Very large mechanical stresses and huge volume changes emerge during intercalation and extraction of Lithium in battery electrodes. Mechanical failure is responsible for poor cyclic behavior and quick fading of electrical performance, especially in energy storage materials for the next generation of Li-ion batteries. A multi scale modeling of the phenomena that lead to mechanical degradation and failure in electrodes is the concern of the present publication. The computational homogenization technique is tailored to model the multi physics events that coexist during batteries charging and discharging cycles. At the macroscale, diffusion–advection equations model the coupling between electrochemistry and mechanics in the whole cell. The multi-component porous electrode, migration, diffusion, and intercalation of Lithium in the active particles, the swelling of the latter are modeled at the micro-scale. A rigorous thermodynamics setting is stated and scale transitions are formulated.