Exact Diffusion-Induced Elastic Fields of a Spherical Core-Shell Nano-Electrode Li-Ion Battery via Spectral Theory

In Li-ion batteries the interface between the nano-size spherical core graphite and its surrounding solid electrolyte interphase (SEI) layer, just inside SEI is susceptible to damage. Thus, accurate determination of the associated elastic fields is one of the challenges in optimizing the lifetime and capacity of Li-ion batteries. The required precision is achieved by considering the core graphite which belongs to the crystal class D _{6 h} as homogeneous spherically isotropic and SEI layer as functionally graded (FG) isotropic material. Moreover, to account for the surface/interface effects appropriately the core-shell nano-structure subjected to the diffusion-induced time-dependent nonuniform eigenstrain field under galvanostatic operation is formulated within surface elasticity theory. Then the exact analytical solution is given via spectral theory. Significant differences between the surface elasticity solutions and those of classical elasticity specially within the SEI layer, reveal the importance of using surface elasticity theory. It is shown that the distribution of the Li-ion concentration and pertinent diffusion-induced stresses are strongly affected by different modes of charging: normal charging, fast charging and low diffusivity. The von Mises criterion and the single-mode delamination fracture criterion are utilized to predict the time to failure of the interface between the core graphite- SEI layer and delamination initiation, respectively.