Predicting Lithium-ion Cell Swelling, Strain, and Stress using GT-AutoLion Simulation

Written by Ajaykrishna Ramasubramanian and Joe Wimmer

February 19, 2021

Lithium-ion batteries (LIBs), used in most commercial electronics and portable devices, occupy a highly privileged position in the energy storage sector and have emerged as a versatile and efficient option for the electrification of automotive transportation and integration of renewable energies. The global market for LIB technology is projected to be over $90 billion by the year 2025. Therefore, the reliability of LIBs is very crucial in such largescale applications and has a direct impact on the societal economics.

It has become increasingly evident that the next-generation high-energy-density batteries will not be realized without understanding the degradation mechanism from the mechanics perspective. On one side, the repetitive volumetric strain in electrodes, ranging from a few percentages (graphite, layered/spinel/olivine oxides) to a few hundred percentages for the materials of ever-increasing energy density, disrupts the structural stability in batteries and deteriorates the capacity retention over cycles. On the other side, the mechanical stress influences the kinetics of electrochemical processes, such as mass transport, charge transfer, interfacial reactions, and phase transitions, thereby impacting the performance, capacity, and efficiency of batteries. Some battery pack designs also contain cooling fins, thermistors, foam separators, and repeating frame elements to hold the cells, maintain temperature, and manage this volume change.

Successful battery engineering at all levels (cell-level, module-level, and pack-level) requires an understanding of the complex linkages between mechanical and electrochemical phenomena in. The mechano-electrochemical model in GT-AutoLion effectively captures this linkage to allow cell engineers, module engineers, and pack engineers  to accelerate the development of battery technology while decreasing the required testing load and cost.

How does the mechano-electrochemical model work?

The electrochemical processes such as the lithiation and de-lithiation process leads to significant volume change in the active material. This volume change leads to a substantial change in cell performance. Thus, to simulate this change in cell performance, a flexible swelling model capable of predicting cell performance under various conditions is implemented in AutoLion. These models include various mechanical strain mechanisms such as casing constraint, foam packing constraint, and an applied cell pressure constraint. The mechanical constraints applied here are analogous to the conditions that occur during battery testing or regular battery usage. Based on this analogy, the conditions can be broadly classified into three major categories (i) Rigid Wall (zero strain and high stress), (ii) Free Expansion (high strain and zero stress), and (iii) Realistic scenario with mixed constraints (non-zero stress and strain), as shown in the figure below.

Figure 1. Electrode swelling in a de-lithiated (discharged) versus lithiated (charged) active material under different mechanical loading conditions (i) Rigid wall, (ii) Free expansion, and (iii) Realistic scenario with mixed constraints

How are the stresses, strains, and changes in porosity on each component captured?

To accurately simulate the cell’s mechanical behavior (e.g., the thickness change, pressure generation, etc.), each cell component’s mechanical response properties are incorporated. The porous electrodes’ mechanical properties are defined based on linear elasticity, porous rock mechanics, or measured stress-strain response of an electrode saturated with incompressible electrolyte. In an electrochemical cell system, the anode and cathode layers will contribute from both externally applied pressure and electrode layer expansion/contraction caused by the active material volume change to their overall strain response. The magnitude of the active material’s volume change is related to the active material state-of-lithiation. The total strain is captured from both these components, and the corresponding stresses are calculated through the constitutive relationships in mechanics.

The balance between the change in porosity and the change in dimension/strain is captured using the material balance. The sample result shown below shows the effect of change in porosity and strain for different stiffness casing constraints.

Figure 2. Effect of casing stiffness (Rigid to Compliant casing) on strain and porosity (i) Strain vs. SOC plot; (ii) Averaged Porosity vs. SOC plot

The material balance also accounts for the change in kinetics through the porosity change and, therefore, the cell’s electrochemical performance. A sample result for a graphite anode with an applied cell pressure is shown below, describing the change in strain and porosity.

Figure 3. Effect of applied pressure on component/total strain on the cell and porosity (i) Strain vs. SOC plot; (ii) Averaged Porosity vs. SOC plot

The AutoLion model allows for a non-ideal lithiation behavior for anode and cathode, which increases the model’s accuracy, showing the importance of accounting for individual active material volume change behavior on cell level predictions.

How are these results useful?

Cell and pack designers currently rely on extensive electrochemical and mechanical testing to appropriately account for the volume change and the developed stresses. This mechano-electrochemical model predicts this volume change, which may reduce the required number of electrochemical and mechanical tests.

This model can help designers estimate cell-level volume change using knowledge of particle-level lithiation-based volume change behavior. The theoretical predictions of individual component strain, capacity balance effects, porosity, and pressure change effects can also be explored using this model. Also, the performance of the cells is highly dependent on the swelling strain evolution as shown in the sample results below.

Figure 4. Effect of swelling on performance of Lithium-ion cell.

The resulting understanding from the model may aid in cell design or determining operational parameters to mitigate adverse effects from active material volume change. Additionally, this model may prove useful to consider how mechanical and electrochemical phenomena intertwine as promising new chemistries such as silicon or Li metal are considered.

Written by Ajaykrishna Ramasubramanian and Joe Wimmer