batteries
Article
Virtual Detection of Mechanically Induced Short Circuits
in a Cylindrical Lithium-Ion Battery Cell Based on Finite
Element Simulation
Klemens Jantscher 1, *, Christoph Breitfuß 1 , Martin Miklau 1 , Khaled Ismail 1 and Peter Dobusch 2
1
2
*
Citation: Jantscher, K.; Breitfuß, C.;
Miklau, M.; Ismail, K.; Dobusch, P.
Virtual Detection of Mechanically
Virtual Vehicle Research GmbH, Inffeldgasse 21A, 8010 Graz, Austria; christoph.breitfuss@v2c2.at (C.B.);
martin.miklau@v2c2.at (M.M.); khaled.ismail@v2c2.at (K.I.)
Kreisel Electric GmbH & Co. KG, Kreiselstraße 1, 4261 Rainbach im Mühlkreis, Austria;
peter.dobusch@kreiselelectric.com
Correspondence: klemens.jantscher@v2c2.at
Abstract: Lithium-ion batteries (LIBs) are commonly used in today’s electric vehicles. Studying their
behaviour under mechanical loading, including short circuits, is vital for vehicle safety. This paper
covers three major topics, (1) a general literature review for the state-of-the-art of LIBs, (2) physical
cell tests for model validation are performed, wherein the occurrence of short circuits is detected and
(3) creating a finite element model (FEM) of an 18650 cylindrical LIB using the most recent testing
and simulation techniques. A variety of short-circuit criteria based on stresses, strains and geometric
parameters have been implemented in the simulation and compared to the test results. It will be
demonstrated that a combination of two geometric criteria, in the radial and axial directions of the
cell, is best suited for virtual short-circuit detection in the simulation. Finally, the short-circuit criteria
are implemented in a post-processing tool that allows fast short-circuit analysis of cells of different
loadings. In the future, this method of short-circuit detection will be used to analyse an assembly of
several battery cells such as, for instance, an automotive or maritime battery pack. Furthermore, the
developed method enables mechanical integration with respect to crash safety in vehicles.
Induced Short Circuits in a
Cylindrical Lithium-Ion Battery Cell
Based on Finite Element Simulation.
Keywords: lithium-ion battery; plastic deformation; short circuit; vehicle safety; finite element
simulation
Batteries 2021, 7, 79. https://
doi.org/10.3390/batteries7040079
Academic Editor: Matthieu Dubarry
Received: 22 August 2021
Accepted: 16 November 2021
Published: 17 November 2021
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
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Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
1. Introduction
Since the development of the first LIBs in the 20th century the technology has passed
through different milestones, starting with primary batteries and ending with the recent
state (secondary batteries) [1]. In 1991, commercial use of this technology began and, since
then, remarkable progress regarding materials [2] and cell design has been made. The
advantages of this technology caused its widespread usage in different fields, such as in
electronics, laptops and electric vehicles. Especially in the automotive sector, the technology
faces great challenges, such as capacity, weight, charging speed and crash safety.
Electric vehicles have become an important part of today’s automotive industry. With
the growing use of this technology, safety concerns need to be addressed. lithium-ion
battery systems are at the center of these concerns, as they can cause fires when damaged.
For manufacturers to assess their safety measures during their development process, precise
simulation models can be very helpful. Especially, the virtual prediction of short circuits
is needed, since short circuits are the main cause of battery-induced fire. This document
gives an overview of the literature on lithium-ion battery mechanical testing, finite element
modelling and short-circuit mechanisms, including their detection. This is followed by
the description of the simulation model design. A state-of-the-art finite element model of
a battery is created and validated using data collected in mechanical tests performed on
several 18650 LIBs. The necessary quantities measured during these tests are force over
displacement and the occurrence of a short circuit, which is obtained by an open circuit
Batteries 2021, 7, 79. https://doi.org/10.3390/batteries7040079
https://www.mdpi.com/journal/batteries
Batteries 2021, 7, x FOR PEER REVIEW
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This is followed by the description of the simulation model design. A state-of-the-art finite
element model of a battery is created and validated using data collected in mechanical
2 of 26
tests performed on several 18650 LIBs. The necessary quantities measured during these
tests are force over displacement and the occurrence of a short circuit, which is obtained
by an open circuit voltage (OCV) measurement. In addition, testing videos are used to
voltage
(OCV)
measurement.
In addition,
testing
videossolvers
are used
to compare
deformation
compare
deformation
behaviour.
Two finite
element
have
been used
to create a
behaviour.
Two
finite
element
solvers
have
been
used
to
create
a
universally
applicable
universally applicable model. Continuing, the main part of this work is the research on
model.
Continuing,
main part
of short
this work
is detection
the research
on the
short
circuit criteria,
short circuit
criteria, the
to realize
virtual
circuit
within
simulation
model.
to realize virtual short circuit detection within the simulation model. Several stress- and
Several stress- and strain-based criteria as well as geometric criteria are investigated.
strain-based criteria as well as geometric criteria are investigated. Finally, the results of
Finally, the results of these investigations are shown and discussed.
these investigations are shown and discussed.
1.1.State
Stateofofthe
theArt
Art
1.1.
The
following
literaturestudy
studygives
givesan
anoverview
overviewofofthe
thestate-of-the-art
state-of-the-artofofmechanical
mechanical
The following literature
batterytesting,
testing,finite
finiteelement
element(FE)
(FE)simulation
simulationofoflithium-ion
lithium-ionbatteries
batteriesfor
forcrash
crashpurposes
purposes
battery
and
virtual
internal
short-circuit
prediction
in
battery
cells.
and virtual internal short-circuit prediction in battery cells.
1.1.1.Battery
BatteryCell
CellMechanical
MechanicalDeformation,
Deformation,Testing
Testingand
andFE
FESimulation
Simulation
1.1.1.
Themechanical
mechanicaldeformation
deformationofofbattery
batterycells
cellsand
andpacks
packsisisaavery
veryimportant
importantaspect
aspectofof
The
battery
safety.
In
designing
a
robust
battery
cell,
one
of
the
key
elements
is
understanding
battery safety. In designing a robust battery cell, one of the key elements is understanding
itslimits
limitsofofmechanical
mechanicalintegrity,
integrity,itself
itselfnecessary
necessaryfor
forelectric
electricintegrity
integrityininany
anyvehicle
vehiclecrash
crash
its
protectagainst
againstananelectric
electric
short
circuit
(SC).
Such
a short
circuit
cause
battery
totoprotect
short
circuit
(SC).
Such
a short
circuit
cancan
cause
the the
battery
to
to produce
amounts
of and
heattoand
tocause
even acause
a fire. Consequently,
indecade,
the last
produce
largelarge
amounts
of heat
even
fire. Consequently,
in the last
decade,
manygroups
research
groups
have investigated
the mechanical
properties
and
the crash
many
research
have
investigated
the mechanical
properties and
the crash
behaviour
ofbehaviour
Li-ion battery
cells and
packs
in aand
sophisticated
In the following,
common
of Li-ion
battery
cells
packs in a way.
sophisticated
way. Inthe
themost
following,
the
standard
mechanical
tests used
in the evaluation
of the
properties,
as well
as the
most common
standard
mechanical
tests used
inmechanical
the evaluation
of the
mechanical
crash
behaviour
of the
battery
cells,
are presented
(Figure cells,
1). A are
summary
of the
literature
properties,
as well
as the
crash
behaviour
of the battery
presented
(Figure
1). A
focusing
onofthe
between on
thethe
experimental
and the
numerical
simulations
of
summary
thecorrelation
literature focusing
correlation tests
between
experimental
tests and
the
battery cell
under various
attachedloading
in the Appendix
A1).
numerical
simulations
of theloading
battery scenarios
cell underis various
scenarios A
is (Table
attached
in
Figure
1 illustrates
the four
testing scenarios
most commonly
on
the Appendix
A (Table
A1).mechanical
Figure 1 illustrates
the four mechanical
testingperformed
scenarios most
18650
lithium-ion
cells. on 18650 lithium-ion cells.
commonly
performed
Figure1.1. (A)
(A) Indentation
Indentation by
byby
a cylindrical
rod;
(C)
Figure
by aa hemispherical
hemisphericalpunch;
punch;(B)
(B)lateral
lateralindentation
indentation
a cylindrical
rod;
three-point bending and (D) compression between two flat plates.
(C) three-point bending and (D) compression between two flat plates.
In the study described in this publication, three of these mechanical tests are performed: lateral indentation by a cylindrical rod, compression between two flat plates and
three-point bending. These three load cases examine the batteries in a radial direction.
Since the simulation model is supposed to work for mechanical abuse in every direction, a
21, 7, x FOR PEER REVIEW
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In the study described in this publication, three of these mechanical tests are perlateral indentation by a cylindrical rod, compression between two flat plates and 3 of 26
three-point bending. These three load cases examine the batteries in a radial direction.
Since the simulation model is supposed to work for mechanical abuse in every direction,
a fourth test isfourth
necessitated,
which is axial
between
two flat
ThisThis
test test is
test is necessitated,
whichcompression
is axial compression
between
twoplates.
flat plates.
less
common
can be
several
of the publications
mentioned
in Table
is less common
but
can bebut
found
in found
severalinof
the publications
mentioned
in Table
A1. A1.
Several are
approaches
are commonly
used
for the simulation
of the jellyroll
Several approaches
commonly
used for the
simulation
of the jellyroll
part ofpart
the of the
lithium-ion
batteries.
They
are
depicted
in
Figure
2
and
described
in
the
following:
lithium-ion batteries. They are depicted in Figure 2 and described in the following:
Batteries 2021, 7, 79formed:
Figure
2. (A) meso-mechanical
model, volume
(B) representative
volume
element
beam
Figure 2. (A)
meso-mechanical
model, (B) representative
element method,
(C) beam
method,method,
(D) scaled(C)
representamethod,
(D)
scaled
representative
sandwich.
tive sandwich.
In a meso-mechanical model, all layers of the jellyroll are simulated individually. Their
In a meso-mechanical
model, all layers of the jellyroll are simulated individually.
properties are homogenous. This type of model has high calculation times [3].
Their properties are
homogenous.
typeelement
of model
has high
calculation
times [3].
The representativeThis
volume
(RVE)
method
is a macroscopic
approach. It
The representative
volume element
(RVE) method
a macroscopic
approach.
usesto this
uses sum properties
for the jellyroll,
which is is
modelled
with solid
elements.It Due
sum properties
for the jellyroll,
whichcan
is be
modelled
with
solid
Due
to this simsimplification,
this model
calculated
very
fast. elements.
