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Interpretation of Simultaneous Mechanical-Electrical-Thermal Failure in a Lithium-Ion Battery Module

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Lithium-ion batteries are currently the state-of-the-art power sources for electric vehicles, and their safety behavior when subjected to abuse, such as a mechanical impact, is of critical concern. A coupled mechanical-electrical-thermal model for simulating the behavior of a lithium-ion battery under a mechanical crush has been developed. We present a series of production-quality visualizations to illustrate the complex mechanical and electrical interactions in this model.
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Interpretation of Simultaneous
Mechanical
-Electrical-Thermal
Failure in a Lithium
-Ion Battery
Module
Preprint
Chao Zhang
, Shriram Santhanagopalan,
Mark J.
Stock, Nicholas Brunhart-Lupo,
and
Kenny Gruchalla
National Renewable Energy Laboratory
P
resented at
SC16: International Conference for High Performance
Computing, Networking, Storage and Analysis
Salt Lake City, Utah
November 13
18, 2016
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16
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Interpretation of Simultaneous Mechanical-Electrical-Thermal Failure in a
Lithium-Ion Battery Module
Chao Zhang1, Shriram Santhanagopalan2, Mark J. Stock1, Nicholas Brunhart-Lupo1, Kenny Gruchalla1
1Computational Science Center
2Transportation and Hydrogen Systems Center
National Renewable Energy Laboratory
Golden, CO
chao.zhang@nrel.gov, shriram.santhanagopalan@nrel.gov, mark.stock@nrel.gov,
nicholas.brunhart-lupo@nrel.gov, kenny.gruchalla@nrel.gov
Abstract—Lithium-ion batteries are currently the state-of-
the-art power sources for electric vehicles, and their safety be-
havior when subjected to abuse, such as a mechanical impact, is
of critical concern. A coupled mechanical-electrical-thermal
model for simulating the behavior of a lithium-ion battery under
a mechanical crush has been developed. We present a series of
production-quality visualizations to illustrate the complex me-
chanical and electrical interactions in this model.
KeywordsLithium Battery, Mechanical Impact, Short Circuit
1. Introduction
The safety behavior of lithium-ion batteries (LIBs) subject-
ed to an external mechanical crush is a critical concern when
employing these batteries in electrical vehicle applications. The
physical phenomena occurring in LIBs are very complicated
and take place in different time and length scales (particle,
electrode, cell and pack), including electro-chemical reactions
at the porous active materials, electrons moving across current
collectors, heat generation due to charge/discharge, chemical
reactions at the interface between the electrolyte and the
electrode, mechanical deformation under external crush, and
most importantly, the coupling effect among these multi-
physics responses. Computational models are an ideal way to
study interactions across these multiple domains and provide
insights to the design of safer LIBs.
Recently, we presented the first coupled mechanical-
electrical-thermal model for simulating short circuits induced
by a mechanical crush and identified the interaction of
mechanical failure and consequential electrical-thermal
response [1,2]. A simultaneous coupling approach on a
representative sandwich (RS) was developed, which predicts
the simultaneous evolution of electrical and thermal responses
associated with mechanical deformation for a single battery
cell [2].
Previous models reported in the literature focus exclusively
on the mechanical response at the cell-level [3-6].
Comparatively fewer studies have examined module-level or
larger battery hardware, which involves thermal propagation
following the formation of internal short circuits [7]. Recently,
Marcicki et al. [7] presented a new method for measuring fault
currents and described a more complete picture of module-
level failure during an abusive crush. In this work, we extend
our approach for modeling the mechanical-electrical failure
behavior of a lithium-ion battery module, which contains 20
battery cells connected in parallel. While the evaluation of me-
chanical failure is straightforward and can be quantified using
the stress/strain response or other failure parameters, the
initiation of short circuit involves a significant change in the
electrical current (an increase of 103~105 times) and a
continuous change in the electrical conductivity of the different
cell components over 2-3 orders of magnitude during the
propagation of short circuit.
