## 1 Introduction

The environmental benefits of electric vehicles (EVs) accelerated their adaptation to transportation in the past decade [1]. However, the safety issues of the high-energy density lithium-ion batteries (LIBs), embedded in these vehicles, are the major hindrance in this adaptation process [2]. These issues are caused mostly by electrical abuse [38], thermal abuse [911], and mechanical abuse loadings [1215]. Compared to the vast studies on the electrochemical and thermal responses of LIBs, the mechanical responses remained understudied. Therefore, the surging need for EVs and the prevalence of LIBs in modern transportation necessitates a more thorough understanding of the safety issues associated with the failure mechanisms of these batteries during mechanical abusive loadings, as an inevitable result of the road collisions.

Lithium-ion batteries are usually made up of alternating layers of anode and cathode electrodes separated by a dielectric micro-porous polymeric layer encased in a shell casing. The mechanical loadings in the event of an EVs crash can damage these embedded LIBs by local indention, bending, buckling, and more practically, a combination of these scenarios. Mechanical deformations can induce internal short circuit by damaging the separator and the electrodes or external short circuit by rupturing the tabs or the connecting busbar. These short circuits cause local bursts of energy, which may lead to fire and explosion in extreme cases [16,17]. Therefore, to improve the safety of EVs, mechanical responses of the LIBs have been studied in the literature for different form factors of LIBs, i.e., cylindrical [12,1824], pouch [14,2530], elliptical [3134], and prismatic [3538] at various levels of cell components, full cells, cell modules, and battery packs.

These studies are composed of both testing and modeling. The tests have been performed on various battery form factors, dry and wet cells [31,32], at different states of charges (SOC) [39,40], temperatures [41,42], quasi-statically, or dynamically [32,43,44]. These experimental tests shed some light on the mechanical responses and failure mechanisms of batteries in practical crash scenarios. However, the explosive and hazardous nature of the LIBs requires a special environment and sometimes complex fixtures for experimental testing. Therefore, researchers propelled toward numerical models that require a limited number of experimental data for calibration and can be used efficiently in predicting the behavior of the cell in various abusive loading conditions.

Detailed, homogenized, and representative volume element (RVE) modelings are the state-of-the-art modeling approaches developed in the literature. Detailed models, where all the layers and the shell casing are calibrated and modeled individually, can be used by battery manufacturers in investigations of the changes in mechanical, thermal, electrochemical, and failure of a cell by altering the material properties of the layers or their cell design [25,45,46]. In RVE modeling, although the calibration method for the layers is the same as in the detailed models, simulations are done on a representative section of the cells, which reduces the computational times enormously. However, this modeling approach is new compared to the other methods and just has been explored for in-plane bucking and failure mechanism investigations [34,47]. In homogenized models, the lumped material property of the electrode stack/jellyroll is assigned to a uniform medium to represent the whole cell behavior. Using a fewer number of elements in the homogenized models makes them comparatively computationally inexpensive [12,14,18,22,26,48,49].

In an electric vehicle, where stacks of cells are presented in the form of battery packs and modulus, the deformation of a single cell is highly under influence of its neighboring cells. The batteries form a cushion foundation for each other during accidental loads in an event of a crash. Also, external short circuit which is mostly due to the rupture of the electrode tabs and the busbar connection is another issue that should be considered when large-scale simulations of a car crash are under investigation. Therefore, predicting the behaviors of a single cell cannot necessarily result in the understanding of the overall deformation and failure mechanism of an electric vehicle in case of a crash. The cost-efficient homogenized models are the only feasible solution to be considered for electric vehicle simulations, where hundreds if not thousands of these batteries are stacked in the form of modulus and packs.

