There is an intense, worldwide effort to develop durable lithium ion batteries with high energy and power densities for a wide range of applications, including electric and hybrid electric vehicles. For improvement of battery technology understanding the capacity fading mechanism in batteries is of utmost importance. Novel electrode material and improved electrode designs are needed for high energy- high power batteries with less capacity fading. Furthermore, for applications such as automotive applications, precise cycle-life prediction of batteries is necessary. One of the critical challenges in advancing lithium ion battery technologies is fracture and decrepitation of the electrodes as a result of lithium diffusion during charging and discharging operations. When lithium is inserted in either the positive or negative electrode, there is a volume change associated with insertion or de-insertion. Diffusion-induced stresses (DISs) can therefore cause the nucleation and growth of cracks, leading to mechanical degradation of the batteries. With different mathematical models we studied the behavior of diffusion induces stresses and effects of electrode shape, size, concentration dependent material properties, pre-existing cracks, phase transformations, operating conditions etc. on the diffusion induced stresses. Thus we develop tools to guide the design of the electrode material with better mechanical stability for durable batteries. Along with mechanical degradation, chemical degradation of batteries also plays an important role in deciding battery cycle life. The instability of commonly employed electrolytes results in solid electrolyte interphase (SEI) formation. Although SEI formation contributes to irreversible capacity loss, the SEI layer is necessary, as it passivates the electrode-electrolyte interface from further solvent decomposition. SEI layer and diffusion induced stresses are inter-dependent and affect each-other. We study coupled chemical-mechanical degradation of electrode materials to understand the capacity fading of the battery with cycling. With the understanding of chemical and mechanical degradation, we develop a simple phenomenological model to predict battery life. On the experimental part we come up with a novel concept of using liquid metal alloy as a self-healing battery electrode. We develop a method to prepare thin film liquid gallium electrode on a conductive substrate. This enabled us to perform a series of electrochemical and characterization experiments which certify that liquid electrode undergo liquid-solid-liquid transition and thus self-heals the cracks formed during de-insertion. Thus the mechanical degradation can be avoided. We also perform ab-initio calculations to understand the equilibrium potential of various lithium-gallium phases.