Novel Method for the Three-Dimensional Simulation of Mechanical

Ageing of Battery Modules

Tolga Bozalp

, Muhammad Ammad Raza Siddiqui

, Holger Opfer

and Thomas Vietor

Volkswagen AG, Berlinger Ring 2, 38440 Wolfsburg, Germany

Technische Universität Braunschweig, Institute for Engineering Design,

Hermann-Blenk-Straße 42, 38108 Braunschweig, Germany

Keywords: Battery Module, Simulation, Mechanical Ageing, Swelling, Pouch Cell, Cycle Life, Multiscale Simulation,

Lithium-ion.

Abstract: This study introduces a novel method for modelling the mechanical ageing behavior of battery modules over

lifetime, based on a simplified, mathematical approach. The focus is placed on the force displacement

behavior of battery modules due to the swelling of its cells in the course of electrochemical ageing. In the first

step, the development of a proper modelling method is conducted, before the implementation of the single-

domain model is carried out. Multiple size scales are included in this model, since cell and battery module

level are considered. The model implementation is realized with two different approaches for examination of

simulation trade-offs regarding accuracy and computing time. In the first approach, the module is modelled

using the Finite-Element-Analysis (FEA) with a high number of elements. In an alternative, more simplified

approach, the module model in form of a mathematical, analogous model is implemented with a significantly

fewer number of elements. In both cases, the model layout is similar. Finally, both the approaches are

validated with experimental measurements and compared regarding accuracy and computing time, amongst

other parameter.

1 INTRODUCTION

The Volkswagen Group is committed to the Paris

Agreement and is determined to be climate-neutral

until 2050 (Mortsiefer et al., 2019). The agreement

was signed in 2015 by the world community and

supports the containment of anthropogenic

greenhouse gas emissions and fight climate change

(Bundesministerium für Umwelt, Naturschutz und

nukleare Sicherheit, 2017). A high market share of

battery-powered electric vehicles (BEV) has the

potential to make a significant contribution to this

agreement. A changed and more environmentally

conscious customer behavior has even more lifted this

issue and can be observed by the steadily rising

number of new vehicle registrations of BEVs

(Kraftfahrt-Bundesamt, 2020).

The motives for acquiring a battery-powered

electric vehicle are diverse. In contrast to

conventional vehicles with an internal combustion

engine (ICEV), the benefits of BEVs for their

immediate environment are enormous. In addition to

being able to drive locally emission-free

(Holstenkamp & Radtke, 2018) and having an at least

twice as high well-to-wheel efficiency, there are

numerous more benefits to add (Doppelbauer, 2020).

Then again, BEVs must increase their

optimization potentials to be able to compete with

conventional vehicles. Even though BEVs shorten the

gap, ICEVs still lead in multiple disciplines like

driving distance and acquisition costs (Frenz, 2019).

Special attention must be paid to the high-voltage

battery system of a BEV, since it is the costliest

component of its power train (Frenz, 2019; Sterner &

Stadler, 2017). A common assembly of a battery

system is portrayed by the modular composition of it.

Here, lithium-ion battery cells are electrically

connected and integrated into a housing to form a

battery module (Dörnhöfer, 2019; Korthauer, 2013).

The integration of the battery module into a battery

system takes place in the next step (Dörnhöfer, 2019;

Korthauer, 2013). Due to the electrochemical

degradation of the built-in battery cells over lifetime,

they experience changes not only on their

electrochemical but also on their mechanical level

(Broussely et al., 2005; Cannarella & Arnold, 2014;

386

Bozalp, T., Siddiqui, M., Opfer, H. and Vietor, T.

Novel Method for the Three-Dimensional Simulation of Mechanical Ageing of Battery Modules.