The material properties of the homogenized models of the electrode stack/jellyroll must represent the summation of the material properties of its constitutive parts. In literature, several studies calibrate the compressive and tensile homogenized material properties of the cells by summing the compression and tension experimental data of the samples extracted from the dissected cells electrode stack/jellyroll and the shell casing [47,50]. In the case of pouch cells, the contribution of the soft laminate pouch is negligible compared to that of the jellyroll. However, in the form factors that have a hard-shell casing, such as prismatic and cylindrical batteries, the metal shell casing has a considerable effect on the overall mechanical response of the cells. Therefore, in pouch cells, Sahraei et al. [14] and Chung et al. [30] used local indentation experimental data (flat circular punch indentation) to calibrate the compression through-thickness property of the cell. Further, the in-plane anisotropy of the pouch cells in compression had been considered by adding the buckling strength of the cell to the through-thickness compression properties [14,34]. In cylindrical cells, the jellyroll had been extracted and compressed between two flat plates to extract the through-thickness compression properties by using the virtual work principle [12,22]. Contrary to the numerous research on cylindrical and pouch cells, prismatic cells have not gotten much attention. Due to the hard-shell casing of the prismatic cells, they can bear higher bending and in-plane loadings compared to pouch cells. Also, the shape of the prismatic cells would allow higher energy density battery modulus compared to the ones consisting of cylindrical cells since they use space more efficiently.

In this article, first, a homogenization method was developed for modeling the prismatic lithium-ion batteries. In this method, a homogenized material model for the jellyroll and the hard-shell casing of the prismatic cell is calibrated through sets of components’ uniaxial tension and compression tests. Then, a failure strain value is calibrated for the homogenized medium of the jellyroll. The method was then validated against experimental data of three different size hemispherical punch tests. Moreover, the validated model was used in the simulation of the stack of the cells to investigate the mechanical behavior of prismatic cells in these types of configurations. The extensive calibration method and the modeling approach detailed in this article are believed to benefit the electric vehicle industry by precisely predicting the deformation and failure mechanisms in large-scale simulations where hundreds of these prismatic LIBs are involved.

The rest of this article is organized as follows. In Sec. 2, the experiments carried out on the components and the full cell will be elaborated. Then, the material and failure calibration of the components and homogenization of the layers of jellyroll into a single part is presented in Sec. 3. In Sec. 4, the finite element model is detailed, and the simulation results of the single and stack of cells in different scenarios are reported in Sec. 5. These are followed by a discussion of the results in Sec. 6, and a conclusion of this study is presented in Sec. 7.

## 2 Experiment Methods

The experiments in this research were done on a commercially available prismatic cell provided by the research sponsors. The battery cell is made up of two stacked jellyrolls encased in a hard aluminum casing. Each of the jellyrolls consists of 35 rolls of a separator–anode–separator–cathode stacked layer. The specifications of this prismatic cell are listed in Table 1, and the photographs of a cell and its jellyrolls are shown in Fig. 1(a). This cell had been cycled heavily before this study, and due to the gas release, the shell casing was inflated at the center. The measured thickness at the center of the cell has a 6 mm difference compared to the edges. In this section, first, the uniaxial tension and compression tests of the components are discussed. The results of this section will be used in Sec. 3 to calibrate the average stress–strain behavior of the jellyroll in tension and compression. The hard-shell casing of the cell went through dog-bone tensile tests for material characterization. Finally, three whole cells were tested in three indentation loading scenarios, and the data are used in Sec. 5.1 to validate the calibrated model. A 200 kN MTS loading frame enclosed with exhaust for ventilation has been used for the experiments. All tests were carried out at room temperature. Studying the effects of varying temperatures on the mechanical properties of the cells is out of the scope of the current study and will be the subject of future research.

Fig. 1
Fig. 1
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Table 1

Specifications of the prismatic tested cell

 Nominal capacity 25.0 Ah Nominal voltage 3.7 V Cell chemistry LiCoO2-graphite Cell thickness (edges) 27 mm Width 91 mm Length 150 mm Anode thickness 63 µm Copper foil thickness 12 µm Cathode thickness 69 µm Aluminum foil thickness 20 µm Separator thickness 25 µm
 Nominal capacity 25.0 Ah Nominal voltage 3.7 V Cell chemistry LiCoO2-graphite Cell thickness (edges) 27 mm Width 91 mm Length 150 mm Anode thickness 63 µm Copper foil thickness 12 µm Cathode thickness 69 µm Aluminum foil thickness 20 µm Separator thickness 25 µm

### 2.1 Component Testing.

For component testing, the prismatic cells were discharged to 0% SOC. Then, the hard-shell casing was cut, and the jellyrolls were extracted. The electrolyte was washed, and jellyrolls were dried before component tests. Samples were cut from the jellyrolls for uniaxial tensile, compression, and biaxial tensile tests. The details of the experiments are elaborated in the following sections.