The differences in the species flux due to the differences in
material properties on either side of the interface and an expo-
nential dependence of the reaction rates on the local over po-
tential further limit the interpretation of the results. For in-
stance, identification of the onset location of short circuit in-
volves isolation of the elements across the interface where the
mechanical failure threshold has been met, followed by identi-
fication of the local electrical resistance of the individual com-
ponents at the interface. The process will be further
complicated with the introduction of multiple cells connected
in parallel within one module. In this case the propagation of
electrical short circuit current resulting from mechanical failure
across different battery cells and the combined effect of short
circuit locations distributed across multiple cells are too com-
plicated to interpret using traditional tools available for data
processing. To help tease apart this complexity, a series of
production-quality visualizations were produced to illustrate
different aspects of the simulation.
2. Modeling & Simulation
The lithium-ion battery studied in this work is comprised of
15 Ah pouch cells with a nominal voltage of 3.65 V, and is
fully charged to 4.15 V prior to each test. The pouch cells have
an in-plane dimension of 226 mm x 164 mm and a thickness of
5.4 mm. Each cell contains 16 cathode layers and 17 anode
layers, stacked periodically and electrically isolated by poly-
meric separator layers. Each of these layers range in thickness
from 8 μm to 120 μm. Modeling the individual layers is
computationally costly. However, predicting a short circuit
involves modeling local damage across each of the individual
components (separators, collectors and active materials).
2
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Figure 1: Cross-sectional view of a pouch cell and schematic of a
representative sandwich (RS): the pouch cell is represented by a sin-
gle RS which represents the proportional thickness of each individual
battery component.
In this work, we employ a representative sandwich (RS)
model (shown in Figures 1 and 2) which we previously
developed [2] to explicitly model each individual component
without loss of computational efficiency or accuracy.
2.1 Coupled mechanical-electrical model
The coupled mechanical-electrical model is built in the
commercial finite element software LS-DYNA [8] using
modules available by default: solid mechanics solver and
electromagnetic (EM) solver. The basic equations for these two
solvers are listed below. The mechanical solver is used to solve
for deformation and predict failure of a structure suffering
external or internal loading conditions. The explicit mechanical
solver seeks a solution to the momentum conservation equation
(1)
where σij denotes components of stress, ui denotes components
of displacement, ρ is the density, fi is the body force density
and t is time. The subscript on σij, j denotes covariant
differentiation, similarly, ui,tt denotes acceleration.
The LS-DYNA EM solver employs the eddy current
approximation [9] which assumes a divergence free current
density and no charge accumulation. Two equations
constituting the system response are solved:
(2)
(3)
where magnetic vector potential and electric scalar
potential ϕ are two unknowns to be solved; κ is the electrical
conductivity, μ is the magnetic permeability and is the
source current density. In LS-DYNA, the mechanical and EM
solvers are fully coupled with each other. Details of the
coupling methodology were presented earlier [2]. The two
solvers have distinct time steps, and generally the mechanical
time step is a lot smaller than the EM time step, in keeping
with the time constants for the relevant physics. At each
mechanical time step, the EM field values are calculated by
linear interpolation.
Figure 2: 3D expanded view of several of the battery module’s layers
and components.
2.2 Mechanical-electrical failure
The objective of this work is to predict the structural
fracture-induced electrical short-circuit of a lithium-ion battery
under an external impact load. Proper failure criteria and
failure parameters should be implemented and defined to
enable this capability.
In this work, a maximum tensile failure criterion was
implemented and the Honeycomb Material Model in LS-
DYNA was utilized to simulate separator failure. The tensile
failure strain is determined as 0.29 based on previous
parametric studies on the failure of a single battery cell sub-
jected to indentation [2]. The electrical contact is defined using
a distance-based criterion, which implies that electrical contact
between two parts initiates when the distance between them is
below a certain threshold value dc. This threshold value is set
to 0.039 mm based on our earlier work [2].
Figure 3: ParaView OSPRay rendered view of the external geometry
of the battery model with impactor for a 20-cell lithium-ion battery
module (left: before impact, right: after impact).
tt
ii
j
ij
u
f
,,
ρρσ
=+
=
+×
×
+
s
jA
t
A
ϕ
κ
µ
κ
)
1
(
3
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Figure 4: ParaView OSPRay rendered view of the internal geometry
of the battery model with impactor for a 20-cell lithium-ion battery
module (left: before impact, right: after impact).
