**5. Conclusions**

Electrochemical failure mechanisms like SEI growth, formation of a covering layer, plating, or gas formation induce mechanical stress and therefore a volume expansion. All factors increasing the probability for sudden death of the battery cell. A straightforward and reliable method for measuring the volume expansion and their influence on the state-of-health of the lithium-ion battery is the strain gauge. As we demonstrated, it yielded stable and reproducible results, when monitoring geometric variations on the micrometer scale.

The diameter change of the lithium-ion battery described a characteristic trend and is SOC and load direction-dependent. For as-received batteries of type Samsung 35E, a mean diameter change of 10.7 μm during a full discharge process was measured. Different phenomena seemed to play a role in the ageing of the battery so that the change in diameter changed as a function of the ageing of the battery. Two effects can be observed over ageing using strain gauges: First, an increase of irreversible diameter change, and second, an increase of reversible diameter change. Both reversible and irreversible expansion increased with ageing. Overall, two different ageing effects led to the diameter change variation. CT measurements showed deformation of the jelly roll and post-mortem analysis showed the formation of a covering layer and the increase in the thickness of the anode.

Finally, direct correlation between the diameter change and the capacity loss of this lithium-ion battery can be identified. Therefore, the strain gauge is a tool for predicting the sudden cell death and might even serve as a diagnostic tool for the state-health, including safety aspects.

**Author Contributions:** Conceptualization, L.K.W., P.D., D.U.S., and E.F.; methodology, L.K.W., G.F., and P.D.; validation, L.K.W.; formal analysis, L.K.W.; investigation, L.K.W.; resources, D.U.S. and E.F.; data curation, P.D. and L.K.W.; writing—original draft preparation, L.K.W. and E.F.; writing—review and editing, L.K.W., P.D., G.F., E.F., and D.U.S.; visualization, L.K.W. and P.D.; supervision, D.U.S. and E.F.; funding acquisition, D.U.S and E.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** The results were generated in the research training group "mobilEM" (GRK 1856/1, 1856/2). We would like to thank the Deutsche Forschungsgemeinschaft (DFG) for funding.

**Acknowledgments:** This work has been done during the time as an associated member of the research training group 'mobilEM' (GRK 1856/1, 1856/2). The authors would like to thank Marcel Eckert for the setup of the test bench; Rita Graff, Martin Graff, and Niklas Kürten for the cell opening and ICP-OES measurements; and Moritz Teuber for proofreading.

**Conflicts of Interest:** The authors declare no conflicts of interest.
