In-Situ Analysis of Expansion Stiffness and Compression Stiffness in Lithium-ion Batteries

1. Introduction

Cell mechanical stiffness affects appearance, module integrity, and abuse resistance of lithium-ion batteries. Mechanical stiffness of cells is commonly split into two concepts:

While compression testing is simple, it is often used as an approximate proxy for expansion stiffness. This study demonstrates that the two are not equivalent: electrochemical state (SOC/DOD) and preload markedly alter expansion stiffness, so direct measurement under cycling conditions is required for accurate module and safety design.

2. Test Information

2.1 Equipment

In-Situ Battery Swelling Analyzer — SWE2110 (IEST). High-precision displacement sensor and load cell enable real-time logging of thickness, force/pressure, temperature, voltage, current, and capacity. The SWE2110 supports constant-pressure and constant-gap control.

Compression stiffness can be measured with a general-purpose compression testing machine under static, non-cycling conditions. Expansion stiffness, by contrast, must be captured while a cell is actively charging and discharging — requiring synchronized, real-time acquisition of force, displacement, temperature, voltage, current, and capacity throughout the cycle. This requirement for simultaneous mechanical and electrochemical data logging during active cycling is what a dedicated in-situ instrument like the SWE2110 provides, distinguishing it from a general-purpose compression tester.

Figure 1. Schematic diagram of the in-situ swelling analysis system(SWE Series)

2.2 Cell Information

Details of the cell used in this study are summarized in Table 1.

2.3 Charging and Discharging Process

3. Results and Analysis

3.1 Expansion Stiffness

Using the constant-pressure mode of the SWE2110, tests were conducted under applied pressures of 10 kg (0.02 MPa), 30 kg (0.06 MPa), 50 kg (0.10 MPa), 100 kg (0.21 MPa), and 200 kg (0.42 MPa). As illustrated in Figure 2, cell thickness increased during charging—corresponding to lithium intercalation in the anode—while higher applied pressure reduced overall expansion.

Results in Table 4 and Figure 3 indicate that stiffness values rise with increasing pressure and vary with the state of charge (SOC) or depth of discharge (DOD):

• Expansion stiffness is highest at the beginning of charge, then decreases and stabilizes.

• During discharge, stiffness initially increases, peaks around 30–50% DOD, and subsequently declines.

Figure 2. Thickness variation curve of charge/discharge of battery cell under different pressures

Figure 3. Trend of cell expansion stiffness for different SOC/DOD states

3.2 Compression Stiffness

Cells at SOC levels of 0%, 30%, 50%, 80%, and 100% were subjected to the same pressure conditions to measure compressive stiffness under static load. Measured compression stiffness values (Table 5, left) were significantly higher than expansion stiffness (Table 5, right), confirming that using compression stiffness to approximate expansion behavior may lead to substantial error.

4. Discussion & Practical Recommendations

4.1 Why expansion stiffness differs from compression stiffness

4.2 Test recommendations

1. Direct in-cycle measurement: Use SWE2110 constant-pressure mode to obtain true expansion stiffness across SOC windows relevant to your application.

2. Multi-pressure characterization: Test multiple preload levels to understand module preload sensitivity.

3. SOC mapping: Measure expansion stiffness at representative SOCs (e.g., 0%, 30%, 50%, 80%, 100%) because stiffness varies nonlinearly with SOC.

4. Statistical sampling: Test multiple cells to capture manufacturing scatter and irreversible changes over cycling.

5. Use both metrics wisely: Use compression stiffness for mechanical packaging studies where external compression dominates; use expansion stiffness for in-service deformation, stress accumulation and module clamp design.

4.3 Implications for design

• Module clamps and springs must be specified considering lower expansion stiffness (i.e., cells exert less constraining force during swelling than predicted from compression tests), otherwise fasteners may be underspecified or overcompensated leading to unnecessary mass/complexity.

• Safety analyses and drop/impact models should incorporate in-cycle stiffness to estimate realistic deformation and potential shorting risks.

5. Summary

This study demonstrates that the SWE2110 system effectively characterizes both expansion stiffness and compression stiffness in lithium-ion cells. Results confirm that cell stiffness is influenced not only by SOC/DOD but also by the magnitude of applied pressure. Crucially, compression stiffness cannot be directly used to estimate expansion stiffness due to measurable differences between the two. These findings underscore the need for dedicated expansion-stiffness testing to ensure accurate mechanical modeling and enhanced safety design in battery development.

6. References

[1] Hoeschele P , Heindl SF , Erker S ,et al. Influence of reversible swelling and preload force on the failure behavior of a lithium-ion pouch cell tested under realistic boundary conditions[J].Journal of Energy Storage, 2023.

[2] ZHU Maoyu,HE Jianchao,YU Ao,et al. Method for testing the expansion stiffness of an cell. Patent No. 202310112653[P][2024-01-15].

7. FAQs