Topological optimization of patterned silicon anode by finite element analysis

A silicon-based anode in lithium-ion battery exhibits several times higher gravimetric energy storage capacity compared to an established carbon-based anode. However, the cycling performance of the silicon anode is poor due to the extremely large volume variation during the intercalation of lithium ions. The micro-structuring of silicon facilitates cycling performance. In particular, patterned microstructures are discussed as a possible solution. The large volumetric change can be adopted in such structures by bending walls and rotation around fixed vertexes. Nevertheless, the cycling performance of known patterned anodes remains poor due to plastic deformations. In this paper, a new square-based-patterned silicon anode is proposed and analyzed using the finite element method. The maximal stress in the topologically optimized structure is below the yield strength of lithiated silicon. In contrast to known structures, the deformed pattern of the new structure is explicitly defined by its initial geometry. A similar modification of the honeycomb-based-patterned anode leads to a slightly larger bending stress, but still below the yield stress of lithiated silicon. The related pure elastic deformation behavior is favorable to a prolonged cycling life of the micro-structured silicon anode. The developed approach can be applied for analysis of other severely swelling metamaterials.