#### 2.1.1 Uniaxial Tensile Tests.

Samples of the anode, cathode, and separator were cut from the jellyrolls with a width of 10 mm for uniaxial tensile tests. Anode and cathode, which are made of metallic current collectors and double-sided coated with granular coatings, exhibit isotropic material properties in the in-plane directions. The micro-porous layers of separators show in-plane anisotropy in the material direction (MD) and the transverse direction (TD) due to their fabrication procedures [51]. Therefore, two sets of samples, cut in MD and TD, were tested for the separator. The gauge length was 35 mm, and they have been performed at 2 mm/min and 4 mm/min strain rates for the electrode and the separator samples, respectively. A tabletop Instron load frame with a 100 N load cell was used for the component testing. The pneumatic grips of the load frame securely held the samples with pneumatic force and surface groves to ensure clamping force on the samples during the tensile tests; see Fig. 1(b). The extracted load–displacement data are shown in Figs. 1(c)1(f).

The tensile properties of the electrodes are mainly controlled by the strength of their metallic foils rather than the weak adhesion of the coating’s particles to the metallic layer or the cohesion between those particles. The anode tensile tests showed that the failure happened at 0.25 mm of displacement with a 25 N load. The copper foil layer of the anode electrode has a relative ductility that allows plastic flow and deformation until reaching failure at 25 N load. The aluminum foil layer of the cathode electrodes shows the same plastic deformation up to a displacement of 0.5 mm and 48 N load. The MD samples of the separator failed around 20 mm displacement and a corresponding load of 40–45 N. Separators in this direction experience wrinkles and can tolerate higher loads. Conversely, the TD samples had an average of 30 mm displacement before sudden rupture with a lower corresponding load of 2.7–3.2 N.

#### 2.1.2 Uniaxial Compression Tests.

Uniaxial compression tests were the next round of experiments. These tests were conducted on 16 mm diameter round samples of the components. Tests on electrodes were on stacks of 20 samples, and tests on separators were on stacks of 40 samples. All experiments were conducted at a speed of 1 mm/min. The compression load–displacement experimental results are shown in Fig. 2. The anode underwent a maximum 16 kN compressive force and a 1.1 mm displacement before load drop. The cathode withstood a force of approximately 24 kN and 1.4 mm displacement before failure. The separator material tolerates a maximum force of 40 kN at 0.8 mm of displacement. In compression tests, the electrodes’ coatings contribute the most to the compression results, while the metal current collectors have minimal strains. The active particles, which are held together by usually a polymer binder, are considered to act as a foam material with pores in-between its constitutive particles. Therefore, at the beginning of a compression test, the distances between the active particles are reduced till these pores are filled. At this stage, no permanent deformation happens on the active particles. As the test progresses and the load increases, the particles experience plastic deformation till the coatings are fully compacted and cracks are formed on the coating. The slopes of the load–displacement in Fig. 2 explicitly demonstrate the explained procedure of deformation in the electrode particles.

Fig. 2
Fig. 2
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#### 2.1.3 Biaxial Tensile Test.

Uniaxial tensile tests show good repeatability in terms of load–displacement trends, see Fig. 1. However, the onset of failure varied between the samples. This issue is rooted in several reasons. First, in the specimen’s preparation process, cutting the samples out of the jellyroll damages the edges of the samples and makes them susceptible to premature failure. The other reason would be the nonuniform pressure of the grips holding the samples in these tests. As a result, to eliminate the mentioned issues and to obtain the correct failure value of the components, a biaxial tests setup is being used, see Figs. 3(a) and 3(b). The samples were clamped between two hollow circular plates using six screws that were tightened with the same torque. There is a circular tongue on one of the hollow plates where the sample sits and a fitting groove on the other one. This structure eliminates the effect of edges in the immature failure of the sample and provides uniform tension in the specimen. These biaxial tests were performed by indenting the samples by a 1/2 inch punch at a speed of 12 mm/min. The load–displacement results of the samples are shown in Figs. 3(c)3(e). It should be noted that failures of separators have two modes that induce soft and hard short circuits [51]. The earlier and later load drop in Fig. 3(e) shows these two modes.