2.3 Numerical implementation
Twenty battery cells are connected in parallel using a bus
bar. Once short circuit initiates within one of these cells, cur-
rent from the other cells flows across the bus bar discharging
multiple cells across the short circuit resistance, resulting in
propagation of the thermal and electrical failure. Each battery
cell model was meshed using solid elements, with 2 elements
through the thickness (z-direction) of each layer, 50 elements
along the length (x-direction) and 50 elements through the
width (y-direction) resulting a total of 25000 elements per cell
for the RS model. The external frames and panels of the battery
module are meshed with an average element size of 3 mm. The
impactor is a cylindrical platen of 150 mm diameter, and is
modeled as a rigid cylinder. There are a total of 745,304
elements in the finite element model.
For the impact simulation, an initial velocity 6.3 m/s,
corresponding to a drop velocity from 2 m height, is assigned
to the impactor. Figures 3 and 4 show the external and internal
geometries before and after the impact. The degrees of freedom
for the back panel are fixed to represent the constraints on the
battery module. Contacts are defined between every two sets of
components to avoid deformation-induced penetration. The
porous active materials and separator are treated as
homogeneous solid materials. The current collectors, tabs, bus
bar, external frames, and panels are modeled using a
computational representation exhibiting isotropic-hardening
plasticity. The electrical properties of all components are
considered to be isotropic. All input parameters are listed in
[2].
The numerical model was solved on the High Performance
Computing system, Peregrine [10] at the National Renewable
Energy Laboratory (NREL). The time step for the mechanical
part is 1×10-8 s, and that for the EM part is 1×10-5 s. The
computational time to simulate 3 ms of the impact test is about
34 hours using 60 large-memory (256 GB) 16-core nodes.
3. Visualization
The comprensive visualization of these data is a challenging
problem. The coupling of mechanical, electrical, and thermal
physical phenomena produce a highly multivariate collection
of data on a variety of components, many of which are
encapsulated or otherwise occluded by other components.
Futhermore, the electrical conductivity of different components
can vary by orders of magnitude. For example, the conductivity
across the cathode active material is as low as 100 S/m, where-
as that across the tabs is 1e7 S/m. The vast differences in
thickness of the different components (from a few microns to
several inches) only compound the interpretation of the flux
evolution. As a result, during mechanical crush, the current
density reaches 300 A/m2 on the surface the active anode and
cathode at the location of the short circuits, but at the same
time the current density exceeds 25,000 A/m2 on the battery
tabs. To help tease apart these complex interactions, a series of
production-quality visualizations were produced to illustrate
different aspects of the simulation, isolating components with
similar electrical conductivty and taking a variety of exploded
and clipped views.
The production-quality visualizations were rendered in
Blender [11] and ParaView [12], with geometry and simulation
data exported using LS-PrePost. LS-PrePost, the pre- and post-
processor from LSTC, was used primarily to process the binary
LS-DYNA output into formats that ParaView could read in
bulk. Custom Perl scripts generated macro files, which were
processed by LS-PrePlot in batch. The exterior and interior
geometry animations were generated from sets of STL files: one
for each of 12 parts at each of 152 time steps. ParaView read
the set of 1824 STL files, and was able to export animations
using OSPRay rendering. OSPRay is a CPU only raytracer
built on top of Intel's Embree [13], which provides superscalar-
accelerated CPU raytracing kernels. Our 16-core workstations
took 2-15 seconds to create each frame at Full HD resolution
with multiple ambient rays and multiple rays per pixel.
Visualizing the direction and magnitude of the local elec-
tric current densities across the different components of the
battery module is the most tangible approach to studying fail-
ure propagation within the module. To visualize the data field
on components, we used LS-PrePlot macro files to set up the
variables, elements, and ranges, and then write a VRML2 file
with color information for each time step. These files were
converted to PLY format via command-line MeshLab
(meshlabserver) [14], which retains the color infor-
mation. Each frame in these clips was rendered from a Para-
View Python script using pvbatch. In this script, the PLY file
is read, several filters applied, including the Calculator filter to
convert the color value back into a scalar or vector, and ulti-
mately visualized as a color texture or 3D vector glyphs using
ParaView's built-in OSPRay renderer.