This method
is generally
accepted
and
is alsocan
used
[4]. very fast. This method is generally accepted and
plification, this
model
beherein
calculated
the beam method, three kinds of beam represent the jellyroll and the hardcase. Axial,
is also used hereinIn[4].
radial
and circumferential
withrepresent
different mechanical
properties
stiffness in
In the beam
method,
three kindsbeams
of beam
the jellyroll
and thedeliver
hardcase.
their directions. A surrounding null-shell is needed for contact reasons. This model has
Axial, radial and circumferential beams with different mechanical properties deliver stiffshort calculation times [5].
ness in their directions.
A surrounding null-shell is needed for contact reasons. This model
The scaled representative sandwich (SRS) is a hybrid method between meso- and
has short calculation
times
[5].
macro-mechanic
modelling. All layers of each type (separator, copper, aluminium, anodeThe scaled
representative
sandwich
hybrid
between
mesoand This
and cathode-active material)
are(SRS)
mergedistoaone
singlemethod
layer, with
cumulated
thickness.
macro-mechanic
modelling.
of each type (separator,
anode- The
method
is faster All
thanlayers
the meso-mechanical
approach,copper,
but it hasaluminium,
some disadvantages.
locationmaterial)
of the short
is not
there
is a non-realistic
stress distribution
and cathode-active
arecircuit
merged
toexact
one and
single
layer,
with cumulated
thickness. [6].
In general,
the
quality of a simulation
modelbut
is limited
by thedisadvantages.
data it is based upon.
This method is faster
than the
meso-mechanical
approach,
it has some
Simplifications,
to
a
certain
degree,
are
always
necessary
in
its
creation,
which cause
The location of the short circuit is not exact and there is a non-realistic stress distribution
inaccuracies in the results.
[6].
In general,
theVirtual
quality
of a simulation
model
is limited by the data it is based upon.
1.1.2.
Internal
Short Circuit
Prediction
Simplifications, toThe
a certain
degree,
are always
necessary
in its creation,
cause inacaccurate
prediction
of an internal
short-circuit
event duewhich
to mechanically
abusive
curacies in theconditions
results. is one of the major research interests in the field of battery technology, because,
once an internal short circuit begins, it may lead to thermal runaway. Due to the criticality
1.1.2. Virtual Internal
Short
Circuit
of such an
event,
manyPrediction
researchers have focused their research on the investigation of
short-circuit
mechanisms
and applied
different
methods
predicting short
circuits. A
The accurate
prediction
of an internal
short-circuit
event
due totomechanically
abusive
summary of the methods found in the literature is attached in the Appendix A (Table A2).
conditions is one of the major research interests in the field of battery technology, because,
once an internal short circuit begins, it may lead to thermal runaway. Due to the criticality
, x FOR PEER REVIEW
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such
Batteries 2021,of
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an event, many researchers have focused their research on the investigation of
4 of 26
short-circuit mechanisms and applied different methods to predicting short circuits. A
summary of the methods found in the literature is attached in the Appendix A (Table A2).
Basically, a short circuit is assumed to be an instantaneous discrete process, i.e., at t
Basically, a short circuit is assumed to be an instantaneous discrete process, i.e., at
≥ tshort there appears
an electrically conductive path between the two layers undergoing
t ≥ tshort there appears an electrically conductive path between the two layers undergoing
the short, as illustrated
in the
example in
in the
Figure
3 [7].in Figure 3 [7].
the short,
as illustrated
example
Figure 3. Diagrammatic representation of an internal short-circuit.
Figure 3. Diagrammatic representation of an internal short-circuit.
Figure 3 shows the cell model and its components. A short circuit is created by a
penetrating
marked
green, connecting
copper
current
collectorby
anda cathode’s
Figure 3 shows
the cell particle,
model and
its components.
A short
circuit
is created
active
material.
Four
different
scenarios
of
a
short
circuit
may
occur
in
the
lithium-ion
penetrating particle, marked green, connecting copper current collector and cathode’s ac[7–9]: scenarios of a short circuit may occur in the lithium-ion cells
tive material. Fourcells
different
The first scenario is a short between the current collectors (copper and aluminium)
[7–9]:
which causes a high turnover of power due to low resistance (<10 mΩ). Due to the good
The first scenario is a short between the current collectors (copper and aluminium)
thermal conductivity of copper, the cell is heated homogeneously and the thermal runaway
which causes a high
turnover
of occur.
power due to low resistance (<10 mΩ). Due to the good
usually
does not
thermal conductivity of
cell isisheated
and
the thermal
runa- and the
Thecopper,
second the
scenario
a short homogeneously
circuit between the
copper
current collector
way usually doescathode
not occur.
active material which rarely occurs. The process is controlled by the high resistance
of this combination
(>100 mΩ).
The the
degradation
of the cathode
material
happens at
The second scenario
is a short circuit
between
copper current
collector
and the
temperatures
than
neededThe
to start
the chemical
decomposition
cathode active material
whichlower
rarely
occurs.
process
is controlled
by the process.
high reThe third
scenario
a short
circuit between
anode active
material
and aluminium
sistance of this combination
(>100
mΩ). isThe
degradation
of the cathode
material
happens
current collector which is the worst-case scenario. The resistance of this combination is low
at temperatures lower than needed to start the chemical decomposition process.
(~100 mΩ) but the thermal conductivity of aluminium is not as high as it is for copper. This
The third scenario is a short circuit between anode active material and aluminium
leads to localized heating of the cell, which leads to decomposition of the anode material,
current collector which
is the further
worst-case
which creates
heat. scenario. The resistance of this combination is
low (~100 mΩ) but theThe
thermal
of aluminium
is notthe
as high
it is for copper.
fourthconductivity
scenario is a short
circuit between
activeasmaterials
of both electrodes,
This leads to localized
heating
of
the
cell,
which
leads
to
decomposition
of
thebecause
anode of
mawhich is the most likely to occur. In this case, resistance is high
the cathode
material
(>100
mΩ).
terial, which creates
further
heat.
In the
several between
methods for
virtual
short-circuit
prediction
found [3–5,10–13]:
The fourth scenario
is literature,
a short circuit
the
active
materials
of bothwere
electrodes,
Mohr–Coulomb
criterion
which is the most• likely
to occur. Infailure
this case,
resistance is high because of the cathode
•
force drop criterion
material (>100 mΩ).
•
criterion
based on unified
strength
theory
In the literature,
several methods
for virtual
short-circuit
prediction were found [3–
•
criterion based on von Mises equivalent strain
5,10–13]:
•
•
•
•
•
•
criterion based on volumetric strain
Mohr–Coulomb
• failure
criterioncriterion
based on main normal strain
force drop criterion
•
criterion based on maximum principal stress
• oncriterion
on von
Mises equivalent stress
criterion based
unifiedbased
strength
theory
criterion based on von Mises equivalent strain
criterion based on volumetric strain
Batteries 2021, 7, 79
5 of 26
•
criterion based on deformation in length and diameter
The Mohr–Coulomb fracture criterion, which takes into account shear, compressive
and normal stresses, and is used to predict the breaking of the jellyroll and the short circuit
that coincides with it [10].
The force drop criterion uses the fact that, under mechanical loading, a drop in force
measurement
coincides with a short circuit [3,4].
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The unified strength theory criterion
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(
σ1 +α·σ3
α
σ1 − 1+
eq
b ·( b · σ2 + σ3 ), σ2 ≤ 1+α
σUni f ied =
(1)
σ1 +α·σ3
1
1+b ·( σ1 + b · σ2 ) − α · σ3 , σ2 ≥ 1+α
is based on the principal stresses (σ1 , σ2 , σ3 ), the ratio between tension and compression
(α) and a weighing factor (b), which, corresponding to twin shear theory, is set as one [13].
The other criteria are explained in detail in Section 4, where they are applied.
Some of these criteria are based on physical data. Such criteria can be used with
meso-mechanical models. With these models, it is also possible to determine the type of
short circuit. Several of these methods are investigated in this publication.
This work puts the focus on cylindrical LIBs. It has to be noted, at this point, that
the described methods are also applicable for other cell designs, such as pouch cells or
prismatic cells [14–16].
2. Mechanical Abuse Testing
For the creation of a reliable simulation model of the 18650 lithium-ion battery, data
from real-life tests is needed. This section describes the experimental setups used and the
data gained therefrom on the batteries’ mechanical behaviours.
2.1. Cell
Figure 6. Radial crush impactor
C1Case
(SOCTesting
comparison) force over displacement (A) and cell specimen after testing (B).
Figure 6. Radial crush impactor C1 (SOC comparison) force over displacement (A) and cell specimen after testing (B).
Figure 6. Radial crush impactorIn
C1the
(SOC
comparison)
displacement
(A) andimpactor,
cell specimen
testing (B). of all
following, onlyforce
the over
load-case
radial crush
as aafter
representative
2.2.
Cell
Testing
cases,
is Testing
discussed. The load-case radial crush impactor will serve as a continuing example
2.2.
Cell
2.2.
Cell
Testing
for all
load
cases
used
throughout
this paper.
Results
and conducted
discussionswith
of the
other
load
The
tests
of the
whole
cell (including
the jelly
roll) were
four
different
The tests of the whole cell (including the jelly roll) were conducted with four different
The
of the
whole
cellB.
(including
the jelly
roll)ofwere
conducted
with used.
four different
casessetups.
aretests
shown
inwith
Appendix
test
Cells
maximal
and minimal
states
charge
(SOC) were
Table 2
test setups. Cells with maximal and minimal states of charge (SOC) were used. Table 2
test
setups.
Cells with
andcell
minimal
states
of charge
(SOC)
were used.
2
Quasi-static
testing
of empty
cases was
done
with three
different
test Table
set-ups
shows
the realized
test maximal
matrix.
shows the realized test matrix.
described
Table 1.
shows
the in
realized
test matrix.
Table 2. Four mechanical abuse tests for type 18650 lithium-ion battery cells.
Table1.
2. Four mechanical
18650 lithium-ion
battery
cells.
Table
mechanical abuse
abuse tests
tests for
for type
empty-type
18650 battery
cell cases.
Table 2. Three
Four mechanical
abuse
tests
for
type
18650 lithium-ion
battery
cells.