DOI: 10.5220/0010572703860393

In Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2021), pages 386-393

ISBN: 978-989-758-528-9

Kampker et al., 2018; Korthauer, 2013; Sterner &

Stadler, 2017). In addition to a continuously

decreasing capacity and an increasing internal

resistance, the ageing of the cells is also expressed

through thickness increase, involving a

corresponding swelling force over lifetime (Bitzer &

Gruhle, 2014; Cannarella & Arnold, 2014;

Grimsmann et al., 2017; Korthauer, 2013; Li et al.,

2020; Sterner & Stadler, 2017). As a result, the

swelling of the battery cells is transmitted on to

module level. It has been shown by using experiments

and simulations with a simplified module setup that

the module swells while overcharging its cells (Jeon

et al., 2007). In the process, it was possible to measure

the deformations of the module endplate over time

(Jeon et al., 2007). Therefore, it can be reasoned that

the swelling of the cells due to their electrochemical

degradation will also lead to significant deformations

on module level. It has also been depicted by

elaborate and time-consuming FEA-simulations that

this behavior over lifetime can be expected (Choi et

al., 2018). When integrating the module into a battery

system, e.g. by fixing it with screws, its ageing

behavior with changing dimensions over lifetime sets

a relevant challenge. In order to effectively and safely

design a battery system with a modular composition,

the swelling behavior of its modules has to be known

in advance.

Consequently, an analysis on the mechanical

ageing behavior of battery modules is necessary for

prevention of integration problems. Due to the time-

consuming and costly testing of battery module

swelling behavior, the benefits of a simulation model

are obvious. In this study, a novel method for

simulating the spatially resolved mechanical ageing

behavior of battery modules of multiple size scales

over lifetime is introduced, which is based on a

simplified, mathematical approach. It is for the first

time that a mechanical ageing model for modules is

also validated against experimental data, according to

the best knowledge of the authors. The model is built

for a module consisting of lithium-ion pouch cells.

2 METHOD DESCRIPTION

Since this study solely focuses on the mechanical

behavior of battery modules, single domain

modelling is applied. In addition, a multi-scale

approach is chosen for the model, because it is also

supposed to make spatially resolved predictions about

swelling and displacement at cell and module level.

While the smallest scale in the model is at component

level, represented by cells and pads for example, the

largest scale is the battery module.

The key aspect of the model is a deformation

analysis of the module and all its components over

lifetime, caused by swelling of the built-in cells due

to their electrochemical degradation. The developed

method for simulation of the mechanical ageing

behavior of battery modules contains multiple steps,

which need to be conducted in the order specified

(Figure 1). In the first step, a three-dimensional (3D)

model of the examined battery module is built in a

corresponding simulation program and discretized

into finite elements. The model includes all

connections and components of the module, like cells

and cushion pads, and arranges them like in the real

module assembly. Afterwards, components and

connections are calibrated and parameterized

according to their real material behavior. This

includes the specification of material properties like

young’s modulus or even force-displacement curves

of applied components. In the third step, a cell

swelling model as a function of cycle dependent

volume increase per discretized finite element is built,

based on experimental lifetime measurements. The

swelling model of the cell is then implemented for

each cell in the module model. After the set-up of the

model is completed, the simulation of the mechanical

ageing behavior of the module is executed in the last

step. In this process, swelling, displacement and

mechanical stress of the cells and other components

is spatially resolved simulated, resulting in a

deformation and displacement of the module

endplates.

Figure 1: Schematic representation of the simulation

method for swelling prediction of battery modules.

Novel Method for the Three-Dimensional Simulation of Mechanical Ageing of Battery Modules

387

3 MODEL DEVELOPMENT

A main issue that must be considered in the

development of simulation models is the conflict of

their accuracy and computing time. Complex models

with a high number of elements promise accurate

results, however they also bring a high computing

time with them. Simplified simulation models with a

significantly fewer number of elements, on the other

hand, execute quickly, but may lack in accuracy.

Another aspect that is equally important as accuracy

and computing time of the simulation model is the

time spent for building a model configuration as well

as its design flexibility. The examination of this issue

represents a further priority of this study next to the

previously described method.

