
universal testing system. The device holds two UXCELL 0.8N, 10 mm
stroke push-pull electromagnet solenoids, with 3D-printed angled egg
supports to stabilize the egg prior to dropping. To actuate the solenoids,
thereby dropping the egg, we wired both solenoids to a pair of 9V bat-
teries, connected in series, to a Single-Pole Single-Throw (SPST) rocker
switch. Experimental setup is shown in Supplementary Fig. S5.
A drop test is carried out as follows: First, we place the egg atop the
solenoid supports and reset the 1kN load cell such that the force reading is
0.0N. To precisely set the drop height, we use the cross-head of the Instron
system, to lower the device until the egg lightly touches the load cell and the
force reading is 0.1N, indicating first contact. We then reset the gauge length
extension to zero and translated the egg assembly upwards to heights of 8.0,
9.0, and 10.0 mm for testing. With the egg in place, we begin data collection
and toggle the SPST rocker switch to “ON” triggering the solenoid arms to
simultaneously retract and release the egg for impact onto the bottom
platen.
We dropped the eggs in three different orientations: horizontal on their
equator, vertical on their sharp end, and vertical on their blunt end. Twenty
eggs were tested per orientation and the drop procedure was repeated at
heights of 8.0mm, 9.0mm, and 10.0mm for a total of 180 eggs tested.
Cracked eggs were identified through analysis of force-time curves recorded
by the Instron system and subsequent visual inspection. A sharp drop in
force was interpreted as a crack event. Conversely, if the egg bounced (as
reflected in the force-time plot as a wave with decreasing amplitude) the egg
was likely intact, although some did crack. To ensure accuracy, we visually
inspected all eggs for hairline fractures after a few days. If we detected a
fracture, the egg was classified as cracked. Raw Data from the dynamic tests
can be found in Supplementary Note 3.
Numerical experiments
Full 3D simulations were conducted using the Finite Element Analysis
software, Abaqus/Explicit. We structured the egg with an exterior eggshel l
modeled as a linear elastic material, and an interior yolk modeled as a
viscous fluid. The average measured dimensions of the experimental
eggs were used to define the model egg geometry. For the yolk, we
adopted mass density and viscosity values as reported in the literature
22,23
,
i.e., 1.02 g/cm
3
, and 1322MPa ⋅ s, respectively. The shel ls Young’smodulus,
Poisson’s ratio, and mass density wer e also taken to agree with reported
values
24–26
i.e., 49GPa, 0.3, and 2.241 g/cm
3
, respectively. We postulated shell
fracture as brittle failure with material parameters calibrated to match the
average experimental curve for static compression in vertical loading
(Fig. 1): the failure stress as 23MPa, the Mode I fracture energy–defining
the energy required for failure–as 3.728 mJ. The calibrated failure stress
of 23MPa matches closely to the value of 19.9MPa determined from
Liu et al.
27
. Additionally, we simulated the half-shell experiments performed
in Liu et al.
27
and were able to capture the same trends. More details of
these simulations can be found in Supplementary Not e 4. To specify the
post-cracking shear behavior, we defined the shear retention factor-crack
opening strain relationship as crack opening strain of 0 corresponding
to shear retention factor of 1, and crack opening strain of 0.002922
corresponding to shear retention factor of 0. For more information
about the latter parameters, the reader is referred to ABAQUS
documentation
28
.
The eggshell domain was discretized using unstructured S4R elements
with an element size of 2mm with reduced integration and finite membrane
strain. Note that when a crack propagates through an element, the failed
element may experience severe distortion. In this case, it is removed from the
mesh once the damaged criterion is satisfied. To accommodate this we
enabled element deletion in the ABAQUS element controls. Mesh depen-
dence analysis confirms that the current approach captures the correct
qualitative trends (see Supplementary Fig. S2).
We analysed the interaction between the yolk and the eggshell via the
Coupled Eulerian-Lagrangian (CEL) technique. To specify the exact loca-
tion of the yolk inside the eggshell, we used a predefined material assignment
after creating a discrete fieldusingthevolumefractiontool.ABAQUStracks
the material flow in each element by using volume fraction, which repre-
sents the percentage of the element’svolumefilled with material at any given
moment. We discretized the yolk domain using a structured mesh of 8-node
brick elements of EC3D8R Eulerian family element type with an element
size of 2 mm. The top and bottom supports are modeled as 3D discrete rigid
plates, which we discretized via unstructured mesh of 4-node 3D bilinear
rigid quadrilateral elements (R3D4).
Static compression tests modeling. To simulate static compression,
we bounded the egg by top and bottom supports. The top support
translates in the vertical direction at a constant velocity, 100 mm/min,
while the bottom support remains stationary. To prevent rotation of the
egg we constrained the top and bottom tips of the egg to move only along
the vertical axis. It is worth mentioning that both 10 mm/min and
100 mm/min velocities were tested experimentally, with no significant
difference observed in the results. To reduce simulation time, we adopted
the 100 mm/min velocity in our simulations, as using 10 mm/min would
have led to excessively long computational times, which are impractical
for model calibration with the Coupled Eulerian-Lagrangian (CEL)
approach. Simulations were conducted using dynamic explicit stepping
with a time period of 0.35 seconds and geometric nonlinearities were
captured by choosing the NLGEOM option.
Drop tests modeling. To model a dynamic drop, we used the same setup
as for static compression, but without the top support. We dropped the
egg from a prescribed height onto the stationary bottom support. We
adopted the same material parameters, egg dimensions, loads, mesh
types, and number of elements as in the compression tests. We modeled
the egg when it reached a height of 0.5 mm from the floor by prescribing
an initial velocity using energy conservation, v ¼
ffiffiffiffiffiffiffi
2gh
p
, which matched
the experimental drop values. We use a dynamic explicit step with a time
period of 0.005 s. For smooth tracking of fracture, we defined the output
frequency of intervals as 50.
Data availability
All of the experi mental data is provided in the Supplementary Information
and available online via GitHub (cohen-mechanics-group/nature-comms-
phys-egg).
Received: 24 October 2024; Accepted: 1 April 2025;
References
1. Swift, J. & Swift, J.Gulliver’s travels (Springer, 1995).
2. Dunlop, J. W. & Fratzl, P. Biological composites. Annu. Rev. Mater.
Res. 40,1–24 (2010).
3. Melnikov, S. et al. One core, two shells: bacterial and eukaryotic
ribosomes. Nat. Struct. Mol. Biol. 19, 560–567 (2012).
4. Schwechheimer, C. & Kuehn, M. J. Outer-membrane vesicles from
gram-negative bacteria: biogenesis and functions. Nat. Rev.
Microbiol. 13, 605–619 (2015).
5. Ferguson, S., Klumpe, H. & Turner, J. The Incredible Egg: Investigating
the design education challenges and complexity of the egg drop
project. Proceedings of the ASME Design Engineering Technical
Conference 6 (2010).
6. Egg drop. https://www.scienceworld.ca/resource/egg-drop/ (2014).
Online; accessed 07 August 2024.
7. Saint Mary’s University. How strong is eggs? https://www.demos.
smu.ca/demos/mechanics/175-how-strong-is-eggs (2015). Online;
accessed 07 August 2024.
8. Rober, M. Egg drop from space. https://www.youtube.com/watch?v=
BYVZh5kqaFg (2022). Online; accessed 07 August 2024.
9. Rober, M. 1st place egg drop project ideas- using science (2015).
https://www.youtube.com/watch?v=nsnyl8llfH4. Online; accessed
07 August 2024.
https://doi.org/10.1038/s42005-025-02087-0 Article
Communications Physics | (2025) 8:182 5