Speed
Boundary
Speed
Boundary
Amount
SOC/%
Abort
Criterion Boundary
Test
Principle
AmountSOC/%
Speed/mm/min
Abort
Criterion
Condition
Test Principle
Principle
Speed
Boundary
Amount
Abort
Criterion
Test
mm/min
Condition
Amount
SOC/%
Abort Criterion
Test Principle
mm/min
Condition
mm/min
Condition
4
100
5
4
100
5
short circuit
4
100
5
circuit
plate
axial
crush
radial
crush
3
5
50% short
deformation
flatflat
plate
short
circuit
flat plate
axial crush
50%
deformation
2
0
5
flat plate
axial crush
50% deformation
2
0
5
50% deformation
2
0
5
4
100
1
short circuit
4
100
1
short circuit
radial crush
flat plate
42
100
short
circuit
radial
crush
plate
radial
crush
3
1 1
50%
deformation
flatflat
plate
0
1
50%
deformation
radial crush
flat plate
2
0
1
50% deformation
24
0
1
50%
deformation
100
1
4
100
1
radial crush inshort circuit
cylindrical im4
100
1
radial crush inshort circuit
cylindrical imradial
crush inshort
circuit
cylindrical
dentation
50%
deformation
pactor im2
0
1
radial
crush impactor 2
3
1 1
50%
deformation
impactor
dentation
50%
deformation cylindrical
pactor
0
dentation
50% deformation
pactor
2
0
1
4
100
1
reproducing in4
100
1
reproducing in4
100
1
short circuit
reproducing
inshort circuit
stallation situa3-point bending
short
stallation situa3-point bending
forcecircuit
drop
2
0
1
situa- in Figure 4. It is a
3-point bending
The
mechanicalstallation
teststion
is shown
forceall
drop
2
0 testbench1used to perform
force drop
2
0
1
tion
custom-built hydraulic press with a load cell that can withstand
tion forces of up to 100 kN. The
maximum force measurement is at 40 kN, restricted by the measurement amplifier.
For axial crush, the specimens are deformed mainly in axial direction. For radial
For axial crush, the specimens are deformed mainly in axial direction. For radial
crush,
the specimens
deformed occurs
mainlyinina radial
axial direction.
crushFor
andaxial
radial
indentation,
the mainare
deformation
direction. For
The radial
threecrush and radial indentation, the main deformation occurs in a radial direction. The threecrush
and
radial
indentation,
the
main
deformation
occurs
in
a
radial
direction.
The
threepoint bending setup, shown above, creates deformation in axial direction, caused by the
point bending setup, shown above, creates deformation in axial direction, caused by the
point
bending
setup,
above,
creates caused
deformation
axial
direction,
caused
by the
bending
motion,
and shown
in a radial
direction,
by theinflat
impactor.
For
the relevant
bending motion, and in a radial direction, caused by the flat impactor. For the relevant
bending
motion,
and inbending
a radial deformation—before
direction, caused by the
flat impactor.
For the relevant
part of the
three-point
a short
circuit occurs—the
deforpart of the three-point bending deformation—before a short circuit occurs—the deforpart
of happens
the three-point
deformation—before
a short circuit occurs—the deformation
mostly bending
in a radial
direction.
mation happens mostly in a radial direction.
mation
happens
mostly
intest
a radial
Figure
6A shows
the
resultdirection.
of cells with 100% SOC and 0% SOC for the load-case
Figure 6A shows the test result of cells with 100% SOC and 0% SOC for the load-case
Figure
6A
shows
the
test
result
of
cells with
100%
SOC
andshort
0% SOC
for thecan
load-case
radial crush impactor. A correlation between
force
drop
and
circuiting
be ob-
Batteries 2021, 7, 79
Batteries 2021, 7, x FOR PEER REVIEW
Batteries 2021, 7, x FOR PEER REVIEW
6 of 26
6 of 24
6 of 24
Figure 4.
4. Hydraulic test bench.
Figure
Hydraulic test bench.
The force-displacement
force-displacement
curves
(Figure 5A)
5A) show
show that
that there
there is
is good
force-displacement curves
curves (Figure
for
The
good repeatability
repeatability for
the
test
The
maximum
deformation
for
the
validation
of
results.
The
maximum
deformation
for
the
simulation
model
the test results. The maximum deformation for the validation of the simulation model
(validation limit)
limit) can
can be
be estimated
estimated at
approx. 5.6
5.6 mm,
mm, based
based on
on occurring
occurring short
short circuits
at approx.
circuits in
(validation
in
cell
tests
(Figure
6).
Figure
5B
shows
the
deformed
specimen
of
test
01.
cell tests (Figure 6). Figure 5B shows the deformed specimen of test 01.
Figure
5.
Results
of
the
cell-case
test
for
the
load-case
radial
crush
impactor (A)
(A) and cell-case
cell-case specimen after
after testing (B).
(B).
Figure 5.
5. Results
Results of
of the
the cell-case
cell-case test
test for
for the
the load-case
load-case radial
radial crush
crush impactor
impactor
Figure
(A) and
and cell-case specimen
specimen after testing
testing (B).
Batteries 2021, 7, 79
Batteries 2021, 7, x FOR PEER REVIEW
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7 of 24
Batteries 2021, 7, x FOR PEER REVIEW
7 of 24
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Figure
Figure6.6.Radial
Radialcrush
crushimpactor
impactorC1
C1(SOC
(SOCcomparison)
comparison)force
forceover
overdisplacement
displacement (A)
(A) and
and cell
cell specimen
specimen after
after testing
testing (B).
(B).
2.2.Cell
CellTesting
Testing
2.2.
Thetests
testsof
ofthe
thewhole
wholecell
cell(including
(includingthe
thejelly
jellyroll)
roll)were
wereconducted
conductedwith
withfour
fourdifferent
different
The
test
setups.
Cells
with
maximal
and
minimal
states
of
charge
(SOC)
were
used.
Table 22
test setups. Cells with maximal and minimal states of charge (SOC) were used. Table
Figure 6. Radial crush impactor C1 (SOC comparison) force over displacement (A) and cell specimen after testing (B).
shows
the
realized
test
matrix.
shows the realized test matrix.
Figure 6. Radial crush impactor C1 (SOC comparison) force over displacement (A) and cell specimen after testing (B).
2.2. Cell Testing
Figure 6. Radial crush impactor C1 (SOC comparison) force over displacement (A) and cell specimen after testing (B).
2.2. Cell
The
tests of
the wholeforce
cell (including
the jelly(A)
roll)
conducted
with
four(B).
different
Radial crush
impactor
C1Testing
(SOC
comparison)
over displacement
andwere
cell specimen
after
testing
Table 2. Four mechanical abuse tests Figure
for 6.type
18650
lithium-ion
battery
cells.
test Cell
setups.
Cells
with
maximal
and minimal
states
charge
(SOC) were
Table 2
TheTesting
tests
of the
whole
cell (including
the jelly
roll)ofwere
conducted
with used.
four different
2.2.
Table 2. Four mechanical abuse tests for type 18650test
lithium-ion
battery
cells.
shows
the
realized
test
matrix.
2.2. Cell
Testing
setups.
Cells with maximal and minimal states of charge (SOC) were used. Table 2
Amount
Amount
SOC/%
SOC/%
Speed
Speed
mm/min
4
24
100
0100
mm/min
5
55
radial crush
42
2
1000
0
15
1
radial crush
radial
crush
indentation
44
22
100
100
0 0
11
11
3-pointcrush
bending
radial
in-
44
2
100
100
0
11
1
axial crush
axial crush
dentation
2
4
3-point bending
2
0
1
The tests of the whole cell (including the jelly roll) were conducted with four different
shows the realized test matrix.
The tests
of the
whole cell (including
the jelly
roll)ofwere
conducted
with used.
four different
setups.
Cells
with
and 18650
minimal
states
charge
(SOC) were
Table 2
Tabletest
2. Four
mechanical
abusemaximal
tests for type
lithium-ion
battery
cells.
test setups.
Cells with
and minimal
states of charge (SOC) were used. Table 2
shows
the realized
test maximal
matrix.
Abort Criterion
Condition
Boundary
Table 2. Four mechanicalBoundary
abuse tests for
type 18650
lithium-ion battery cells. Test Principle
shows the realized
test matrix.
Speed
Boundary
Abort
Criterion
Test Test
Principle
Amount
SOC/%
Abort Criterion
Principle
Table 2. Four mechanical
abuse tests for type 18650 lithium-ion battery
cells.
mm/min
Condition
Speed
Boundary
Condition
Amount
SOC/%
Criterion
Test Principle
abuse
tests forAbort
type 18650
lithium-ion battery cells.
4 Table 2. Four
100mechanical
5
mm/min
Condition
shortAmount
circuit
SOC/%
4
100
2
0
Amount
SOC/%
50%short
deformation
100
24 circuit
0
axial crush
axial crush
axial crush
radial
crush
axial crush
radial crush
radial
radialcrush
crushindentation
radial
crush
radial
crush
in-
44
100
100
2
00
short
circuit
422
100
50%
deformation
0
100
244
0
100
50% deformation
4
100
2
2
0
0
100
24 circuit
0
shortcircuit
short
100
44
100
0
42
100
50%
deformation
22
00
50% deformation
dentation
radial
crush inradial
crush indentation
3-point
bending
dentation
3-point bending
4
shortCriterion
circuit
Abort
flat
plate
50%
deformation
Abort
Criterion
short
circuit
50%
deformation
short
short circuit
circuit
short
circuit
50%
deformation
50%
deformation
short
circuit
50% deformation
50%
deformation
short
circuit
short
circuit
50%
deformation
short
circuit
50% deformation
50%
deformation
short
circuit
short
circuit
short
circuit
50%
deformation
50%
deformation
force
drop
short
circuit
flat plate
flat plate
Boundary
flat plate
Boundary
Condition
Condition
flat plate
Test Principle
Test Principle
flat
flat plate
plate
flat plate
flat plate
cylindrical
flat plateimpactor
flat
plateimcylindrical
pactor
cylindrical imreproducing
incylindrical
impactor
cylindrical
flat plate
pactor im-
stallation
reproducing
inpactorsituationsitua100
stallation
reproducing
inforce
drop
0
100
short circuit
tion situareproducing
installation
short
circuit
force
0 axial crush,
1 the specimens
stallation
For
aredrop
deformed mainly
in situaaxial direction. For radial
tion
force drop
0
1
tion
crushFor
andaxial
radial
indentation,
the
main
deformation
occurs
in
a
radial
direction. For
The radial
threecrush, the specimens are deformed mainly in axial direction.
point and
bending
setup,
shown above,
creates
deformation
direction,
caused
the
crush
radial
indentation,
the main
deformation
occursininaxial
a radial
direction.
The by
threeFor
axial
crush,
the
specimens
are
deformed
mainly
in
axial
direction.
For
radial
bending
motion,
and shown
in a radial
direction,
caused
by theinflat
impactor.
For
the relevant
point
bending
setup,
above,
creates
deformation
direction,
caused
the
For
axial
crush,
the specimens
are
deformed
mainlyinaxial
ina radial
axial
direction.
For by
radial
crush
and
radial
indentation,
the main
deformation
occurs
direction.
