Computational and experimental approach of the phenomenology
in the impact of a hen eggshell
Jordi Marcé-Nogué1, Marco A. Pérez1, Lluís Gil1, Bernat Vila2, Josep Fortuny3, Albert G. Selles3,
Àngel Galobart3
1
Departament de Resistència de Materials i Estructures a l’Enginyeria, Universitat Politècnica
de Catalunya - BarcelonaTech, Terrassa, Spain
2
Grupo Aragosaurus–IUCA, Paleontología. Facultad de Ciencias. Universidad de Zaragoza.
50009 Zaragoza, Spain.
3
Institut Català de Paleontologia, Edifici ICP, Universitat Autònoma de Barcelona, Campus de
Bellaterra, Barcelona, Spain
Abstract
An impact test of the crash of a hen egg and a computational simulation using Finite element
Analysis (FEA) have been implemented to determine the different types of failure occurred
correlating with the values and the stress maps obtained in the computational simulation.
The experimental procedure consists in releasing seventeen eggs from a height which
determines the incident kinetic energy and hence the incident velocity while a Transitory
Analysis was developed to simulate the dynamical impact of the eggshell on the floor. With the
results obtained, a newly classification for the types of failure the eggshells was proposed.
Introduction
The impact of an eggshell and its strength has little been studied [1], [2]. In experimental way,
eggshell strength is evaluated from a non-destructive and quasi-static compression test [3],
[4], using a transducer [5] or introducing a dynamical test method using modal analysis [6]. The
mechanics and mechanisms of failure of hens eggs have been examined experimentally under
contact loading conditions [7]. In computational mechanics, the dynamic mechanical
behaviour of the egg has been evaluated with Finite Element Analysis (FEA) from simple
structural models [8][9] to highly nonlinear transient dynamic analysis [4] including the study
of the rupture by impact loading [1]. FEA has also been used to evaluate the effects of
variations in certain geometrical and material parameters of the egg on the structural and
acoustic frequency response functions [10] or to study the microstructure-controlled stability
of selected eggshells of Indian dinosaurs [11].
The avian egg is a biological structure of high complexity. It contains an air chamber and a
viscous liquid formed by the egg yolk and the albumen surrounded by two membranes and the
external covering of the eggshell. Eggshell strength is regulated by a certain number of
variables such as genetic origin, the age of the laying hen, feed composition, diseases, climatic
conditions or management by the farmer [12].
According to previous works, there is a stress at which the eggshell rupture starts [4]. This
stress is independent on the eggshell geometry, size and thickness and on the loading force
orientation. This stress can be used as the fracture stress which is affected only by the eggshell
material properties. Below this stress value, a no rupture of the shell with or without cracks is
produced in the eggshell while up to the fracture stress, different types of failure appear. In
this work an impact test of the crash of a hen egg has been studied to determine the different
types of failure occurred to correlate it with the values and the stress maps obtained by a
computational simulation done with FEA.
Methods: test
The experimental program was conducted for a total of seventeen hen eggs specimens. The
test procedure consists in releasing the egg from a height which determines the incident
kinetic energy and hence the incident velocity. Tests were performed by crashing the
specimens on a rigid support. To evaluate the impact damage resistance, specimens were
dropped from height levels varying in the range from 50 to 1500 mm. Prior to each test,
specimens were geometrically characterized and its mass was determined. After each test, the
thickness of the shell has been measured. With the aim of visualize the impact event details, a
high-speed camera MotionBLITZ Cube4 were used. The camera recording frequency was 1878
Hz, which represents a time resolution of 529 μs per frame. Recording results allows
identifying the initiation and propagation of the failure modes.
Results
For each test (Table 1), the distance where the eggs start to fall and the impact velocity had
been recorded. Geometric parameters are also obtained for each egg (height, width, mass and
thickness). The crash of the egg in the floor has been divided three types of failure:
a) CASE A: Total crash and spill of the yolk (Figure 1)
b) CASE B: Crack and spill of the yolk. The egg bounces. (Figure 1)
c) CASE C: Partial crack and no spill of the yolk. The egg bounces. (Figure 1)
The classification of the type of failure is done by observation of the failure in the egg for each
test.
