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 , . In experimental way, eggshell strength is evaluated from a non-destructive and quasi-static compression test , , using a transducer  or introducing a dynamical test method using modal analysis . The mechanics and mechanisms of failure of hens eggs have been examined experimentally under contact loading conditions . In computational mechanics, the dynamic mechanical behaviour of the egg has been evaluated with Finite Element Analysis (FEA) from simple structural models  to highly nonlinear transient dynamic analysis  including the study of the rupture by impact loading . 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  or to study the microstructure-controlled stability of selected eggshells of Indian dinosaurs . 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 . According to previous works, there is a stress at which the eggshell rupture starts . 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 ,  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 . 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 . 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 . 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). References  Š. Nedomová, J. Trnka, P. Dvořáková, J. Buchar, and L. Severa, “Hen’s eggshell strength under impact loading,” Journal of Food Engineering, vol. 94, no. 3–4, pp. 350–357, Oct. 2009.  J. Trnka, J. Buchar, L. Severa, Š. Nedomová, and P. Stoklasová, “Effect of Loading Rate on Hen’s Eggshell Mechanics,” Journal of Food Research, vol. 1, no. 4, pp. 96–105, Oct. 2012.  P. W. Voisey and J. R. Hunt, “Measurement of eggshell strength,” Journal of Texture Studies, vol. 5, no. 2, pp. 135–182, Jul. 1974.  S. Nedomova, L. Severa, and J. 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Paganelli, “The initial density of avian eggs derived from the tables of Schönwetter,” Journal of Ornithology, vol. 130, no. 2, pp. 207–215, Apr. 1989. 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.