The current density distribution on the surface of the ac-
tive anodes and cathodes in the plane of the mechanical
crush was of particular interest, as this was a direct represen-
tation of internal short circuits. To visualize the in-plane
current density on the surface of the anodes and cathodes, we
produced an illumination-based visualization using Blend-
er’s Cycles rendering system with a surface light emission
shader (see Figure 5). We once again used the exported
VMRL2 geometry from LS-PrePlot, which provided the
shells of the simulation meshes with the x-component of cur-
rent density encoded into the vertex color of that geometry.
4
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Figure 5: Blender rendered exploded view of the in-plane current
density distribution on the surface of the active anode and cathode,
illustrating the locations of the short circuit.
The color of the emitted light was provided by simulated
blackbody radiation; the current density was mapped to the
range of 0 to 14,000° K, which gives a strong blue-white hue
at the maximum. The strength of this emission was also con-
trolled by current density, c. By normalizing the density into
the range [0,1] (that is, the absolute value of the current densi-
ty as divided by its maximum), the irradiance (W/m2) is given
as the quantity (c + 1)5. To marginalize regions that do not
experience high current density, we use the normalized current
density to mediate (by linear mix) between this emission
shader and a translucent bidirectional scattering distribution
function. Frames were rendered on a visualization server
equipped with 3 Nvidia K6000 GPUs, using 576 samples per
pixel.
4. Discussion
In the absence of an external electrical load across
the busbar, there should be no internal in-plane current. How-
ever, during an external crush one or more of the internal cell
components reaches or exceeds the mechanical failure criteria
resulting in a drop in electrical resistance and initiation of al-
ternate pathways for the electric current to flow from the posi-
tive to the negative electrodes. Of these numerous pathways,
the evolution of an electrical short-circuit across specific sets
of components, is determined by the physical proximity be-
tween the energized layers, the rate of decrease of electrical
resistance in the layer across as well as the existence of con-
duction pathways far away from the local element subjected to
mechanical failure. The simultaneous visualization of multi-
ple physical variables of interest, such as the components of
the von Mises stress together with the local current density
distribution enabled accurate determination not only the loca-
tion where mechanical failure or short-circuit originates, but
also the mechanism of failure propagation. For instance, on
Figures 3 and 4, we see that the structural integrity provided
by the end-plates significantly reduces the mechanical impact
on the cells’ internal components; however, from Figure 5, it
is obvious that electrical short-circuits happening in the cells
farthest from the impactor are primarily due to the mechanical
resistance of the end-plates located right next to these cells.
Without a simultaneous visualization of the entire
module’s multi-physics response, it would have been impossi-
ble to track the propagation of a secondary set of failure
events that originate from the rear end of the module, as a re-
sult of packaging. Such results have far-reaching implications
for design of battery packs in this example, one would con-
sider the mechanical properties of packaging between the end-
plates and the cells, in addition to the separation between indi-
vidual cells.
Acknowledgments
The Computer Aided Engineering for Batteries (CAEBAT)
project of the Vehicle Technologies Office, Office of Energy
Efficiency and Renewable Energy, U.S. Department of Energy,
under contract number WBS1.1.2.406, supported this study.
The research was performed using computational resources
sponsored by the Department of Energy's Office of Energy
Efficiency and Renewable Energy and located at the National
Renewable Energy Laboratory.
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... In a review of mechanical modelling of lithium-ion batteries, Zhu identified aspects of mechanical behaviour inherent to lithium-ion cells that should be represented by accurate homogenized material models that included [10]: the pressure dependence of the compression stiffness of porous layers, the poromechanics of the electrolyte-filled porous structure of the jellyroll, anisotropy of individual layers, plasticity, and crack propagation. Despite the complexity of multi-physics in the jellyroll [11][12][13], a notable consensus has arisen within a growing body of research that structural properties can be adequately approximated in solid mechanical terms for the practical finite element simulation of lithium-ion cells [6,[14][15][16][17][18][19]. Due to the common motivation of simulating automotive crash events, research has been predominantly concerned with bending and compression deformation. ...
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