The
threepart
of
the
three-point
bending
deformation—before
a
short
circuit
occurs—the
deforbending
and in a radial
direction,
caused by
the flat
For theThe
relevant
crush bending
andmotion,
radial
indentation,
the main
deformation
occurs
a impactor.
radial
direction.
threepoint
setup,
shown
above,
creates
deformation
ininaxial
direction,
caused by
the
mation happens
mostly
in a radial
direction.
part
the three-point
bending
deformation—before
a in
short
circuit
occurs—the
deforpointofbending
setup,
above,
creates deformation
axial
direction,
by
the
bending
motion,
and shown
in
atest
radial
direction,
by the
Forcaused
theload-case
relevant
Figure
6A shows
the
result
of cells caused
with 100%
SOCflat
andimpactor.
0% SOC for
the
mation
happens
mostly
in
radial
direction.
bending
motion,
and inbending
a aradial
direction,
caused by the
flat impactor.
For the relevant
part
of
the
three-point
deformation—before
a
short
circuit
occurs—the
deforradial crush6A
impactor.
A correlation
force
drop
and
circuiting
be obshows the
test result
ofbetween
cells with
100%
SOC
andshort
0% SOC
for thecan
load-case
part Figure
of happens
the three-point
bending
deformation—before
a short
circuit
occurs—the
deformation
mostly
in
a
radial
direction.
served,crush
which
was expected.
Xia et al.
[17] also
identified
the short
force circuiting
drop as ancan
indicator
radial
impactor.
Aincorrelation
between
force
drop and
be obmation
happens
mostly
a radial
direction.
6A shows
the
test
result
of cellsforce
withlevel
100%for
SOC
andSOC
0% SOC
for thetoload-case
for a Figure
short
circuit.
The
cells
show
aethigher
100%
compared
0% SOC
served,
which
was
expected.
al.cells
[17] with
also identified
the
force
dropfor
asthe
an load-case
indicator
Figure
shows
the
test Xia
result
of
100%
SOC
and
0% SOC
radial
crush6A
impactor.
A range.
correlation
between
force
drop
and
short
circuiting
canreasons
be obat the
same
deformation
This
higher
force
level
can
obtain
from
different
for
a
short
circuit.
The
cells
show
a
higher
force
level
for
100%
SOC
compared
to
0%
radial crush
impactor.
A correlation
between
force
drop and
short
circuiting
can
beSOC
observed,
which
was
Xia et
al.
[17]density,
also
identified
the
force
drop asofanthe
indicator
[18].
charged
cellexpected.
has arange.
higher
packing
caused
by
the
swelling
anode.
at
theAsame
deformation
higher
forceidentified
level
can the
obtain
from
different
reasons
served,
which
wasThe
expected.
XiaThis
al.
[17]force
also
force
drop
as antoindicator
for
a short
circuit.
cells show
aethigher
level for 100%
SOC
compared
0% SOC
[18].
A
charged
cell
has
a
higher
packing
density,
caused
by
the
swelling
of
the
anode.
forthe
a short
The cells
showThis
a higher
force
level
forcan
100%
SOCfrom
compared
to 0%
SOC
at
samecircuit.
deformation
range.
higher
force
level
obtain
different
reasons
at theAsame
deformation
higherdensity,
force level
can by
obtain
from different
[18].
charged
cell has arange.
higherThis
packing
caused
the swelling
of thereasons
anode.
[18]. A charged cell has a higher packing density, caused by the swelling of the anode.
24
short circuit
2
short
circuit
force 2drop
3-point bending
3-point bending
Speed
5
Speed
mm/min
5
mm/min
55
51
5
15
11
11
1
11
11
1
1
11
1
11
50% deformation
reproducing
cylindrical
iminstallation
situation
pactor
For axial crush,1 the specimens are deformed mainly in axial direction. For radial crush
100
reproducing inand radial indentation, the main short
deformation
circuit occurs in a radial direction. The three-point
stallation
situa-caused by the bending
bending
deformation
in axial
direction,
force
drop
0 setup, shown
1 above, creates
tion
motion, and in a radial direction, caused by the flat impactor. For the relevant part of the
three-point bending deformation—before a short circuit occurs—the deformation happens
mostly
a radial
direction.
Forinaxial
crush,
the specimens are deformed mainly in axial direction. For radial
Figure
6A
shows
the test
cells with occurs
100% SOC
and 0%
SOC forThe
thethreeloadcrush and radial indentation,
theresult
main of
deformation
in a radial
direction.
case
radial
crush
impactor.
A
correlation
between
force
drop
and
short
circuiting
can
be
point bending setup, shown above, creates deformation in axial direction, caused by the
observed,
which
was
expected.
Xia
et
al.
[17]
also
identified
the
force
drop
as
an
indicator
bending motion, and in a radial direction, caused by the flat impactor. For the relevant
for aof
short
The cells
show deformation—before
a higher force level fora100%
compared
to 0% SOC
at
part
the circuit.
three-point
bending
shortSOC
circuit
occurs—the
deforthe
same
deformation
range.
This
higher
force
level
can
obtain
from
different
reasons
[18].
mation happens mostly in a radial direction.
A charged
has a higher
caused
theand
swelling
of the
When
Figure cell
6A shows
the testpacking
result ofdensity,
cells with
100%by
SOC
0% SOC
for anode.
the load-case
force
is
applied,
this
leads
to
a
higher
level
of
internal
friction.
The
swollen
anode
also
has
radial crush impactor. A correlation between force drop and short circuiting can be oba higher bending stiffness. Finally, lithium ions can induce mechanical stresses which also
served, which was expected. Xia et al. [17] also identified the force drop as an indicator
heightens the stiffness of the jellyroll. The earliest detections of short circuits appear at the
for a short circuit. The cells show a higher force level for 100% SOC compared to 0% SOC
same displacement, of 5.6 mm, for both states of charge. Figure 6B shows the deformed
at the same deformation range. This higher force level can obtain from different reasons
specimen of test 01 at 100% SOC.
[18]. A charged cell has a higher packing density, caused by the swelling of the anode.
Batteries 2021, 7, 79
When force is applied, this leads to a higher level of internal friction. The swollen anode
also has a higher bending stiffness. Finally, lithium ions can induce mechanical stresses
which also heightens the stiffness of the jellyroll. The earliest detections of short circuits
8 of 26
appear at the same displacement, of 5.6 mm, for both states of charge. Figure 6B shows
the deformed specimen of test 01 at 100% SOC.
3.
3. Mechanical
Mechanical Modelling
Modellingof
ofan
an18650
18650Lithium-Ion
Lithium-IonBattery
BatteryCell
Cell
Within
the
scope
of
this
paper,
a
macro-mechanical
cell
model
for afor
type-18650
lithiumWithin the scope of this paper, a macro-mechanical cell model
a type-18650
lithion
battery
is
developed.
The
following
steps,
which
are
also
shown
in
Figure
7,
are
needed
ium-ion battery is developed. The following steps, which are also shown in Figure
7, are
for
the validation
of the model:
needed
for the validation
of the model:
••
••
••
••
••
cell-case
cell-casetesting
testing(see
(seeSection
Section2)
2)
cell
testing
(see
Section
cell testing (see Section2)
2)
model
modelbuild-up
build-up
cell
cellcase-model
case-modelvalidation/optimization
validation/optimization
cell
model
validation/optimization.
cell model validation/optimization.
Figure7.7.FE-model
FE-modeldevelopment
developmentsteps.
steps.
Figure
Model
ModelBuild-Up
Build-Upand
andValidation
Validation
The
finite
element
model
is built
up using
the representative
volume
element
approach.
The finite element
model
is built
up using
the representative
volume
element
apAs
described
above,
this
method
is
commonly
used
in
crash
simulation
to
model
the
jellyroll
proach. As described above, this method is commonly used in crash simulation to
model
part
of the battery
To create
universally
useable simulation
model, two
different
the jellyroll
part ofcell.
the battery
cell.a To
create a universally
useable simulation
model,
two
finite
element
LS-DYNA,
are used.areThe
model
first built
in
different
finitesolvers,
elementAbaqus
solvers,and
Abaqus
and LS-DYNA,
used.
The is
model
is firstup
built
Abaqus and then translated to LS-DYNA. The translated model is not changed any further,
up in Abaqus and then translated to LS-DYNA. The translated model is not changed any
to keep both models comparable.
further, to keep both models comparable.
The cell, as well as the FE-model, are shown in Figure 8. Details of the cell, such as
The cell, as well as the FE-model, are shown in Figure 8. Details of the cell, such as
the contact and the notch at the top part are omitted to reduce calculation time. Due to the
the contact and the notch at the top part are omitted to reduce calculation time. Due to the
deep-drawing process in which the cell cup is produced, the material thickness varies in
deep-drawing process in which the cell cup is produced, the material thickness varies in
different parts of the cell cup. In the model, this is addressed by defining different parts
different parts of the cell cup. In the model, this is addressed by defining different parts
with different shell thicknesses.
with different shell thicknesses.
Batteries 2021, 7, x FOR PEER REVIEW
9 of 24
Batteries 2021, 7, 79
Batteries 2021, 7, x FOR PEER REVIEW
9 of 26
9 of 24
.
Figure 8. (A) 18650 cylindrical lithium-ion cell; (B) cell-cup model; (C) cell model also showing jel.
lyroll.
Figure
cylindrical
lithium-ion
cell;cell;
(B) cell-cup
model;
(C) cell
also showing
jellyroll.
Figure8.8.(A)
(A)18650
18650
cylindrical
lithium-ion
(B) cell-cup
model;
(C)model
cell model
also showing
jellyroll.The material used to simulate the cell cup is a steel model. Shell thicknesses, as men-
Theabove,
material
to simulate
cell
cup
is a steel model. Shell thicknesses, as
tioned
varyused
between
0.23 mmthe
and
0.31
mm.
mentioned
above,
vary
between
0.23
mm
and
0.31
The material
used
to simulate the
cell cup is amm.
steel model.
thicknesses,
menFigure
9 shows
a comparison
of force-displacement
curvesShell
gained
from theas
testing
Figure
9
shows
a
comparison
of
force-displacement
curves gained
from the testing
tioned
above, vary
between
0.23Figure
mm and
mm.a comparison
and
simulation
of the
cell cup.
100.31
shows
of deformation
for and
both
simulation
of
the
cell
cup.
Figure
10
shows
a
comparison
of
deformation
for
both
models.
Figure
9
shows
a
comparison
of
force-displacement
curves
gained
from
the
testing
models.
and simulation of the cell cup. Figure 10 shows a comparison of deformation for both
models.
Figure9.9.Force-displacement
Force-displacementcurves
curvesofofthe
thecell
cellcup’s
cup’sload-case
load-caseradial
radialcrush
crushimpactor.
impactor.
Figure
Figure 9. Force-displacement curves of the cell cup’s load-case radial crush impactor.
Batteries
Batteries2021,
2021,7,7,79x FOR PEER REVIEW
10 of
of 26
24
Batteries 2021, 7, x FOR PEER REVIEW
10 of 24
Figure
Figure10.