In the light of the above mentioned aspects, the

development of the model according to the described

method is realized with two different approaches. The

first approach focuses on a complex simulation of the

battery module with a high resolution and number of

elements. For this case, a commercial FEA software

is used. In an alternative, more simplified approach,

the method is realized by a mathematical, analogous

model, which is based on a reduced set of mechanical

equations. This approach has a significantly reduced

number of elements and equations in comparison to

the complex FEA. In the following two subsections,

the model development with each approach is

separately depicted.

3.1 Finite-Element-Analysis

The commercial software Abaqus FEA is used for the

model building and subsequent simulation of the

battery module. The finite-element-method is well

suitable for multi-body-simulation and therefore it

fits for the simulation of a battery module, which

consists of numerous components like cells, pads,

endplates and other. As described, the aim of the

simulation with this approach is to have a high

resolution of the spatially resolved swelling behavior

of the module over its lifetime. For that reason, each

component of the investigated battery module is

modelled in 3D and parameterized at first. Modelled

components of the battery module are its cells,

cushion pads, module frame, endplates, thermal resin

and busbars, amongst other things. In the next step,

the components are assembled the same as in the

examined module (Figure 2).

FEM-simulation is based on the setup and

solution of a system of equations, which are based on

physical laws ("Dubbel Taschenbuch für den

Maschinenbau 1: Grundlagen und Tabellen", 2020).

The size of the equation system and therefore the

computing time mainly depend on the number of

finite elements configured in the meshing process

ahead of the simulation. Therefore, the resolution of

the battery module by finite elements is accordingly

chosen to find a good compromise between

computing time and accuracy (Figure 3).

Figure 2: CAD-model of the examined battery module.

Figure 3: Meshed model of the examined battery module.

SIMULTECH 2021 - 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

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In order to implement the swelling behavior of the

built-in cells in step 3, it has to be experimentally

determined at first. For that reason, the examined cell

is placed in a test jig and cycled several hundred

times, building up a steadily growing swelling force.

In this process, the swelling force of the cell is

measured, using a load cell.

The measured cell swelling data is used for

building a swelling model for the cell, which is then

implemented into the FEM-model in the last step of

the pre-processing process.

3.2 Simplified, Mathematical

Modelling

A mathematical, analogous model for the mechanical

ageing behavior of battery modules has been

developed in the commercial software MATLAB as

an alternative approach to the complex FEM-

software. The focus of this approach is to accelerate

the model building process as well as to reduce the

computing time, while maintaining model accuracy.

The model is based on an algorithm, which is

capable of automatically discretizing a module into

finite elements and building up a corresponding

mathematical equation system, describing the three-

dimensional mechanical interaction behavior of the

elements by physical laws. The equation system can

be described in matrix notation as following:









∙{u} (1)

Here [K] stands for the global stiffness matrix,

whereas {F} for the global force and {u} for the

global displacement vector:



⋮



= 

⋯ K

⋮⋱⋮

⋯ K

∙



⋮



(2)

In this way, it resembles the computing process of

FEM-software, but it distinguishes itself by using a

reduced and simplified equation set. In the

mathematical modelling, the algorithm needs

information about the module, its assembly and

material properties of the components as well as

general model information like the chosen number of

finite elements and the discretization of the module

model. The input data are entered via a user interface

according to the data of the investigated battery

module. In comparison to the FEM-approach, a fewer

number of elements is chosen in this process to create

the battery module model; hence, it is very efficient

in terms of computing time. Further information

regarding module and component geometry and

assembly and their material properties must also be

provided in the user interface. Due to the wide

number of selection options in the preprocessing

process, the developed model offers maximum

flexibility for modelling battery modules of different

geometries, assemblies, materials, cells and further

characteristics. A geometric visualization of the

configured battery module is also available for

verification of the input data. Furthermore, the model

can accommodate the experimentally determined

swelling behavior of individual battery cell as the

input boundary conditions, representing step 3 of the

pictured method in Figure 1. After setting up the

model parameters and input data, all the components

of the battery module are created as 3D link elements

with linear interpolation and thus the complex model

can be simplified by using a mathematical system of

equations. The simulation model then solves the

system of mathematical equations to illustrate the

swelling behavior of an entire battery module as well

as its components over lifetime. Finally, the

visualization of the deformed module geometry with

the representation of displacement, tensions and

compressional forces using different colours are

implemented for the meaningful interpretation of

simulation results.

