the tiptoe. The stress distribution near the area of the groove structure is more obvious; while the
stress distribution near the inverted triangle area gradually declines and even disappears. The result
indicates that the tiptoe surface morphology is beneficial to improve the thrust of sand. The stress
field area is much smaller than that of the posture of the groove touching sand, and deformation of
sand is not very obvious. The phenomena indicate that the tiptoe of ostrich foot toenail has the
effect of separating sand, which is beneficial to insert into sand. According to the Fig. 12(c) under
the posture of the inverted triangle face touching sand, the sand stress mainly concentrate at the
sides of the inverted triangle surface, and the stress field and the stress value are small. The result
indicates that the disturbance of the inverted triangle surface on sand is very weak, which is
beneficial to decrease the resistance of inserting into sand.
The above analysis results show that the toenail groove structure has a better fixation effect on
sand, the tiptoe structure is beneficial to insert into sand, and the disturbance of the inverted
triangular structure on sand is weak and the resistance of toenail inserting sand is small.
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(a)
(b)
(c)
Fig. 12 The stress distributions of three different postures of toenail inserting into sand
6. FEM analysis in ostrich foot toenail dynamically traveling on sand
6.1 Acquisition of kinematic parameters of ostrich foot toenail traveling on sand
A healthy adult male ostrich was selected, the high-speed camera system was used to record
the dynamic changing process of gestures when ostrich running on sand. The motion data of ostrich
was imported to the software TEMA for the kinematic analysis. Because the volume of ostrich foot
toenail occupies a very small proportion of the whole ostrich volume, especially it is difficult to
capture the motion state of toenail when ostriches run at high-speed. In order to facilitate to achieve
the motion parameters, the motion of the 3rd toe was regarded as a rigid body motion and the shape
of the 3rd toe does not changed during running on sand. According to the size relationship between
the 3rd toe and the toenail, the toenail movement patterns was obtained through the proportional
conversion when the movement patterns of the 3rd toe was acquired. Therefore, the tip of the 3rd
toe and the toe metatarsal joint were selected as the marker points[14], as shown in Fig. 13.
Because ostrich running speed is very fast, the velocities and the accelerations of ostrich foot
toenail are much higher. Our goal is to discuss the interaction relationship between ostrich foot
toenail and sand, and study the effects and the contribution of ostrich foot toenail during the process
of ostrich traveling on sand; at the same time, considering the requirement of calculation stability,
one tenth of the actual high-speed photograph measurement values were selected as the velocity and
the acceleration of ostrich foot toenail in the numerical simulation. The velocities of ostrich foot
toenail in the numerical simulation are given by Eq. 1, Eq. 2, Eq. 3 and Eq. 4.
The end of ostrich foot toenail:
Horizontal velocity: y=-67.6x3+2484x2-21683x-34830
(1)
3
2
Vertical velocity:
y=19.2x -522.6x +7763.9x-37425
(2)
The tip of ostrich foot toenail:
Horizontal velocity: y=-36.9x3+1415.7x2-13674x-58663
(3)
3
2
Vertical velocity:
y=45.2x -812.8x +5259.7x-21686
(4)
6.2 Initial conditions of ostrich foot toenail dynamically traveling on sand
At the start of FEM analysis in ostrich foot toenail dynamically traveling on sand, there is 5o
between the wear surface of the toenail and the sand plane. The process from toenail touching sand
to toenail leaving sand completely was considered as a cycle during the process of FEM analysis.
Ostrich foot toenail has three degrees of freedom, the velocity along the Y axis and the Z axis, the
angular velocity around the X axis. The loads and constraints of ostrich foot toenail are shown in
Fig. 14.
Fig. 13 The selected marker points
Fig. 14 Dynamic loads and constraints of toenail
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6.3 The simulation result analysis of ostrich foot toenail dynamically traveling on sand
The velocity fields along the X axis and the Z axis of ostrich foot toenail dynamically traveling
on sand were shown in Fig. 15 and Fig. 16. Seen from Fig. 15 and Fig. 16, the maximum sand
velocity along the Z axis VZmax is larger than the maximum sand velocity along the X axis VX
max. When t=0.005s, VXmax=2.905m/s, VZmax=3.661m/s; when t=0.01s, VXmax=3.001m/s,
VZmax=4.030m/s. The results show that the sand velocities along both sides of the inboard groove
of ostrich foot toenail are obviously smaller than those along the surface of ostrich foot toenail
groove. At the same time, the sand velocities along the X axis or the sand velocities along the Z axis
are obviously smaller than the average velocities of the whole sand in the sand-bin. The sand
velocities at the area of ostrich foot toenail groove evidently declined, which indicates ostrich foot
toenail plays the effects of sand fixation and flow limitation during the process of ostrich foot
toenail traveling on sand.
(a) t=0.005s
(b) t=0.01s
(a) t=0.005s
(b) t=0.01s
Fig. 15 Dynamic velocity fields along the X axis Fig. 16 Dynamic velocity fields along the Z axis
The equivalent stress distribution of ostrich foot toenail dynamically traveling on sand was
shown in Fig. 17. Seen from Fig. 17, the sand stress field mainly concentrates at the bottom of the
tiptoe, and the stress value and the deformation quantity are great. The maximum stress value of
sand appears at the area of the tiptoe touching sand, which indicates that the reaction forces of sand
at this area has the most obviously effect on the end of ostrich foot toenail.
Fig. 18 shows the changing curve of the maximum stress of sand during ostrich foot toenail
travelling on sand. Seen from Fig. 18, a peak stress exists at the beginning of ostrich foot toenail
touching sand. With ostrich foot toenail moving, the stress value declines and then increases. This
phenomenon indicates that the sands receives the applied force of ostrich foot toenail and gains the
acceleration after ostrich foot toenail contacting with sand, and then the sand stress at the tiptoe
goes down because the contacting degree decreases. With the sand being compacted, its velocities
continue to decrease, the contact degree between the toenail and sand goes up again, the sand stress
also goes up (before t=0.007s). After that, the relative displacement between the toenail and sand
diminish, the sand stress tends to stable, and the sand provides the largest stress in this phase (from
t=0.007s to t=0.011s). The toenail left sand in the next stage, the sand stress decreases rapidly, and
finally reduces to zero (after t=0.011s).
Fig. 17 Dynamic stress distribution at t=0.01s Fig. 18 The changing curve of sand maximum stress
7. Conclusion
The reverse engineering technology was used to reconstruct the three-dimensional model of
ostrich foot toenail. The quasi-static analytical results of ostrich foot toenail inserting into sand
show that the toenail groove structure has a better sand fixation effect, the tiptoe structure is
beneficial to insert into sand, and the disturbance of the inverted triangular structure on the sand is
weak and the resistance of the toenail inserting into sand small. The analysis in ostrich foot toenail
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dynamically traveling on sand indicates that the sand stress near ostrich foot tiptoe is the largest,
which can help to improve the thrust of traveling on sand. According to the velocity field analysis,
ostrich foot toenail plays the effect of sand fixation and flow limitation during the process of ostrich
foot toenail traveling on sand.
Acknowledgement
The authors are grateful for the financial support by National Natural Science Foundation of
China (No. 51275199).
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