  Volumetric expansion of silicon anode particles in a lithium-ion battery
during charging may lead to the generation of undesirable internal stresses.
For a cylindrical particle such growth may also lead to failure by buckling if
the expansion is constrained in the axial direction due to other particles or
supporting structures. To mitigate this problem, the possibility of reducing
axial growth is investigated theoretically by studying simple modifications of
the solid cylinder geometry. First, an annular cylinder is considered with
lithiation either from the inside or from the outside. In both cases, the
reduction of axial growth is not found to be significant. Next, explicit
physical constraints are studied by addition of a non-growing elasto-plastic
material: first, an outer annular constraint on a solid silicon cylinder, and
second a rod-like inner constraint for an annular silicon cylinder. In both
cases, it is found that axial growth can be reduced if the yield stress of the
constraining material is significantly higher than that of silicon and/or the
thickness of the constraint is relatively high. Phase diagrams are presented
for both the outer and the inner constraint cases to identify desirable
operating zones. Finally, to interpret the phase diagrams and isolate the key
physical principles two different simplified models are presented and are shown
to recover important qualitative trends of the numerical simulation results.