Figure 1 Types A,B and C of the casuistry of the crash of the egg in the floor
Distance
[mm]
1500
1400
1300
1200
1100
1000
900
800
700
600
500
400
300
200
150
100
50
Impact
velocity
[mm/s]
5424,94
5240,99
5050,35
4852,22
4645,64
4429,45
4202,14
3961,82
3705,94
3431,03
3132,09
2801,43
2426,11
1980,91
1715,52
1400,71
990,45
Egg height
[mm]
Egg Width
[mm]
Mass [gr]
54,37
57,75
56,14
55,85
56,59
55,72
54,88
52,56
55,29
55,48
56,79
55,26
57,86
55,29
55,74
56,86
59
44
43,36
44,32
44,69
44,3
43,16
44,27
42,98
44,49
43,76
43,78
44,71
43,5
44,54
44,08
42,87
42,94
58,3
61,6
61,2
61,3
61
57,6
59,7
56,5
59,1
59,3
61
61,5
61,1
61,6
59,8
57,9
59,9
Eggshell
Thickness
[mm]
0,47
0,49
0,44
0,41
0,41
0,44
0,43
0,47
0,41
0,41
0,45
0,42
0,41
0,44
0,46
0,47
0,4
Type of
failure
A
A
A
A
A
A
A
A
A
A
A
A
B
B
B
B
C
Table 1 - Results obtained in the impact test of the hen eggshells
Methods: FEA
A Transitory Finite Element Analysis was developed to simulate the dynamical impact of the
eggshell on the floor (Figure 2) using the Finite Element Package ANSYS 14.0 in a Dell
Precision™ Workstation T7600 with 32 GB (4X8GB) and 1600 MHz. The floor was considered
made of concrete (E= 30 GPa and  = 0.18) and was meshed with solid elements. The eggshell
is considered as a homogeneous isotropic linear elastic material with E = 0.0035 GPa and  =
0.45 [4], [13] and the egg yolk, the albumen and the air inside the eggshell chamber are
considered as an hydrostatic pressure of a liquid of 1,025 g/cm3 [14]. The eggshell has been
meshed with shell elements with thickness of 0.41 mm (which is the average value of the
different eggshell thickness of Table 1).
Figure 2 - Definition of the problem in FEA
Different tests are considered modifying the impact velocity. The value of the velocity is
associated to a height (h) according to the energetic equilibrium between potential and kinetic
energy.
Results
The maximum Von Mises stress recorded in the eggshell depending on the different velocities
are shown in Table 2. The type of failure is associated with the results obtained previously in
the tests. In the Figure 4 shows that the tendency of the results are to level off to certain value
of threshold for a high impact velocities and to change abruptly for very low values of velocity.
It is also shown in Figure 4 the Von Mises stress distribution just in the moment of the impact
between the eggshell and the soil. This is just when the maximum Von Mises stress recorded in
Table 2 is reached.
Figure 3 Von Misess stress distribution for Case A, B and C when the maximum value of stress is reached
Initial velocity
[mm/s]
7500
5000
4000
3000
2000
1000
500
100
50
Maximum Von Mises
stress [MPa]
1383
1261
1210,3
1131,3
942,61
554
293,66
82,27
70,74
Distance [mm]
2869,90
1275,51
816,33
459,18
204,08
51,02
12,76
0,51
0,13
Type of failure
A
A
A
A
B
B-C
C
C
C
Table 2 Results obtained in the simulation done with FEA of the impact of the hen eggshell
1600
Von Mises Stress [MPa]
1400
1200
1000
800
600
400
200
0
0
100
200
300
400
500
600
700
800
900
1000
Distance [mm]
Figure 4 - Equivalent Von Mises stress [MPa] versus distance where the egg is smashed [mm]
Discussion
According to the values obtained in the Computational simulation, the maximum tensile stress
as a measure of the eggshell strength can be evaluated around the 550 MPa. In the results
showed in Table 1 of the experimental tests, the type of failure C is only obtained below a
velocity of 1000 mm/s, which is related in the computational simulation with a value below the
554 MPa obtained. This result correctly agree with previous results obtained in impact
analyses of hen eggshell [1].
It is also interesting to point that Figure 4 shows different distribution of Von Mises stress
depending on the type of failure. These observed distributions of stress can be correlated with
the different types of failure observed in the experimental test when the fracture of the
eggshell is with a partial crack, a crack or a total crash of it.
For case C a very low concentrated peak stress is sited just in the point of impact. This value is
lower than the threshold 500 MPa, and for instance, the eggshell is not breaking due the
impact (as Figure 1 shows). For case B the peak stress is also concentrated but important stress
values are appearing in the surrounds of the impact point. This different distribution generates
a crack in the eggshell without the total crash of the shell as shown in Figure 1. For case A, the
maximum values of stress are located in a wider point and important values of stress are
located in the bottom half of the eggshell generating the total crash of the eggshell.
In Figure 4 can also be observed a close dependence of the eggshell rupture force on the
velocity that can be probably described by a logarithmic function, as it is possible in case of
many engineering materials and according the observations done [2].
Conclusions
The numerical results obtained in both tests (experimental and computational) have highly
correlation with the results obtained in previous works. For instance, the newly proposed
classification for the types of failure it is a very good tool to understand in further works the
failure mechanisms of the eggshells.
