Cycling lifetime and capacity of rechargeable Lithium ion batteries require significant improvement, in order to confront with the increasing demands of energy storage. The electrochemical performance of the batteries depends greatly on the battery electrodes, particularly the electrochemical and mechanical behavior of the active particles in the electrodes. The Lithium transport mechanism and the mechanical fracture during (de-)intercalation are two of the major factors responsible for the degradation and capacity loss of the battery cell . These two aspects can interact with each other, which makes it more difficult to understand their influence on battery degradation. The following three complications can be present: 1) The lithium transport in the electrolyte is usually governed by the Fick diffusion mechanism, while the transport of Lithium inside the particle can involve phase segregation, especially for these active materials with high theoretical capacity, such as Si anodes and LiFePO4 cathodes. 2) Moreover, the electrochemical reaction happens not only on the particle surfaces, but also on the surfaces of cracks which initiate and propagate during (de-)intercalation. 3) The interface of phase segregation can interact with crack behavior and particle surfaces. The former interaction can lead to complicated fracture behavior such as branching, while the latter influences the chemical reaction rate.
In this work a finite strain phase field fracture model will be presented, which accounts for phase segregation, electrochemical reactions, surface tension, and fracture behavior in a systematic manner. With this model we can unveil the three complications listed above straightforwardly. The model is derived from variational analysis. To meet the demand of higher-order continuity arising from the Cahn-Hilliard equation, isogeometric finite element method is employed for the numerical implementation. Simulation results will be demonstrated to reveal the electrochemical reactions on particle surfaces, phase interfaces, and crack surfaces, as well as their in?uence on mechanical and charging behavior. Results show that the ratio between the timescale of reaction and the diffusion can have a significant influence on phase segregation behavior [2,3], so does the anisotropy of diffusivity. In return, the distribution of the lithium concentration influences greatly the reaction on the surface, especially when the phase interfaces appear on exterior surfaces or freshly cracked surfaces. The reaction rate increases considerably at phase interfaces, due to the large lithium concentration gradient. Moreover, simulations demonstrate that the segregation of a Li-rich and a Li-poor phase during delithiation can drive the cracks to propagate .
 M. Ebner, F. Marone, M. Stampanoni, V. Wood, Visualization and quantification of electrochemical and mechanical degradation in Li ion batteries, Science 342 (6159), 2013, pp. 716720.
 Y. Zhao, P. Stein, B.X. Xu, Isogeometric analysis of mechanically coupled CahnHilliard phase segregation in hyperelastic electrodes of Li-ion batteries, Computer Methods in Applied Mechanics and Engineering 297, 2015, pp. 325-347.
 Y. Zhao, B.X. Xu, P. Stein, D. Gross, Phase-field study of electrochemical reactions at exterior and interior interfaces in Li-Ion battery electrode particles, arXiv preprint arXiv:1511.06240.