10.Simulation
Simulationof
ofdeformation—load-case
deformation—load-caseradial
radialcrush
crushimpactor.
impactor.
Figurecorrelation
10. Simulationbetween
of deformation—load-case
radial
crush impactor.
There is a good
the testing and
simulation
results. Also, the
There is a good correlation between the testing and simulation results. Also, the reresults of both simulations fit together very well.
sults of both simulations
very well.
Therefit
is together
a good correlation
between the testing and simulation results. Also, the reJellyroll Material:sults of both simulations fit together very well.
Jellyroll Material:
The jellyrollJellyroll
itself isMaterial:
modelled by a solid mesh, as can be seen in Figure 8C. A honeyThe jellyroll itself is modelled by a solid mesh, as can be seen in Figure 8C. A honeycomb material is used
tojellyroll
represent
jellyroll. by
This
material
several
advantages.
The
itselfthe
is modelled
a solid
mesh,has
as
can
be seen
in Figure 8C.ItIt
A honeycomb material is used
to represent
the
jellyroll. This
material
has
several
advantages.
features orthotropic
behaviour,
the
properties
in three This
orthogonal
be
comb
material iswhere
used to
represent
the jellyroll.
materialdirections
has severalcan
advantages.
It
features orthotropic behaviour, where the properties in three orthogonal directions can be
adjusted independently
without lateral
contraction.
The
materialinmodel
was first created
features orthotropic
behaviour,
where the
properties
three orthogonal
directions can be
adjusted independently
without lateral
contraction.contraction.
The material
model
was
first created
adjusted
independently
without lateral
The
material
model was first created
for Abaqus. Material
properties
were optimized
in LS-OPT using
the
force-displacement
for Abaqus. Material
properties
were
optimized
in
LS-OPT
using
the
force-displacement
for Abaqus.
properties
werewas
optimized
in LS-OPT
using the There
force-displacement
curves from testing.
Finally,Material
the material
model
translated
to LS-DYNA.
are
curves from testing.
Finally,testing.
the material the
model was model
translated
to LS-DYNA.
There are
curves
was
translated
todescribed
LS-DYNA.
differences between
the from
honeycomb Finally,
materials inmaterial
the two solvers
which
will be
inThere are
differences
between
the honeycomb
in materials
the two solvers
which
will
be described
differences
between thematerials
honeycomb
in the two
solvers
which
will be described
the
following.
the following.
in the
following.
For
Abaqus,intension/compression
and shear behaviour are defined via tangent modFor Abaqus, tension/compression
and shear are
behaviour
arevia
defined
via modtangent modForFigure
Abaqus,
tension/compression
and shear characteristic
behaviour
defined
tangent
uli [19].
11 shows
the tension/compression
for
the x direction;
y and z
uli
[19].
Figure
11
shows
the
tension/compression
characteristic
for
the
x
direction;
uli defined
[19]. Figure
11 shows the tension/compression characteristic for the x direction; y and y and
are
analogously.
z are defined analogously.
z are defined analogously.
Figure 11. characteristic
Tension/compression
characteristic Abaqus.
Figure 11. Tension/compression
Abaqus.
xx (defined
by R-S), Ebyxx S-T)
(defined
S-T)
and E xxby
(defined
by the
T-U)three
are the three
E0 xx (defined byER-S),
E1 xx (defined
andby
E2 xx
(defined
T-U) are
Figure 11. Tension/compression
characteristic
Abaqus.
tangent
moduli.
The
stress
at
point
Q
is
the
tensile
stress
above
which
the
material has
tangent moduli. The stress at point Q is the tensile stress above which the material has
ideally0plastic behavior. Points
V and W mark the path for unloading. The first quadrant
E xx (defined by R-S), E1xx (defined by S-T) and E2xx (defined by T-U) are the three
of this diagram corresponds to the tension characteristic whereas the third represents
tangent moduli. The stress at point Q is the tensile stress above which the material has
compression.
0
1
2
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Batteries 2021, 7, 79
11 of 24
11 of 24
ideally plastic behavior. Points V and W mark the path for unloading. The first quadrant
11 of 26
plastic behavior.
Points
V and
W mark
the path forwhereas
unloading.
quadrant
ofideally
this diagram
corresponds
to the
tension
characteristic
the The
thirdfirst
represents
of this diagram corresponds to the tension characteristic whereas the third represents
compression.
compression.
Figure 12 describes the shear characteristic for the xy direction; yz and zx are defined
Figure
describes the
theshear
shearcharacteristic
characteristicforfor
direction;
yz and
zx defined
are deFigure 12 describes
thethe
xyxy
direction;
yz and
zx are
analogously.
fined
analogously.
analogously.
Figure 12. Shear characteristic in Abaqus.
Figure
Figure12.
12.Shear
Shearcharacteristic
characteristicin
inAbaqus.
Abaqus.
The characteristic is very similar to tension/compression but only two tangent moduli
The characteristic
is very similar to tension/compression
but only two tangent moduli
TheThese
characteristic
very similar
tension/compression
but only two tangent moduli
are used.
are G0xy, is
defined
by A-Btoand
G1xy, defined by B-C.
are used. These are G00xy , defined by A-B and G11 xy , defined by B-C.
are For
used.
These aretension/compression
G xy, defined by A-B in
and
Gand
xy, defined
byasB-C.
LS-DYNA,
x, y
z as well
shear in xy, yz and zx are
For LS-DYNA, tension/compression in x, y and z as well as shear in xy, yz and zx
For
LS-DYNA,
tension/compression
in x,[20].
y and
z as
well as in
shear
in xy, yz in
and
zx are
defined
via
stress–strain
curves
or
load
curves
This
is
shown
the diagram
Figure
are defined via stress–strain curves or load curves [20]. This is shown
in the diagram
in
defined via stress–strain curves or load curves [20]. This is shown in the diagram in Figure
13.
Figure 13.
13.
Figure13.
13.Load
Loadcurve
curveLS-DYNA.
LS-DYNA.
Figure
Figure 13. Load curve LS-DYNA.
These load curves are defined in tabular form and only in the first and second quadrant.
These load curves are defined in tabular form and only in the first and second quadThis means the negative stresses are also defined as positive. The first quadrant corresponds
These
loadthe
curves
are defined
tabular
form and
in the
first
and
second quadrant. This
means
negative
stressesinare
also defined
as only
positive.
The
first
quadrant
corto compression and the second to tension. The load curves use total strain and are reached
rant. This
the negative
stresses
aretoalso
defined
positive.
quadrant
corresponds
tomeans
compression
and the
second
tension.
Theasload
curvesThe
usefirst
total
strain and
via the slope defied by the Young’s modulus.
responds
to
compression
and
the
second
to
tension.
The
load
curves
use
total
strain
and
are reached via the slope defied by the Young’s modulus.
The translation of the material parameters from Abaqus to LS-DYNA is done via
are The
reached
via theof
slope
defied byparameters
the Young’s
modulus.
translation
the material
from
Abaqus to LS-DYNA is done via refreference points in the stress–strain diagrams, as depicted in Figure 14.
translation
of the material
parameters
from Abaqus
to LS-DYNA
is done via referenceThe
points
in the stress–strain
diagrams,
as depicted
in Figure
14.
erence points in the stress–strain diagrams, as depicted in Figure 14.
Batteries 2021, 7, x FOR PEER REVIEW
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2021, 7,
7, 79
x FOR PEER REVIEW
12 of 24
12 of
of 26
12
24
Figure 14. Stress–strain characteristics for Abaqus (A) and LS-DYNA (B).
Figure 14. Stress–strain characteristics for Abaqus (A) and LS-DYNA (B).
The Points P1 through P5 are taken from the Abaqus model and translated to the LSThe Points
Points P1
P1through
through P5 aretaken
taken from
the
Abaqus
model and
translated
to LSthe
The
Abaqus
model
translated
to the
DYNA
model. P2,
which hasP5a are
non-zero from
strainthe
in Abaqus,
has to and
be shifted
to zero
strain.
LS-DYNA
model.
P2,
which
has
a
non-zero
strain
in
Abaqus,
has
to
be
shifted
to
zero
strain.
DYNA
model.part
P2, represents
which has the
a non-zero
strain
in Abaqus,
has to which
be shifted
to included
zero strain.
The
excluded
elastic part
of the
characteristic,
is not
in
The excluded
excluded part
part represents
represents the
elastic
part
of
the
characteristic,
which
is
not
included
in
The
the
elastic
part
of
the
characteristic,
which
is
not
included
in
the LS-DYNA load curve but defined separately by Youngs’ modulus.
the
LS-DYNA
load
curve
but
defined
separately
by
Youngs’
modulus.
the LS-DYNA
load
curve
but
defined
separately
by
Youngs’
modulus.
The final comparison of the force-displacement curves obtained from testing, and the
The final
final comparison
comparison of
of the
the force-displacement
force-displacement curves
obtained from
and
the
The
from testing,
testing,
and15.
the
simulation
is shown to beexemplary
for the load-casecurves
radialobtained
crush impactor
in Figure
simulation is
is shown
shown to
to beexemplary
beexemplary for
simulation
for the
the load-case
load-case radial
radial crush
crush impactor
impactor in
in Figure
Figure 15.
15.
Figure 15. Force-displacement curves of the cell load-case radial crush impactor.
Figure 15. Force-displacement curves of the cell load-case radial crush impactor.
Figure 15. Force-displacement curves of the cell load-case radial crush impactor.
One can see a good correlation between testing (black) and simulation results, especanbeginning.
see a good Between
correlation
between
and simulation
results,forces
especiallyOne
at the
1 mm
and 5testing
mm of(black)
displacement
the simulated
One
can
see a good
correlation
between
testing
(black) and simulation
results,
especially
at
the
beginning.
Between
1
mm
and
5
mm
of
displacement
the
simulated
forces
are
are higher than measured ones. There are also deviations between the two simulations
cially
at
the
beginning.
Between
1
mm
and
5
mm
of
displacement
the
simulated
forces
are
higher
than measured
There are also
deviations between
using
using different
solversones.
(Abaqus—red,
LS-DYNA—blue).
Thisthe
is two
mostsimulations
likely caused
by
higher
than
measured
ones.
There
are
also
deviations
between
the
two
simulations
using
different
solversin(Abaqus—red,
LS-DYNA—blue).
Thisabove.
is most
likely
caused model
by the was
difthe differences
material formulation,
as mentioned
The
simulation
differentin
solvers
(Abaqus—red,
LS-DYNA—blue).
This The
is most
likely caused
by
thevalidifferences
material
formulation,
as mentioned
above.
simulation
model
was
validated for
four different
load cases
(Table 2). The
final model
is always
a compromise
ferences
in
material
formulation,
as
mentioned
above.