Fig. 3
Fig. 3
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#### 2.1.4 Tensile Test on the Aluminum Casing.

In prismatic cells, a hard-shell casing encased the jellyroll. As a result, the mechanical property of this shell casing plays an important role in the crashworthiness of these batteries. In this regard, to precisely characterize the material property of this casing, tensile tests had been carried out on dog-bone samples extracted from various locations of the casing, see Fig. 4(a). Specimens 1 and 2 were extracted from the side face of the cell and had a thickness of ∼1.52 mm. The deep-drawn material on the other faces of the cell, where the other samples were extracted, has thicknesses of ∼0.72 mm. The extracted specimens and their dimensions have been reported in Fig. 4(a). As shown in Figs. 4(b) and 4(c), the tensile behavior of the metal sheet has been changed due to this deep drawing and should be taken into account for precise modeling of the prismatic cells.

Fig. 4
Fig. 4
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### 2.2 Cell-Level Testing.

Punch indentation tests were conducted on the battery cells that had previously undergone extensive cycling to the end of life and were slightly inflated due to gas release, see Fig. 1(a). In these tests, three different sizes of hemispherical punches, 12.5 mm, 28.575 mm, and 44.45 mm, were used to indent these cells at a speed of 1 mm/min, see Fig. 5(a). During these tests, an ohmmeter was connected to the tabs to measure the electrical resistance of the cell. The experiment results are shown in Fig. 5(b). It was observed that the force increased as the punch got larger in diameter. In addition, the electrical resistance of the batteries dropped at or very near the maximum sustained force, reinforcing the relationship between mechanical failure and electrical failure.

Fig. 5
Fig. 5
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## 3 Homogenized Material Characterization

The architecture of a lithium-ion battery cell consists of alternating cathode, anode, and separator layers that exhibit distinct mechanical properties. To fully understand the behavior of the cell in various loading conditions, precise material calibration for each of the layers has great importance. In addition, finite element modeling as an efficient tool in this fast-growing electrification era plays an important role in the development of new, efficient, and safe batteries. However, due to the multiscale and complex nature of these batteries, using a detailed model of the batteries is not feasible in studies where hundreds of these batteries are involved, e.g., electric vehicles. Therefore, a homogenized medium, which can replicate the same behavior and yet be computationally cheaper, is highly desired. As a result, in this section, the homogenized material properties of the cell are calibrated using experimental and simulation data of the layers. This section is organized as follows. First, the compression properties of the cathode and anode layers were calibrated by using the experimental data of the components in compression. This procedure had been validated by finite element modeling of the stacks of layers in compression using abaqus explicit software. Then, to calibrate the strain failure of the layers in tension, biaxial simulations had been performed on the layers and their corresponding failure strain values were extracted. Finally, the compression and tensile properties of the layers were used to characterize the smeared homogenized properties of the prismatic cell.

### 3.1 Finite Element Modeling of the Components.

Cathode and anode are double-sided coated metallic layers of aluminum and copper, respectively. To precisely characterize these layers, the material properties of the coatings and the metallic foil layers are needed. The uncoated metal current collector in most cases is not available from the manufacturer separately. In this study, it is assumed that the metal current collector properties are the same as aluminum and copper samples tested in the previous research done by the authors [50]. To obtain the properties of the coating from the experiments, the following assumptions have been made:

• In compression, it is assumed that all layers of metal and coating are under the same stress, but varying strains. Therefore, total force and displacement of the 20-layer specimen test are used to extract the stress–strain response of the coating, by removing the contribution of metal foils as follows:

