# Evaluation of Modelling and Simulation Strategies to Investigate the Mechanical Integrity of a Battery Cell Using Finite Element Methods

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Battery Modelling

^{®}Xeon

^{®}Gold 5122 CPU @ 3.60 GHz and 3.59 GHz processors. All Simulations were performed using 8 CPU’s and 64 GB RAM. For mechanical simulations of a battery cell in this study, an explicit solver from LS DYNA was selected.

## 3. Modelling Approaches

#### 3.1. Heterogeneous Modelling Method

#### 3.2. Homogeneous Modelling Method

#### 3.3. Hybrid Modelling Method

#### 3.4. Sandwich Modelling Method

#### 3.5. Partial Modelling Method

#### 3.6. Anisotropic Material Properties of Separator

## 4. FE Simulations

^{−1}was defined to depict the movement of the punch. In order to be considered as quasi-static, it was specified that the proportion of kinetic energy must not exceed 1% of the total energy [17]. To keep the cell in place during the indentation process, the movements and rotations of the cell were constrained. A planer RIGIDWALL was created underneath the battery cell.

#### 4.1. Heterogeneous Cell Model

_{z}= 42 MPa was used and for the transverse directions $E$

_{xy}= 38 MPa. This results in the respective values of $G$

_{z}= 16.15 MPa and $G$

_{xy}= 14.62 MPa for the shear modulus.

#### 4.2. Homogeneous Cell Model

_{z}= 57 MPa and the E modulus in the plain compression direction was $E$

_{xy}= 90 MPa. The shear modulus was calculated according to Equation (3). Due to Poisson’s ratio of ϑ = 0.01, it can be neglected for this calculation. This results in a value of $G$

_{z}= 28.5 MPa and $G$

_{xy}= 45 MPa for the respective shear moduli through thickness and plain directions.

#### 4.3. Hybrid Cell Model

#### 4.4. Sandwich Cell Model

#### 4.5. Partial Cell Model

## 5. Results

## 6. Discussion

^{−1}[5] whereas in this study the velocity was set to 1 m s

^{−1}. Lowering the indenter velocity in a simulation results in a substantial increase in simulation time. The current study is performed by referring to the material data from different literature and using the available computational power. Furthermore, the effect of electrolytes is not considered in this study. Sahraei et al. [18] state that dry pouch cells (without electrolyte) had higher stiffness compared to wet (with electrolyte) pouch cells. The calibration of both simulation models can be done by assigning a specific failure strain value corresponding to drop in force. In the future, for better calibration and validation of the FE Model, a material characterisation test data and spherical indentation test data from the same battery cell should be used.

## 7. Conclusions

- The finite element models developed with each method predicted the behaviour of the battery cell after indentation with sufficient accuracy and displayed local deformation of the cell near indenter.
- The coefficient of friction between the sphere and the cell significantly influenced the force response of the cell. Similarly, the failure strain of the separator also affected the cell failure.
- When the models were suitably calibrated by parametric studies, a sudden drop in the force was observed in the force displacement diagram. This drop indicates mechanical failure of the battery cell. Therefore, each method is suitable for prediction of failure of the battery cell.
- The anisotropic material properties of the separator can be incorporated in the finite element model with all described modelling techniques. A selection of a suitable material model facilitates the directional behaviour of the separator.
- Symmetry boundary conditions allow for the creation of partial models of battery cells and these models can also predict the mechanical failure when they are suitably calibrated.
- The number of elements in the model and number of contact interfaces had a huge impact on computational time as well stiffness of the model.
- Accuracy of the modelling method could not be predicted only on the basis of its complexity or realistic construction. It also depends on the selection of a suitable material card and appropriate input parameters.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Construction and working of a lithium ion battery: (