The
simulation
model
was
validated
fortofour
different
load cases.
cases (Table 2). The final model is always a compromise that
that has
work
for all load
dated
for four
different
load cases (Table 2). The final model is always a compromise that
has
toThe
work
for
all
load
cases.
presented model is only validated for the used type of cell under quasistatic
has to
work
for all load cases.
The
presented
is only
validated
the used
type of cell
conconditions.
Cells ofmodel
different
materials
willfor
behave
differently.
Theunder
speedquasistatic
of mechanical
The
presented
model is only validated
for the
used type
of speed
cell under
quasistaticloadconditions.
of different
behave
differently.
The
of mechanical
loadingCells
can also
have an materials
influence will
on cells’
behaviours
[21].
ditions.
Cells
of
different
materials
will
behave
differently.
The
speed
of
mechanical
loading can also have an influence on cells’ behaviours [21].
ing
can also
haveCircuit
an influence
on cells’ behaviours [21].
4. Virtual
Short
Detection
4. Virtual
Short Circuit
The validated
finiteDetection
element simulations (see details in Section 3) of the 18650 cylindri4. Virtual Short Circuit Detection
cal lithium-ion
battery
and
the testing
results of
thedetails
mechanical
cell tests
2)cylinserve
The validated
finite
element
simulations
(see
in Section
3) of (Section
the 18650
validated
finite element
(seeof
details
in Section
3)
ofbe
the
18650
cylinas theThe
basis
for thebattery
creation
of short-circuit
criteria.
These
criteria
should
useable
in
the
drical
lithium-ion
and
thesimulations
testing results
the mechanical
cell
tests
(Section
2)
drical
lithium-ion
battery
and
the
testing
results
of
mechanical
cell
tests
(Section
2)
post-processing
and
have
to
detect
short
circuits
at
the
same
values
of
displacement
as
serve as the basis for the creation of short-circuit criteria. These criteria should be useable
serve as the basis for the creation of short-circuit criteria. These criteria should be useable
Batteries 2021, 7, 79
13 of 26
observed in the physical tests. Table 3 summarizes the values of impactor displacement at
the occurrence of a short circuit for the four used load cases.
Table 3. Impactor displacement at the occurrence of a short circuit for four tested cell-load cases.
Load Case
Impactor Displacement at Short Circuit/mm
axial crush
radial crush
radial crush impactor
three-point bending
5.5
5.6
5.4
6.5
As mentioned in Section 1.1.2, there are several methods for virtual short-circuit
prediction. Most of these are used and tested in the following.
The Mohr–Coulomb criterion was not used. It uses the fracture of the jellyroll, which
was not detected during the tests. The force-drop criterion was not used, because it only
works in a simplified setup, where it is easy to pinpoint and where the force is measured.
Since the model is intended to be usable in complex 3D-loading scenarios e.g., a full-scale
vehicle simulation, this is difficult to realize.
4.1. Strain Based Short Circuit Criteria
The jellyroll, in the cell model, is simulated using solid elements. During postprocessing, strains of each element are analysed for every time step.
The strain-based criteria are tested in two ways, local and global. The local approach
looks at each element individually. Should the quantity chosen for the short-circuit criterion
exceed a certain threshold value, a short circuit is expected. This approach focuses on
areas of high deformation, where ruptures in the physical jellyroll could occur and cause a
short circuit.
The global approach works quite similarly. It calculates the mean value from a chosen
quantity of jellyroll elements and compares it to a threshold value. Should this mean value
exceed the threshold, a short circuit is expected analogously. This approach considers
the overall deformation of the cell, which might cause a short circuit even without high
deformations at one spot.
The tested short-circuit criteria are discussed in the following.
Maximum Principal Strain:
For this criterion, the maximum absolute value of the three principal strains, ε1 , ε2
and ε3 ,
ε MaxPr = MAX (|ε 1 |, |ε 2 |, |ε 3 |)
(2)
is calculated, which results in the maximum principal strain εMaxPr .
Volumetric Strain:
The sum of the three principal strains,
ε Vol = ε 1 + ε 2 + ε 3
(3)
is calculated and gives the volumetric strain.
Von Mises-Equivalent Strain:
For this criterion, equivalent strain is calculated
s
ε Equ =
2
1 2
2
2
2
2
2
∗ ε x + ε y + ε z + ∗ ε xy + ε yz + ε zx ,
3
2
(4)
using the strain values of the stress tensor, εx , εy , εz , εxy , εyz and εzx , gained from simulation.
Principal Strain (2D) and Strain in the Axis Direction:
Batteries 2021, 7, 79
14 of 26
For this criterion, the principal strains are calculated for the two-dimensional case,
based on the two radial directions orthogonal to the cell axis. For these two principal strains,
ε 1,2
εx + εy
=
∓
2
s
εx − εy
2
2
+ ε2xy
(5)
the strain values from the simulation are used.
Three of the four load cases mainly deform the cells in radial directions, whereas, in
the fourth, the cells are deformed mainly in the axial direction. Threshold values working
for the three radial load cases will likely not be reached in the axial case.
The 2D principal strain criterion assesses strain in the directions affected by the radial
load cases. For the axial-crush load case, strain in the axial direction, εz , is taken as an
additional criterion. For this criterion to work, the threshold value should not be reached
in any of the three radial load cases.
4.2. Stress Based Short-Circuit Criteria
For these criteria, during post-processing, the stresses of the jellyroll elements are
analysed for every time step.
The stress-based criteria are tested in two ways, locally and globally. These two
approaches are the same as discussed above for the strain-based short-circuit criteria.
Maximum principal stress:
For this criterion, the maximum absolute value of the three principal stresses, σ1 , σ2
and σ3 ,
σMaxPr = MAX (|σ1 |, |σ2 |, |σ3 |)
(6)
is calculated, the maximum principal stress σMaxPr .
Von Mises equivalent stress:
For this criterion, the equivalent stress σEqu
r
σEqu =
2 + σ2 + σ2
σx2 + σy2 + σz2 − σx ∗ σy − σy ∗ σz − σz ∗ σx + 3 ∗ σxy
zx
yz
(7)
is calculated using the stress values of the stress tensor, σx , σy , σz , σxy , σyz and σzx , gained
from simulation.
4.3. Geometric Short Circuit Criteria
For these criteria, the deformation parameters of the cell are analysed for every time
step. These parameters are in general deduced from nodal displacements. Should such
a deformation parameter exceed a certain threshold value, a short circuit is detected. In
general, nodal positions of the finite element mesh are analysed.
Axial and Radial Geometric Criterion:
For the geometric approach, the problem is split into two parts; the axial geometric
criterion and the radial geometric criterion. This is justified by the fact that the short circuit
is caused by different mechanisms in the axial and radial loading of the cell. In the radial
case, the layers of the jelly roll start rupturing if the load exceeds a certain level. The
ruptured layers then cause a short circuit. In the axial case, the conductive parts connecting
the jellyroll and battery terminals are damaged, thereby causing a short circuit.
The axial geometric criterion is based on the distance between the flat sides at the top
and bottom of the cylindrical cell. Two groups of nodes are defined. One includes all nodes
from the top side, the other includes all nodes of the bottom side (see Figure 16). If caused
by deformation, the distance between any top-node and any bottom-node falls below the
threshold value, a short circuit is detected. The purpose of this criterion is the detection of
a short circuit for axial loading of the battery cell. In order for the criterion to be feasible,
Batteries 2021, 7, x FOR PEER REVIEW
Batteries 2021, 7, 79
15 of 24
15 of 26
detection of a short circuit for axial loading of the battery cell. In order for the criterion to
cases, except
at theexcept
point 15
radial
load cases,
where
a short
circuit
should
be detected
therein.
at
the point
where
a short
circuit
should be
detected therein.
Batteries 2021,
x FOR PEER
REVIEW
the7,feasible,
threshold
value
mustvalue
not bemust
reached
in any
of the
be
the
threshold
not be
reached
inradial
any ofload
the
of 24
detection of a short circuit for axial loading of the battery cell. In order for the criterion to
be feasible, the threshold value must not be reached in any of the radial load cases, except
at the point where a short circuit should be detected therein.
Figure
Figure16.
16.Cell
Cellmodel
modelwith
withthe
thetop
topand
andbottom
bottomnodes
nodesused
usedfor
forthe
theaxial
axialgeometric
geometriccriterion.
criterion.
Figure 16. Cell model with the top and bottom nodes used for the axial geometric criterion.
Theradial
radialgeometric
geometriccriterion
criterionisisbased
basedon
onthe
thedistance
distancebetween
betweenpairs
pairsof
ofnodes
nodeslocated
located
The
The radial
geometric
criterion
is based
onnodes
the distance
between
pairs
of nodes
on
directly
opposite
points
of
the
cell-cylinder
mantle.
All
on
the
cylinder
mantle
are located
on directly
points of the cell-cylinder mantle. All nodes on the cylinder mantle
on directly opposite points of the cell-cylinder mantle. All nodes on the cylinder mantle
used
and,and,
altogether,
10081008
pairspairs
of nodes
are defined.
An example
of such
pair is
shown
are
used
altogether,
of nodes
are defined.
An example
ofasuch
a pair
is
are used and, altogether, 1008 pairs of nodes are defined. An example of such a pair is
in Figure
17.
shown
in Figure
17.
shown in Figure 17.
Figure
An exemplary
pair
of nodes
cell
caseused
used for
for the
criterion.
Figure 17.
An 17.
exemplary
pair of
nodes
on on
thethe
cell
case
theradial
radialgeometric
geometric
criterion.
Figure
the
absolute
nodal
distancebefore
in
millimetres
and after deforFigure 17. An exemplary
nodes
onabsolute
the 17
cellshows
case
used
for the in
radial
geometric
criterion.
Figurepair
17 of
shows
the
nodal
distance
millimetres
and afterbefore
deformation.
mation.
If caused by deformation, the distance between any such pair of nodes falls below the
If caused
by deformation,
the distance
between any
suchand
pairafter
of nodes
falls below
Figurevalue,
17 shows
the
absolute
distance
in millimetres
before
deforthreshold
the
short
circuit is nodal
detected.
The purpose
of this criterion
is the detection
the threshold value, the short circuit is detected. The purpose of this criterion is the detecmation.
of a short circuit for
radial
loading
of the
battery
cell. For
it to
workcell.
it isFor
necessary
that
tion
of a short
circuit
for radial
loading
of the
battery
it to work
it isthe
necessary
If caused
byisdeformation,
the
distance
between
any
such
pair
of
nodes
falls
below
threshold
value
not
reached
in
the
axial-crush
load
case,
except
after
the
point
where
a point
that the threshold value is not reached in the axial-crush load case, except after the
the
threshold
value,
the
short
circuit
is
detected.
