Lithium ion battery is one of the most promising energy storage equipment due to its high energy density and long life cycle, and it has various applications in marine industry. Coupled diffusive-mechanical process during cycling has significant influence on ion diffusion and stress evolution. This may cause large deformation of electrodes which is the main reason of crack nucleation and propagation. As a consequence, this will have a negative effect on battery performance in terms of electrical capacity and thermal stability, and can cause failure of the battery. Hence, crack propagation and stress evolution during lithiation of the electrode plate is under investigation in this study. Peridynamics, as a new computational technique, is utilized for this purpose and various validation and demonstration cases were considered to demonstrate the capability of the developed framework.