3.2.1 Interim Analysis Regarding

Preprocessing

The preprocessing of the two approaches differs

significantly. The simplified, mathematical

modelling technique allows the user an easy use

regarding model building due to the practical user

interface. As described in section 3.2, it also spares

the user the long-lasting component modelling,

parametrization and subsequent module assembly

and meshing process (Figure 4). Instead, the user

simply needs to provide the required input

information by filling out an interface and the

algorithm takes care of the rest. This way the

simplified model is even predestined for the use in

optimization studies as well.

Figure 4: Comparison of preprocessing time for both

modelling approaches.

~30

~0,5

FEA Mathematical Modelling

Time / h

Comparison of Preprocessing Time

For Both Modelling Approaches

Novel Method for the Three-Dimensional Simulation of Mechanical Ageing of Battery Modules

389

4 EXPERIMENT

A pouch module, consisting of 24 electrically

connected cells, is used for the experimental

investigation. The experimental setup for the

mechanical ageing test and its functionality is

schematically illustrated in Figure 5. The investigated

battery module is placed in a temperature chamber

and fixed on a metal surface. Afterwards, it is

equipped with distance sensors on specific locations

on its surface (Figure 6). The module inside the

chamber is conditioned to an elevated room

temperature for accelerated ageing and swelling

behavior and then cycled by the battery cycler with a

constant current rate for several hundred cycles.

During the entire time, the deformation of the module

is measured by the applied distance sensors.

Figure 5: Experimental setup for deformation measurement

of battery modules.

Figure 6: Swelling measurement points on device under

test.

5 RESULTS

The results of the experiment are shown in Figure 7.

The graphic shows a comparison of the deformation

at the measured positions. It is noticeable that

Position 2 clearly experiences more deformation in

comparison to Position 1 and 3 and therefore a

bulging of the module frame takes place.

Furthermore, the experimental data reveal that the

module has a high slope regarding swelling during the

first 100 cycles, before the slope decreases and

becomes linear for the following several hundred

cycles. Position 2 experiences a larger deformation

due to the fact, that the module frame has a lower

stiffness in its center section in comparison to the

sections closer to side, where it is welded to the

endplates, which increase stiffness and stability.

Figure 7: Experimental results for battery module swelling.

The module swelling simulation by both FEA and

simplified, mathematical approach deliver good

results over lifetime, which are close to the

experimental data. A comparison of the relative

dimension increase at Position 2 is shown in Figure 8.

The deviation between FEA and experiment is under

10% over the entire 400 cycles. A major benefit of the

FEA is its ability to simulate non-linear material

behavior. On the other hand, the simplified,

mathematical approach is currently limited regarding

this aspect and only allows cycle-independent,

constant material behavior, which is depicted by the

green line in Figure 8. A further simulation is

conducted with the simplified model by adapting its

cell material behavior, in order to compare its ability

regarding accuracy to the FEA. In this case, the cell

stiffness in the simplified approach is firstly

parametrized with the same value, which was used in

0,2

0,4

0,6

0,8

0 100 200 300 400

Relative

Dimension Increase / %

Cycle

Experimental Results

Position 1 Position 2 Position 3

SIMULTECH 2021 - 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

390

the FEA for 100 cycles. In the next step, the increase

of cell stiffness for the next 300 cycles is determined

in the FEA and then applied by a corresponding

function in the simplified model. By doing so, the

dark blue line in Figure 8 clearly brings out that the

simplified approach also can accurately predict

module deformation even in the later stages of

cycling and that cell material stiffness has a great

influence on the prediction of the module

deformation. Remaining differences after 100 cycles

presumably arise from non-linearity of further

module components.

Figure 8: Comparison of battery module relative dimension

increase in experiment and simulation at position 2.