The
purpose
of
this
criterion
is
the
detecshort circuit should
be detected
therein.
where
a short circuit
should be detected therein.
tion of a short circuit for radial loading of the battery cell. For it to work it is necessary
5. Results
that
the threshold value is not reached in the axial-crush load case, except after the point
whereIna this
short
circuit the
should
be detected
therein.
chapter,
results
of the analysis
of the different criteria used for the virtual
detection of a short circuit, described in the preceding section, are presented. Every shortcircuit criterion was tested for the two solvers, Abaqus and LS-DYNA, and for the four
mechanical load cases used for testing the battery cells. The result for each such test is the
Batteries 2021, 7, x FOR PEER REVIEW
16 of 25
5. Results
In this chapter, the results of the analysis of the different criteria used for the virtual
16 of 26
detection of a short circuit, described in the preceding section, are presented. Every short‐
circuit criterion was tested for the two solvers, Abaqus and LS‐DYNA, and for the four
mechanical load cases used for testing the battery cells. The result for each such test is the
value
value of
ofthe
theimpactor
impactor displacement
displacement at
at which
which the
the short
short circuit
circuit occurred.
occurred. These
These values
values are
are
compared
to
those
from
testing.
Finally,
to
assess
the
different
short
circuit
criteria,
compared to those from testing. Finally, to assess the different short circuit criteria, two
two
additional
additional values
values are
are analysed.
analysed.
The first value is the maximum deviation in displacement at short circuit between
The first value is the maximum deviation in displacement at short circuit between
testing and simulation of any of the four load cases.
testing and simulation of any of the four load cases.
The second value is the maximum deviation in displacement at short circuit between
The second value is the maximum deviation in displacement at short circuit between
the solvers for any of the four load cases.
the solvers for any of the four load cases.
These values are presented in Table 4. For better visualization, the two values assessing
These values are presented in Table 4. For better visualization, the two values
the criteria are colour coded. With respect to deviations from testing, values up to 1.5 mm
assessing the criteria are colour coded. With respect to deviations from testing, values up
are green, values between 1.5 mm and 2.0 mm are orange and values above 2.0 mm are red.
to 1.5 mm are green, values between 1.5 mm and 2.0 mm are orange and values above 2.0
With respect to deviations between solvers, values up to 0.5 mm are green, values between
mm are red. With respect to deviations between solvers, values up to 0.5 mm are green,
0.5 mm and 1.0 mm are orange and values above 1.0 mm are red.
values between 0.5 mm and 1.0 mm are orange and values above 1.0 mm are red.
Batteries 2021, 7, 79
equivalent stress—global
max. principal strain—local
max. principal strain—global
Abaqus
LS‐DYNA
Abaqus
LS‐DYNA
Abaqus
LS‐DYNA
Abaqus
LS‐DYNA
Abaqus
LS‐DYNA
Abaqus
LS‐DYNA
Abaqus
LS‐DYNA
Abaqus
LS‐DYNA
*
*
4.42
4.01
*
*
*
*
4.14
3.49
3.28
3.36
*
*
5.25
3.16
5.62
5.62
3.57
4.32
5.62
4.23
3.04
3.32
5.46
5.62
5.51
5.72
5.10
3.96
3.57
1.68
3.74
3.83
5.36
5.30
3.78
5.36
5.36
5.36
2.85
2.66
4.90
5.00
2.70
5.36
5.30
1.98
4.56
4.51
4.85
4.37
5.10
6.84
4.51
4.75
3.36
3.36
5.10
4.90
3.00
6.44
4.85
1.92
1.92
1.97
2.08
2.11
1.58
1.42
2.25
2.33
3.12
3.12
2.26
2.18
3.48
1.69
2.08
4.56
Maximum Deviation between Solvers/mm
Deviation from Testing Values/mm
equivalent stress—local
Displacement at SC‐Occurrence
Three‐Point Bending/mm
equivalent strain—global
Displacement at SC‐Occurrence
Radial Crush Impactor/mm
equivalent strain—local
Displacement at SC‐Occurrence
Radial Crush/mm
volumetric strain—global
Displacement at SC‐Occurrence
Axial Crush/mm
volumetric strain—local
FEM Solver Used for Simulation
Short Circuit Criterion
Table 4. Results for virtual short-circuit detection for four mechanical load cases using different criteria.
Table 4. Results for virtual short‐circuit detection for four mechanical load cases using different criteria.
0.09
0.75
1.74
0.24
0.65
0.21
3.44
3.32
Batteries 2021, 7, 79
Batteries 2021, 7, x FOR PEER REVIEW
17 of 26
18 of 25
axial and radial geometric criterion
testing values
4.32
3.28
3.28
3.28
*
*
*
*
5.51
5.51
5.54
5.41
5.46
5.62
5.36
4.66
5.62
3.20
3.36
4.19
4.49
5.65
2.63
2.56
5.25
5.30
3.78
2.81
5.36
4.70
4.51
4.79
5.36
3.04
3.04
5.57
5.30
6.44
3.36
4.05
2.52
6.38
6.53
6.48
Maximum Deviation between Solvers/mm
Abaqus
LS‐DYNA
Abaqus
LS‐DYNA
Abaqus
LS‐DYNA
Abaqus
LS‐DYNA
Abaqus
LS‐DYNA
Deviation from Testing Values/mm
Displacement at SC‐Occurrence
Three‐Point Bending/mm
principal strain 2D—global
Displacement at SC‐Occurrence
Radial Crush Impactor/mm
principal strain 2D—local
Displacement at SC‐Occurrence
Radial Crush/mm
max. principal stress—global
Displacement at SC‐Occurrence
Axial Crush/mm
max. principal stress—local
FEM Solver Used for Simulation
Short Circuit Criterion
Tablefor
4. Cont.
Table 4. Results for virtual short‐circuit detection
four mechanical load cases using different criteria.
3.44
3.44
2.26
2.26
1.58
3.12
2.45
3.96
1.46
1.16
1.04
0.27
3.08
1.53
0.30
* For the axial‐crush load case several values are missing. In these cases, no short circuit occurred, as the values for the
given criterion were by far smaller than for the other three load cases. Therefore, axial crush was excluded, here. We have
refrained from using an additional axial criterion, as was done for the geometric approach, because the results for the
radial tests in these cases were not as good as with the geometric criteria.
The strain criterion in the axial direction (Section 4.1) was omitted, as the analysis of
the 2D
principal
strain criterion
showed
no promising
and
these two
criteria
would
The
strain criterion
in the axial
direction
(Sectionresults
4.1) was
omitted,
as the
analysis
of
have
only
worked
in combination.
the 2D
principal
strain
criterion showed no promising results and these two criteria would
of axial and radial geometric criterion offered the best results for
haveThe
onlycombination
worked in combination.
the short-circuit
measurement,
test results.
In addition,
it worked
for both
The combination
of axial compared
and radialwith
geometric
criterion
offered the
best results
for
FEM
solvers
and
there
was
little
deviation
in
the
results
between
them.
The
used
threshold
the short‐circuit measurement, compared with test results. In addition, it worked for both
values
are: and there was little deviation in the results between them. The used threshold
FEM solvers
The
axial geometric criterion was61.6 mm, which is 94.8% of the original cell length
values are:
for the
Abaqus
and LS-DYNA
solvers.
The axial geometric
criterion
was61.6 mm, which is 94.8% of the original cell length
TheAbaqus
radial geometric
criterion
was a minimal node-pair distance of 14.7 mm (81.7% of
for the
and LS‐DYNA
solvers.
original
diameter)
for
LD-DYNA
and
15.0
mm (83.3%
of original
diameter)
formm
Abaqus.
The radial geometric criterion was
a minimal
node‐pair
distance
of 14.7
(81.7%
of original diameter) for LD‐DYNA and 15.0 mm (83.3% of original diameter) for Abaqus.
6. Conclusions
A finite element model of a cylindrical Li-ion battery cell for two different solvers,
6. Conclusions
validated by physical tests, was presented. Several methods of virtual short-circuit deA finite element model of a cylindrical Li‐ion battery cell for two different solvers,
tection were explored and assessed. Finally, a method using two geometric short-circuit
validated by physical tests, was presented. Several methods of virtual short‐circuit
criteria was developed to produce satisfactory results in predicting short circuits in all
detection were explored and assessed. Finally, a method using two geometric short‐circuit
four load cases, with both solvers. To the authors’ knowledge, no other publication has
criteria was developed to produce satisfactory results in predicting short circuits in all
featured a validated model working with two different FEM solvers, and few publications
four load cases, with both solvers. To the authors’ knowledge, no other publication has
Batteries 2021, 7, 79
18 of 26
have used approaches for both the axial and radial mechanical loading of cylindrical cells.
Raffler et al. [5] published a model based on the beam method that produced very good
results for axial and radial loadings, though a three-point bending load case was not used
there. This load case presents a special loading scenario, combining primarily axial compression and, to a lesser degree, radial compression [3]. Wang et al. [22] achieved good
results for the same four load cases used in the current work. They used detailed layered
simulation model, which, due to calculation time, would probably not be applicable for
large-scale simulations.
The current battery model with short circuit prediction can now be used in the simulation of larger assemblies, such as battery modules, car battery packs or even complete
vehicle simulations. For example, it is possible to simulate a full vehicle crash and gain
information on which of the individual battery cells installed in the car might suffer a short
circuit due to mechanical abuse during the crash. This enables the crashworthy design and
integration of battery packs in vehicles.
Author Contributions: Conceptualization, C.B. and P.D.; finite element modelling methodology, K.J.,
C.B. and M.M.; software, K.J.; validation, K.J. and C.B.; formal analysis, C.B. and K.J.; investigation,
C.B. and K.J.; data curation, K.J.; writing—original draft preparation, K.J. and K.I.; writing—review
and editing, C.B., K.J., P.D. and K.I.; visualization, K.J.; supervision, C.B.; project administration, C.B.;
funding acquisition, C.B. All authors have read and agreed to the published version of the manuscript.
Funding: The publication was written at VIRTUAL VEHICLE Research GmbH in Graz and is
partially funded by the COMET K2—Competence Centers for Excellent Technologies Program of the
Federal Ministry for Transport, Innovation and Technology (BMVIT), the Federal Ministry for Digital
and Economic Affairs (BMDW), the Austrian Research Promotion Agency (FFG), the Province of
Styria and the Styrian Business Promotion Agency (SFG). This work was conducted as part of the
research project SafeBattery. The K-project SafeBattery (FFG project number 863073) is funded by the
BMVIT, BMDW, Austria and Land Steiermark within the framework of the COMET—Competence
Centers for Excellent Technologies program. The COMET program is administered by the FFG.
