Integrated mechanical-electrochemical modeling and prediction of capacity fade and lifetime of batteries is important for cell design, determination of the optimal operation condition and control, and cell maintenance. In this talk I will present some of our recent work in these areas, including a comprehensive capacity fade model and its experimental validation and application for battery optimization; a multiscale approach that couples mechanics and electrochemistry consistently at both particle and electrode scales which enables simulating various electrode phenomena, and its validation against explicit simulation of particle networks; and simulation of concurrent dendrite growth, SEI formation and penetration of lithium metal electrodes. The materials strategy for improving the battery performance and application of machine learning for battery design will be discussed. I will also briefly talk about our work on developing black phosphorus (BP) and BP composite electrodes. BP has a theoretical capacity of 2,596 mAh/g, which is significantly higher than that of current generation anodes (graphite, 372 mAh/g). I will discuss how we synthesize BP materials, the characterization of its performance, and how integrated mechanical-electrochemical analysis can guide the design of BP composites.