Equal stress for compression: σMetal = σcoating

Total displacement: Δ = ɛMetaltMetal + ɛcoatingtcoating

Coating strain in compression: $εcoating=Δ−εMetaltMetaltcoating$

• (ii)

In tension, it is assumed that coating and metal layers are stretching together, so they go through the same strains, but stress is different in each of these components based on their strength. Therefore, the stress–strain of the coating in tension is calculated from:

Equal strain for uniaxial tension: ɛMetal = ɛcoating

Total force: F = σMetalAMetal + σcoatingAcoating

Coating stress in tension: $σcoating=F−σMetalAMetalAcoating$

Due to the nature of the metallic and granular coatings, elastic–plastic and crushable foam material models were used in the software to model the metallic layers and coatings, respectively. The crushable foam material model in abaqus software, which is based on the Deshpande-Fleck material model, assumes that the evolution of the yield surface is controlled by the volumetric compacting plastic strain experienced by the material. The definition of yield surface and its evolution in the software is done by three parameters: compression yield stress ratio, hydrostatic yield stress ratio, and true plastic versus plastic strain hardening curve. The compression yield ratio is defined as the ratio of initial yield stress in uniaxial compression and yield stress in hydrostatic compression. The hydrostatic yield stress ratio is defined as the ratio of the yield strength in hydrostatic tension and the yield stress in hydrostatic compression. These values are reported in detail for cathode and anode layers in Table 2.

Table 2

Calibrated material properties of the components and their corresponding abaqus input parameters

Thickness (mm)ElementsMaterialDensity (kg/m3)Young’s modulus (GPa)Poisson’s ratiokaktbHardening curves
AnodeCu foil0.012932 (S4R)E-Pc89301100.343NANA
Coating0.063935 (C3D8R)C-Fd8790.5000.011400
CathodeAl foil0.020932 (S4R)E-P2680700.33NANA
Coating0.069935 (C3D8R)C-F216216000.011600
Thickness (mm)ElementsMaterialDensity (kg/m3)Young’s modulus (GPa)Poisson’s ratiokaktbHardening curves
AnodeCu foil0.012932 (S4R)E-Pc89301100.343NANA
Coating0.063935 (C3D8R)C-Fd8790.5000.011400
CathodeAl foil0.020932 (S4R)E-P2680700.33NANA
Coating0.069935 (C3D8R)C-F216216000.011600
a

Compression yield stress ratio.

b

Hydrostatic yield stress ratio.

c

Elastic–plastic.

d

Crushable foam.

To validate the calibrated material properties, the 20-layer compressions specimen was modeled by an equivalent sample where all coating thicknesses were added in one coating part and all the metal thicknesses were added in one metal part. abaqus elements with C3D8R formulation were used for the simulations and the coating elements were merged with the metal elements, Fig. 6(a) shows the schematic of the simulated sample in compression, and Fig. 6(b) shows the comparison of the force–displacement from the model versus the experiment. Simulations for both anode and cathode show very close predictions of the test data.

Fig. 6
Fig. 6
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In the next step, abaqus software is used to simulate the biaxial tests. Electrodes were modeled in a 29 mm diameter circular shape with fixed boundary nodes. A spherical punch with a 25 mm diameter was used to deform the single-layer electrode. The load–displacement results of the biaxial simulations were compared against the experimental data, see Fig. 7. Close prediction of the experimental results was achieved from the models. The failure for the anode layers was observed to happen in the strain range of $εf∼0.0419−0.0518$, and for the cathode layers, the failure strain was in the range of $εf∼0.0252−0.0317$. A parametric study on the effects of the coefficient of friction between the punch and the sample showed negligible effects of this parameter on the results. The aforementioned two sets of simulations validate the extracted material properties of these components.

Fig. 7
Fig. 7
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### 3.2 Homogenized Compression Properties.