Acknowledgments: The authors thank the consortium members of the SafeBattery project for their
valuable input to this work. The Authors also thank Jonas Pucher for his contribution in coding the
post-processing tool that was used for the virtual short-circuit prediction analysis.
Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design
of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript, or
in the decision to publish the results.
Batteries 2021, 7, 79
19 of 26
Appendix A
L. Greve et al.,
2012 [10]
cylindrical
nickel–cobalt
oxide (NCA)
cell, (GAIA,
HP 602030
NCA-45
Ah/162 Wh)
T. Wierzbicki, E.
Sahraei 2013 [4]
cylindrical
cell 18650
x
x
x
x
x
x
x
x
FE-Platform
SOC
Others
Axial Compression
Three-Point Bending
Indentation Hemispherical Punch
Radial Compression Flat Plates
x
10%
LS-DYNA
0%
virtual
performance
solution
(VPS)
10%
LS-DYNA
Results
cylindrical
cell 18650
Model Scale
E. Sahraei et al.,
2012 [3]
Lateral Indentation Cylindrical Rod
Cell Type
Publications
Table A1. Summary of the publications regarding mechanical testing of cylindrical cell 18650.
meso-scale
A very good
correlation has been
obtained between
the test results and
numerical
simulation.
macro-scale
A very good
correlation was
obtained between
the test results and
numerical
simulation.
RVE
Good agreement
between simulation
and corresponding
tests
The jellyroll failure
began at about
4–5 mm of
displacement.
Y. Xia et al., 2014
[17]
cylindrical
cell 18650
J. Xu et al., 2015
[11]
cylindrical
nickel–cobalt
oxide (NCA)
cell, (GAIA,
HP 602030
NCA-45
Ah/162 Wh)
x
–
LS-DYNA
meso-scale
The outer shell
developed an
axisymmetric fold.
No internal failure
point in the jellyroll.
After 14 mm of
deformation,
jellyroll elements
started to fail,
ultimately forming
two longitudinal
cracks at a 15-mm
punch intrusion
x
x
x
ABAQUS
meso-scale
A good agreement
between experiment
and simulation
results
Batteries 2021, 7, 79
20 of 26
x
W. Wang et al.,
2018 [25]
cylindrical
cell 18650
x
x
L. Wang et al.,
2019 [22]
cylindrical
cell 18650
(NCA)
x
x
M. Sheikh et al.,
2020 [26]
cylindrical
cell 18650
Samsung
2200 mAh
x
x
x
x
x
x
Results
x
x
Model Scale
cylindrical
cell 18650
x
FE-Platform
B. Liu et al., 2018
[12]
x
SOC
cylindrical
cell 18650
Others
L. Tang et al.,
2017 [24]
Axial Compression
cylindrical
cell 18650
Three-Point Bending
J. Zhu et al., 2016
[23]
Indentation Hemispherical Punch
Cell Type
Radial Compression Flat Plates
Publications
Lateral Indentation Cylindrical Rod
Table A1. Cont.
0%
ABAQUS/
Explicit
meso-scale
Good agreement
between tests and
simulation.
–
ABAQUS/
Explicit
macroscale
Good agreement
between tests and
simulation.
ABAQUS
meso-scale
Good agreement
between tests and
simulation.
different
SOC
LSDYNA
meso-scale
Good agreement
between tests and
simulation.
0%
LSDYNA
meso-scale
Good agreement
between tests and
simulation.
meso-scale
The model is
capable of
capturing cell
mechanical
response.
different
SOC
(0%, 25%,
50% and
75%)
LSDYNA
Batteries 2021, 7, 79
21 of 26
L. Greve et al.,
2012 [10]
cylindrical
nickel–cobalt
oxide (NCA)
cell, (GAIA, HP
602030 NCA-45
Ah/162 Wh)
T. Wierzbicki, E.
Sahraei 2013 [4]
cylindrical cell
18650
J. Xu et al., 2015
[11]
cylindrical
nickel–cobalt
oxide (NCA)
cell, (GAIA, HP
602030 NCA-45
Ah/162 Wh)
J. Zhu et al.,
2016 [23]
x
x
x
x
x
x
x
force peak
A good correlation
between the test and
simulation values was
obtained
For each load
case the output
voltage, force,
displacement,
and temperature
versus time were
recorded.
x
stress state-based
criteria
SC predictions were in
good agreement with the
experimental
observations
SC prediction
based on the drop
of voltage which
coincides with the
drop of force
A good correlation
between the test and
simulation values was
obtained
unified strength
theory (UST)
A good correlation
between the test and
simulation values was
obtained
The cause of SC
during axial
compression was
clarified based on
the understanding
and analysis of the
mechanical
behaviour.
A good agreement
between tests and
simulation.
x
x
cylindrical cell
18650
Short Circuit Criterion
Axial Compression
Three-Point Bending
Indentation Hemispherical Punch
Radial Compression Flat Plates
x
Remarks
cylindrical cell
18650
Results
E. Sahraei et al.,
2012 [3]
Lateral Indentationby a Cylindrical Rod
Cell Type
Publications
Table A2. Summary of the publications regarding the short circuit prediction due to mechanical deformations.
x
x
global radial
deformation of the
cell model
M. Raffler et al.,
2017 [5]
cylindrical cell
18650
x
x
x
global axial
deformation of the
positive pole of the
cell model
A good correlation
between the short circuit
deformation of the cell
and the strain values of
the simulation model for
the different load cases
was found.
Batteries 2021, 7, 79
22 of 26
L. Wang et al.,
2019 [22]
M. Sheikh et al.,
2020 [26]
cylindrical cell
18650
(NCA)
cylindrical cell
18650
Samsung 2200
mAh
x
x
x
x
equivalent plastic
strain
A good agreement
between simulation and
experimental results.
stress state-based
criteria
Suitable for the four
loading conditions
Suitable for
predicting minor
and major
internal short
circuits
strain state-based
criteria
Good prediction of the
SC except for minor
SC-behaviour in bending
case.
Only suitable for
major internal
short circuits
displacement at SC,
mean temperature
at SC and mean
maximum
temperaturechange
criterion
The simulation shows
that quasi-static loading
is suitable to predict SC.
x
x
Remarks
Results
x
Short Circuit Criterion
Radial Compression Flat Plates
x
Axial Compression
Lateral Indentationby a Cylindrical Rod
cylindrical cell
18650
Three-Point Bending
Cell Type
B. Liu et al.,
2018 [12]
Indentation Hemispherical Punch
Publications
Table A2. Cont.
Appendix B
The following figures show additional results of the tests described in Section 2.
Figure A1 shows the test result for the cell-case tests for the axial-crush load. The
results show good repeatability up to a displacement value of 10 mm.
Figure A2 shows the test result for the cell case tests for the load radial crush. The
results show good repeatability over the entire displacement interval.
Batteries 2021, 7, x FOR PEER REVIEW
Batteries 2021, 7, 79
21 of 24
Figure A1 shows the test result for the cell-case tests for the axial-crush load. The
results show good repeatability up to a displacement value of 10 mm.
23 of 26
Figure A1 shows the test result for the cell-case tests for the axial-crush load. The
results show good repeatability up to a displacement value of 10 mm.
Figure A1. Results of the cell-case test for the load-case axial crush (A) and cell-case specimen after testing (B).
Figure A2 shows the test result for the cell case tests for the load radial crush. The
results show good repeatability over the entire displacement interval.
Figure A1. Results of the cell-case test for the load-case axial crush (A) and cell-case specimen after testing (B).
Figure A2 shows the test result for the cell case tests for the load radial crush. The
results show good repeatability over the entire displacement interval.
Figure A2.
Results of
of the
the cell-case
cell-case test
test for
for the
Figure
A2. Results
the load-case
load-case radial
radial crush
crush (A)
(A) and
and cell-case
cell-case specimen
specimen after
after testing
testing (B).
(B).
Figure A3
A3 shows
shows the
the test
test result
result for
for 0%
0% SOC
Figure
SOC and
and for
for 0%
0% SOC
SOC for
for the
the load
load case
case axial
axial
crush. The measurement of voltage was not possible due to the given test set-up (no access
to cell
cell contacts).
contacts). In
In literature,
literature, it
it has
has been
been noted,
noted, that
that there
there is
is aa correlation
correlation between
between the
the force
force
to
A3 shows
0% appears
SOC andatfor
0% SOC
for of
thedeformation
load case axial
dropFigure
and short
circuit the
[3]. test
Theresult
short for
circuit
a similar
level
drop and short circuit [3]. The short circuit appears at a similar level of deformation for
for
crush.
The measurement
of voltage was not possible due to the given test set-up (no access
both states
of charge.
both states of charge.
to cell contacts). In literature, it has been noted, that there is a correlation between the force
drop and short circuit [3]. The short circuit appears at a similar level of deformation for
both states of charge.
Figure A2. Results of the
cell-case
for the load-case
radial was
crushnot
(A)possible
and cell-case
after
testing
(B).(no access
crush.
Thetest
measurement
of voltage
due specimen
to the given
test
set-up
Batteries 2021, 7, 79
Batteries 2021, 7, x FOR PEER REVIEW
24 of 26
22 of 24
Figure A3.
A3. Axial
Axial crush
crush C1
C1 (SOC
(SOC comparison)
comparison) force
force over
over displacement
displacement (A)
and cell
Figure
(A) and
cell specimen
specimen after
after testing
testing (B).
(B).
Figure A4 shows the test result for 0% SOC and for 0% SOC for the load-case radial
Figure A4 shows the test result for 0% SOC and for 0% SOC for the load-case radial
crush. During the radial crush tests, forces exceeded the maximum of the measurement
crush. During the radial crush tests, forces exceeded the maximum of the measurement
signal. A short circuit was still reached.
signal. A short circuit was still reached.
Figure A4.
A4. Radial
Radial crush
crush C1
C1 (SOC
(SOC comparison)
comparison) force
force over
over displacement
displacement (A)
and cell
Figure
(A) and
cell specimen
specimen after
after testing
testing (B).
(B).
Figure A5
SOC
forfor
the
three-point-bending
Figure
A5 shows
showsthe
thetest
testresult
resultfor
for0%
0%SOC
SOCand
andfor
for0%
0%
SOC
the
three-point-bendload
case.
Possible
reasons
for
the
first
drop
in
force
are
the
cracking
of the
cellcell
case
or
ing load case . Possible reasons for the first drop in force are the cracking
of the
case
a defect/cracking inside the cell, without causing a short circuit. The second force drop
or a defect/cracking inside the cell, without causing a short circuit. The second force drop
coincides with the measured short circuit.
coincides with the measured short circuit.
Batteries 2021, 7, 79
Batteries 2021, 7, x FOR PEER REVIEW
25 of 26
23 of 24
Figure A5. Three-point
Three-point bending C1 (SOC comparison) force over displacement (A) and cell specimen after testing (B).
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