Acknowledgments
This research has been supported by project CGL 2011-30069-C02-01 of the Ministerio de
Ciencia e Innovación. B. Vila acknowledges support from the Ministerio de Ciencia e
Innovación (Subprograma Juan de la Cierva (MICINN-JDC) 2011).
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Jordi Marcé-Nogué (Igualada, 1979) has Bachelor degree of Industrial Engineering issued from
Universitat Politècnica de Catalunya (Spain) in 2003 and PhD degree Resistència de Materials i
Computational Biomechanics from Universitat Politècnica de Catalunya in 2009.
He started as a research fellow in the Departament de Estructures a l’Enginyeria and from
2006 he has being a assistant teacher in Escola Tècnica Superior d’Enginyeria i Aeronàutica de
Terrassa (UPC) and a researcher at Laboratory for the Innovation of Structures and Materials
(LITEM)
Marco A. Pérez (Terrassa, 1981) has a Bachelor of Science in Mechanical Engineering (2005)
and a PhD degree of Structural analysis by Universitat Politècnica de Catalunya, Barcelona
Spain (2012) about composite advanced materials behaviour under impact loads.
He started as a research fellow in the Department of Strength of Materials and Structural
Engineering and from 2006 has being researcher at Laboratory for the Innovation of Structures
and Materials (LITEM) and assistant professor at the Escola Tècnica Superior d’Enginyeria i
Aeronàutica de Terrassa (UPC). His research activity is focused on composite materials, plate
and shells finite elements, dynamic analysis, musical acoustics and nondestructive testing.
Lluís Gil (Barcelona, 1966) achieved a civil engineering degree in 1992 and a PhD from
Universitat Politecnica de Catalunya UPC in 1997.
He currently is associate professor at UPC in the field of aerospace structures. Now is the
Director of research of the Laboratory for the Innovation of Structures and Materials (LITEM).
Co-author of 27 international journal and 45 conference contributions and 1 patent. Interested
in modal analysis, composites and new applications of recycled materials.
Bernat Vila i Ginestí (Sabadell, 1980) has a Bachelor degree in Geological Sciences (2003)
issued from Universitat Autònoma de Barcelona (Catalonia), and a Master in Paleontology
(2007) and a PhD in Sciences (2010) issued from Universidad Autónoma de Madrid (Spain).
Currently he has a postdoctoral position in the Department of Paleontology at the University of
Zaragoza (Aragosaurus Group) and is an associated researcher in the Department of the
Mesozoic Faunas at the Institut Català de Paleontologia.
Josep Fortuny (La Roca del Vallès, 1980) has a Degree of Biology (Zoology) at the Universitat
Autònoma de Barcelona, Barcelona, Catalonia (2006) and a PhD of Geology by the Universitat
de Barcelona, Barcelona, Catalonia (2011) about the early tetrapods from the Permian and
Triassic periods and its paleobiology using biomechanical approaches.
He started in paleontology as scholar in Institut de Paleontologia de Sabadell and after he got a
predoctoral contract. Currently, he has a postdoctoral position in the Institut Català de
Paleontologia Miquel Crusafont (Barcelona, Catalonia) and he is the coordinator of the Virtual
Paleontology Research Group. His research focus on the paleobiology of early tetrapods using
non invasive tecniques as CT scanners and biomechanical approaches as Finite Element
Analysis (FEA).
Dr. Fortuny is member of the Society of Vertebrate Palaeontology (SVP) and the Association
des Géologues du Permien et du Trias (AGPT).
Albert G. Sellés (Mataró, 1982) graduated in Bachelor degree in Geology for Universitat de
Barcelona in 2007; where, together with Universitat Autònoma de Barcelona, also complete a
Master degree in Palaeontology in 2008. He obtained the PhD degree in Earth Science for
Universitat de Barcelona in 2012 (Barcelona, Spain).
From 2008 to 2012, he was a research fellow in the Mesozoic Department of Institut Català de
Paleontologia (Sabadell, Spain). Currently, he is working in the Department of Palaeobiology of
Macquarie University (Sydney, Australia), where develops technical and research tasks as
active collaborator of the Palaeobiology Database.
Àngel Galobart (Sabadell, 1961) has a Degree of Biology (Zoology) in 1984 and a PhD of
Geology in 1997, both by th Universitat Autònoma de Barcelona, Barcelona, Catalonia. He
started in paleontology in the Institut Paleontologic Miquel Crusafont (former Institut Català
de Paleontologia) as fieldwork assistant in 1985 and gets it first position in the institution as
fossil preparator in 1991. In 2001 wins the position of fossil vertebrate collections Curator and,
finally, in 2007 becomes head of the Mesozoic Group Research of Institut Català de
Paleontologia. During his career he has worked on plio-pleistocene mammals and dinosaurs
and other mesozoic vertebrates. He has leaded several research projects of Science Ministry of
Spain and directed more than 150 fieldtrip campaignes.
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Computational and experimental approach of the