The homogenized stress–strain response under compression was calculated in two steps. First, the average response of a representative four-layer building block of the jellyroll, containing a layer of an anode, a layer of a cathode, and two layers of separators were calculated using the same principles explained in Sec. 3.1. This means considering that when all layers will be in compression together, they will be tolerating the same stress, while their strains will be different. The total stress of the RVE will be equal to the force/area of any of the samples. The total strain of the RVE will be calculated by adding displacements of all samples divided by the total thickness of all layers. See the dashed line in Fig. 8 for the stress–strain curve of the RVE. This battery cell consists of two jellyrolls stacked on top of each other with 35 layers of anode–separator–cathode–separator. By comparing the thickness of these stacked jellyrolls using the data reported in Table 1 and considering the shell casing thickness reported in Fig. 4(a), a 1.28 mm gap is calculated. This value corresponds to the summation of the gap distances between the layers and the whole stacked layers with the casing. Therefore, in the homogenized characterization of the jellyroll, this gap distance has been taken into consideration by shifting the calibrated average RVE compression curve by its corresponding strain value of 0.05 mm/mm, and see the black solid line shown in Fig. 8.

Fig. 8
Fig. 8
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### 3.3 Homogenized Tension Properties.

For calculating the average tensile property of the jellyroll, again similar principles explained in Sec. 3.1 were used. The in-plane tensile curves of the component have been summed considering under tension all layers have similar displacement, but each has a different contribution to the total force. As the material is a continuum under in-plane tension and no gaps are present, the RVE tension does not require any shifting, see the dashed line in Fig. 9. The additional factor in tension is the sequential failure of the layers. This type of softening in the average properties can lead to instability in finite element models. The material model used for the simulation of the homogenized jellyroll, as explained in the next section, requires a single tensile cutoff value as the input parameter. This tensile cutoff value was calculated by a constant line that will have equivalent strain energy absorbed, which was 15.78 MPa for the present assembly, and see the black solid line shown in Fig. 9.

Fig. 9
Fig. 9
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## 4 Finite Element Modeling of the Cell

To validate the developed characterization method, a finite element model of the full cell was built using the calibrated material properties. ls dyna software version R10.0 was used in this section of the study. The pouch cell model consisted of 5698 solid elements with MAT_63 (MAT_CRUSHABLE-FOAM) for the jellyroll and 2623 shell elements with MAT_24 (MAT_PIECEWISE_LINEAR_PLASTICITY) for the aluminum casing. A tensile principal strain value of 0.05 was added as the failure criterion to the model using MAT_ADD_EROSION. This value was calibrated to simulate the initiation of an element failure at the onset of a load drop in the small hemispherical punch test simulation. As mentioned, the tested prismatic cells were inflated at the center of their shell casing due to prior failure and gas release. Therefore, this bulging is modeled by two circular slopes as shown in Fig. 10(a) and validated in small punch indentation simulations, see Fig. 10(b). As shown, modeling the bulged shape of the cell, which happened because of the gas release due to the heavy cycling of the battery before mechanical testing, has a great influence on the prediction of the load–displacement results, and there would be a great discrepancy if the normal shape of the cell would be modeled for the simulations.

Fig. 10
Fig. 10
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## 5 Results

The results section consists of two major parts. First, the model is validated against experimental data in three different punch indentation loadings. Then, a stack of four cells is simulated in small punch indentation for two scenarios of with and without spacer between the cells.

### 5.1 Full Cell Modeling.

As explained in Sec. 2, small (12.5 mm), medium (28.575 mm), and large (44.45 mm) hemispherical punch indentations were performed on the cell, and the load–displacement data were reported in Fig. 5(b). These hemispherical punches were modeled with rigid shell elements in LS DYNA to simulate the indentation tests on the calibrated prismatic cell. The results of these simulations are reported in Fig. 11. These results show the capability of the model in the prediction of load–displacement, shape of deformation, and most importantly the onset of failure during abusive loadings.

Fig. 11
Fig. 11
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### 5.2 Cell Stack Simulation.

Homogenized battery models provide researchers a cost and time-efficient tool in heavy simulations of EV accidents where stacks of these battery cells are involved in the form of modules and packs. In this article, the calibrated finite element model is used in the punch indention simulation of a stack of four cells. In these simulations, the same material model, which was calibrated for the cell, is used with a not-bulged geometry of the cells to represent new battery cells.

