Use BatteryDict-Degradation for the simulation of battery volumetric changes due to lithium intercalation of active materials.

After a finished charging or discharging simulation of a battery or a half cell, the mechanical expansion or contraction of the cell as well as the stresses and strains resulting from this deformation can be computed. To this purpose, ElastoDict’s FeelMath solver is called internally from BatteryDict-Degradation.

The expansion, , of an active material in each coordinate direction depends on the changes in lithium concentration during charging simulation,

with the concentration expansion coefficient, and the lithium concentration at the start and end of the (charging) simulation and the length of the material in the coordinate direction under consideration. It is computed analogously to the thermal expansion of a material due to temperature change.

Note that the concentration expansion coefficient used in BatteryDict-Degradation is a coefficient for the linear expansion in each coordinate direction. In literature, one can often find the maximal volumetric expansion due to intercalation. To get the coefficient required here, use

where is the initial volume, is the maximum absolute volume change due to lithium intercalation, is the maximum relative volume change in percent, and is the maximum (removable) lithium concentration. Also refer to Wenzler et al., 2023.