In the following Figures 9 and 10, a comparison

between battery module normalized dimension

increase in experiment and simulation is shown.

Figure 9: Comparison of battery module normalized

dimension increase in experiment and simulation at

position 1.

Figures 9 and 10 confirm that the results of both

simulation approaches correspond well with the

experiments on all positions over lifetime. They also

confirm the linear characteristic of the current

simplified, mathematical approach and

simultaneously reveal its optimization potentials due

to its limitations regarding that.

Figure 10: Comparison of battery module normalized

dimension increase in experiment and simulation at

position 2.

Regarding computing time on the other hand, the

simplified mathematical approach shows his real

potential due to the small number of finite elements

used for the simulation (Figure 11).

Figure 11: Comparison of computing time and experiment

duration.

6 CONCLUSION

A novel method for predicting the spatially resolved

mechanical ageing behavior of battery modules over

lifetime has been developed and implemented, which

is based on a simplified, mathematical approach.

Additionally, the method has also been realized with

a complex FEA for comparison purposes, especially

regarding accuracy and computing time. For

0,2

0,4

0,6

0,8

0 100 200 300 400

Relative

Dimension Increase / %

Cycle

Position 2

Experiment

FEA with Non-Linear Cell Material Behavior

Mathematical Modelling with Constant Cell Material

Behavior (Nominal Stiffness)

Mathematical Modelling with Stiffnes Function for

Cell Material Behavior

0,2

0,4

0,6

0,8

0 100 200 300 400

Normalized

Dimension Increase / -

Cycle

Position 1

Experiment

FEA with Non-Linear Cell Material Behavior

Mathematical Modelling with Constant Cell Material

Behavior (Nominal Stiffness)

Mathematical Modelling with Stiffnes Function for Cell

Material Behavior

0,2

0,4

0,6

0,8

0 100 200 300 400

Normalized

Dimension Increase / -

Cycle

Position 2

Experiment

FEA with Non-Linear Cell Material Behavior

Mathematical Modelling with Constant Cell Material

Behavior (Nominal Stiffness)

Mathematical Modelling with Stiffnes Function for Cell

Material Behavior

~3200

~60

~0,03

2000

4000

Experiment FEA Mathematical

Modelling

Time / h

Comparison of Experiment

Duration and Computing Time

Novel Method for the Three-Dimensional Simulation of Mechanical Ageing of Battery Modules

391

assessment and validation of the developed models,

an experimental study was conducted, where a high

voltage battery module consisting of 24 electrically

connected lithium-ion pouch cells was exposed to

elevated temperatures for accelerated electrochemical

degradation and swelling of its cells and cycled

several hundred times. During the cycling, it was

equipped with distance sensors, which measured the

spatially resolved deformations of the module from

the outside. The recorded data of the module swelling

due to electrochemical ageing was then compared to

the simulation results. According to the best

knowledge of the authors, this has been the first time

a mechanical ageing model for modules has been

validated against experimental data. The first set of

simulation results of both modelling techniques has

proven their ability to predict the spatially resolved

module swelling behavior over lifetime with good

accuracy. The simplified model in his current

working status works well for fast predictions. It is

also suitable for optimization studies due to the

developed algorithm, which automatically builds up

mechanical models for different module designs and

configurations by using data, which are entered in a

user interface. On the other hand, the FEA delivers

accurate results with a higher resolution, but with a

longer preprocessing and computing time. In

comparison to the real experiment, which took about

four and a half months, both model approaches can

reduce this duration massively.

7 OUTLOOK

The optimization of the simplified, mathematical

approach is ongoing, in order to extend its simulation

abilities, like the simulation of non-linear material

behavior, in order to reach higher accuracy. In the

process of that, the model equations are being

optimized by taking into account further in-depth

physical effects. In addition, sensitivity studies

regarding the number of finite elements are being

conducted.

Further experimental and simulative studies for

different module types are also ongoing. In doing so,

the modelling of prismatic battery modules is also

being realized.

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