**a**) charging and discharging of a microcell; (

**b**) schematic representation of a microcell.

**Figure 3.**Modelling approaches of a battery cell with FE method: (

**a**) heterogeneous modelling; (

**b**) homogeneous modelling; (

**c**) hybrid modelling; (

**d**) sandwich modelling.

**Figure 4.**Types of heterogeneous modelling: (

**a**) all layers resolved including current collectors; (

**b**) unresolved anode and cathode.

**Figure 9.**A battery cell model using a partial modelling technique: (

**a**) half model; (

**b**) quarter model.

**Figure 10.**Simulation of a spherical indentation test for a battery cell using the heterogeneous modelling strategy.

**Figure 11.**(

**a**) Stress distribution on a deformed battery cell after indentation simulation. (

**b**) Force-displacement outputs of isotropic and anisotropic models with the heterogeneous modelling method.

**Figure 12.**Simulation of a spherical indentation test for a battery cell with a homogeneous modelling strategy.

**Figure 13.**Force-displacement outputs with the homogeneous modelling method: (

**a**) influence of coefficient of friction on isotropic model; (

**b**) influence of coefficient of friction on anisotropic model.

**Figure 14.**Simulation of a spherical indentation test for a battery cell with a hybrid modelling strategy.

**Figure 15.**Force-displacement outputs with hybrid modelling method: (

**a**) influence of coefficient of friction on isotropic model; (

**b**) comparison between the isotropic and anisotropic model.

**Figure 16.**Simulation of a spherical indentation test for a battery cell using a sandwich modelling strategy.

**Figure 17.**Force-displacement outputs using a sandwich modelling method: (

**a**) influence of coefficient of friction on isotropic model; (

**b**) influence of failure strain on isotropic model; (

**c**) influence of failure strain on anisotropic model.

**Figure 18.**Simulation of a spherical indentation test for a battery cell with partial modelling strategy: (

**a**) half model and deformed state; (

**b**) quarter model and deformed state.

**Figure 19.**Force-displacement outputs using the partial modelling method: (

**a**) influence of coefficient of friction on half model; (

**b**) influence of coefficient of friction on quarter model.

**Figure 20.**Comparison of the force-displacement outputs among all models: (

**a**) models with isotropic material properties; (

**b**) models with anisotropic material properties.

Simulation Data | Heterogeneous Model | Homogeneous Model | Hybrid Model | Sandwich Model | Partial Model | Literature [5] | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

Half | Quarter | ||||||||||

Cell Elements | 179,200 | 17,600 | 97,600 | 12,800 | 8800 | 4400 | |||||

Sphere Elements | 726 | 726 | 726 | 726 | 726 | 726 | |||||

Nodes | 376,544 | 20172 | 198,358 | 26,896 | 11,060 | 6020 | |||||

Components | 112 | 1 | 57 | 8 | 1 | 1 | 1 | ||||

Material Behaviour | iso. | aniso. | iso. | aniso. | iso. | aniso. | iso. | aniso. | iso. | iso. | iso. |

Max. Force [N] | 5516 | 2291 | 7102 | 6330 | 5898 | 1912 | 7575 | 6217 | 7572 | 7924 | 7900 |

Displacement [mm] | 3.10 | 3.18 * | 2.95 | 2.88 | 2.96 | 2.34 | 3.45 * | 3.45 * | 3.09 | 3.15 | ca. 2.90 |

Failure | Yes | No | Yes | Yes | Yes | Yes | No | No | Yes | Yes | Yes |

Calculation Time | 40 h | 95 h | 2 min | 2 min | 17 h | 20 hrs | 25 min | 32 min | 14 s | 8 s | - |

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**MDPI and ACS Style**

Kulkarni, S.S.; Vysoudil, F.; Vietor, T. Evaluation of Modelling and Simulation Strategies to Investigate the Mechanical Integrity of a Battery Cell Using Finite Element Methods. *Energies* **2021**, *14*, 2976.
https://doi.org/10.3390/en14112976

**AMA Style**

Kulkarni SS, Vysoudil F, Vietor T. Evaluation of Modelling and Simulation Strategies to Investigate the Mechanical Integrity of a Battery Cell Using Finite Element Methods. *Energies*. 2021; 14(11):2976.
https://doi.org/10.3390/en14112976

**Chicago/Turabian Style**

Kulkarni, Shraddha Suhas, Filip Vysoudil, and Thomas Vietor. 2021. "Evaluation of Modelling and Simulation Strategies to Investigate the Mechanical Integrity of a Battery Cell Using Finite Element Methods" *Energies* 14, no. 11: 2976.
https://doi.org/10.3390/en14112976