During punch indentation, most of the deformation has been tolerated by the first cell and the other cells form an elastic foundation underneath the first cell. Figure 12 shows the load–displacement result of the cell stacks and the sequence of deformation up to the onset of mechanical failure at approximately 9 mm of displacement. Understanding this sequence of mechanical failure, which would dictate the onset of short circuit, has great importance in battery module and pack designs. In the cell stack indentation, the onset of failure is postponed to higher displacement values since other cells act as a cushion for the indented cell.

Fig. 12
Fig. 12
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To investigate the effect of the spacer in the stack of cells, a 1 mm thick aluminum sheet was placed in-between the cells. As shown in Fig. 13, the simulation results of the stack of cells with and without spacer show the same short circuit failure at approximately 9 mm displacement.

Fig. 13
Fig. 13
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## 6 Discussion

The precision of a single battery cell model, as the building block of the energy storage systems in EVs, plays an important role in safety investigations. However, the crashworthiness analysis of an EV requires accurate prediction of the deformation of the whole energy system, which includes components such as the busbar, the cooling systems, the packing structure, and the neighboring effects of the other cells. Therefore, the generalization of battery safety from cell level to battery pack level is not straightforward.

By using normalized intrusion as the depth of deformation to the thickness of the simulated specimen, the stacks of the cell fail around 8% intrusion compared to 17% of a single cell, and see Fig. 14. This illustrates that the failure analysis in a single cell cannot be generalized for the stacked of cells’ analysis and therefore EV safety evaluations. It should be noted that the analysis of the stack of six cells is just an example to show the limitation of single-cell results in predicting pack level phenomena. In actual battery packs, there are unlimited ways that cells can be put together, and each may result in a different final intrusion percentage limit. The takeaway point from this analysis is that modeling methods should be extended to module and pack level studies and ultimately to the integration of the battery pack to the full vehicle model. These topics are currently under investigation by the authors’ team.

Fig. 14
Fig. 14
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It should also be noted that there are various ways to calibrate the homogenized material properties of a cell. As shown in this article, samples of the jellyroll and the shell casing cut from the battery cell were tested and characterized and the average tensile and compressive responses of the components were used. This method requires extensive and repeatable test results to obtain reliable results. The advantage of this approach is that hypothetical changes in the components can be used to calculate the final effects they could have on the homogenized response. In a different approach, mechanical tests such as flat punch indentations, three-point bending, and in-plane compression can be done on the jellyroll to extract the homogenized responses. This method requires fewer number of experiments for calibration compared to the previous approach. This approach had been developed for cylindrical cells by the authors in the previous studies [12,22].

A limitation of both of the aforementioned methods is that the component samples and the specimen were tested in ex situ conditions without the presence of electrolyte and confinement shell casing. To consider in situ conditions, a third approach is to use analytical methods to extract the homogenized cell properties from cell-level testing. In this method, first, the whole battery cell undergoes mechanical deformation such as flat/hemispherical indentation [14,26,30] or compression between two flat plates (radial compression) [12,22] to extract the overall response of the cell. The extracted load–displacement results of these experiments include both the response of the jellyroll/s and the shell casing. By removing the contribution of the shell casing and using an analytical approach to calibrate the response of the jellyrolls, the in situ homogenized material properties of the cell can be calibrated. The authors and the collaborators developed this method for the pouch and cylindrical cells in previous publications [22,26] and are working on the extension of that method for the current prismatic cells. This will be the subject of the next publication of the team on prismatic battery cell modeling.

Another valuable discussion here is whether prismatic cells with a larger thickness of the cell and shell casing have an advantage over the two other commonly used form factors of lithium-ion batteries, i.e., pouch and cylindrical cells. For this purpose, a comparison of these three cells under the same type of punch loading with the small hemispherical punch is included in Fig. 15(a). In a first look at the onset of short circuit for these three cells, it can be observed that the peak force at the onset of failure for the pouch, prismatic, and cylindrical cells are at displacements of 2.6 mm, 4.5 mm, and 6.5 mm, respectively, which indicates a smaller displacement to failure for the pouch cell and a later failure displacement for the cylindrical form factor when compared to the prismatic cells. It is interesting to see that the force–displacement curve of the prismatic cell is very similar to the cylindrical cell. These are the two form factors with hard-shell casing and wound jellyrolls that have central gaps. In the graph of the prismatic cell, the increase in force after the onset of failure is shown with a dotted line, and this section gets even closer to the curve of the cylindrical cell. A question to be asked here is what causes the prismatic cells to have an earlier failure when compared to the cylindrical cells. By using engineering intuition, one would expect that the cell with a larger thickness of 27 mm would tolerate higher displacement as it will reach the same level of strain at a later point. However, evaluating the shell casings of the prismatic and cylindrical tests after these experiments indicates that a fracture of shell casing happens in the prismatic cell, while the cylindrical cell casing remains intact until jellyroll fractures. Therefore, initiation of failure in prismatic cell jellyrolls is a consequence of the earlier failure of the shell casing. One reason for the early failure of the shell casing could be the consumption of ductility of the metal during the deep drawing process, where the thickness decreases from 1.5 mm for the raw material to 0.7 mm for the sides of the can, where the load is exerted. This is a ratio of reduction in thickness of about 53%, which significantly reduces the failure strain of the metal. In the case of cylindrical cells, the original thickness of the can before deep drawing, as can be measured in the bottom of the can, is 0.3 mm, [12], and at the central part of the can where the load is exerted, the thickness is about 0.25 mm while decreasing to 0.18 mm at the top. This means the thickness reduction during the drawing process for the cylindrical casing at the location of punch indentation is only about 16%. Therefore, material still has significant ductility left, which prevents it from early failure of the shell casing.

Fig. 15
Fig. 15
Close modal

Using a normalized thickness measurement for the displacement, the relative displacement to failure for these cells are 16.6%, 34.6%, and 36.1% for the prismatic, pouch, and cylindrical cells, respectively, see Fig. 15(b). In this case, the failure percentage and even shape of the load–displacement curve become very similar between the pouch and cylindrical cells, indicating the thin shell casing of the cylindrical cell (0.25 mm) does not provide a significant effect on the normalized displacement to failure. However, the early failure of thicker shell casing (0.7 mm) of prismatic cells causes a much lower percentage of normalized deformation to failure for these cells. This may seem to counter-intuitive at the first glance, as one would expect a thicker shell casing will provide superior protection against failure for the prismatic cells. However, the history of the manufacturing and drawing process of these cans seems to have a significant effect on their protective effect, at least in this kind of loading. It should be noted here that we are only comparing one type of loading and a single-cell test experiment. As seen in the stack configuration discussion, the performance of any of these cells in their final assembly will be ultimately a function of the cell arrangement and configuration at the module and pack level.

## 7 Conclusions

In this study, a combined experimental, computational analysis was performed to characterize the homogenized response of prismatic lithium-ion batteries from its constitutive components, i.e., electrodes and separators. Once, a cell model was developed and validated against cell-level experiments, a model of a stack of four prismatic cells was developed and used to study the changes in the properties when going from cells to modules of batteries. The results show that stacking of the cells does not significantly change the sustained deformation before failure. This means care should be taken when cell-level material properties are used to simulate the response of the module of batteries. The normalized displacement before failure is smaller in a module compared to a cell. In addition, the effects of aluminum spacers on the overall response of a cell stack were studied. No considerable difference was observed between the stacked with the spacers and the one without them. A comparison of the prismatic cell with two other common form factors, pouch and cylindrical, indicates that the prismatic cells fail much earlier than those other cell types when a normalized to thickness approach is used. This early failure is believed to be a consequence of the low ductility of the deep drawn (53% thickness reduction) shell casing of prismatic cells.

## Acknowledgment

The authors would like to acknowledge partial funding from the Ford-MIT alliance. The authors would like to thank and acknowledge Brandy Dixon for conducting a part of the reported experiments.

## Conflict of Interest

There are no conflicts of interest.

## Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

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